Redesigning Harvesting Processes and Improving Working Conditions in Agribusiness

Abstract

We collaborate with a leading mushroom producer in North America to investigate the potential benefits of redesigning agribusiness operations, specifically, harvesting processes, to enhance both firm performance and working conditions of employees. We consider two harvesting protocols: The dominant status-quo practice, namely Harvest-all and an alternative, namely Selective Harvesting. In the Harvest-all protocol, workers pick all crop units in the areas assigned to them, regardless of the crops’ size and maturity, resulting in higher productivity but lower average value (quality) of the harvested produce. Workers also remain in demanding physical postures for longer periods of time, resulting in ergonomic stress. In contrast, under the Selective Harvesting protocol, workers take multiple rounds to completely harvest the assigned area, picking in each round only the select crop units that are near their peak monetary value. This results in lower productivity but higher average quality of the harvested produce and better ergonomic conditions. We develop mathematical models to analyze the two harvesting protocols, provide a complete analytical characterization of the optimal managerial decisions under each protocol, and examine how these decisions are influenced by relevant contextual factors. In addition, we characterize the performance of each harvesting protocol along three key performance metrics of interest: Firm profitability, worker monetary welfare, and worker ergonomic welfare. Using both analytical and calibrated numerical methods we show that adopting Selective Harvesting over Harvest-all can create win–win scenarios where both the firm and workers are better off. However, our analysis reveals that the firm’s and workers’ interests may not always be fully aligned. We subsequently demonstrate that the misalignment can be reduced by making adjustments to the compensation structure so that workers’ earnings match the maximum potential value while having minimal impact on firm profitability. Our models illustrate the benefits of careful process redesign in creating better working conditions for employees and advancing firms’ social responsibility practices.

1. Introduction

The agriculture sector in the United States is highly reliant on unskilled manual labor, with farm workers comprising nearly 56% of the labor force within that sector (Bureau of Labor Statistics, 2021). This labor is utilized for a range of activities, including land preparation, plant growth management, harvesting, and packaging, as shown in Figure 1. Our focus in this paper is on harvesting operations. An optimal management of these operations is critical to agribusiness managers for several reasons. First, the harvesting process is costly, constituting as much as 39% of the total landed cost in the case of hand-harvested produce such as berries, asparagus, coffee, cotton, and mushrooms (USDA, 2018). Therefore, improvements to harvesting operations can result in significant benefits for agribusiness firms. Second, inefficient harvesting processes can lead to substantial reductions in production yield and loss of revenue. For example, incorrect timing of the harvesting of quick-to-perish produce such as mushrooms and sugarcane can significantly decrease their value (Lamsal et al., 2017). Finally, harvesting operations are labor-intensive and can pose health risks to workers due to the repetitive body movements involved, which can result in stress on joints and muscles (Fan et al., 2009). Figures 2 and 3 illustrate this ergonomic issue in the context of the mushroom industry, where harvesting mushrooms often requires workers to reach and twist at awkward angles. Doing this for extended periods of time can put stress on the workers’ bodies. Therefore, exploring alternative harvesting approaches to reduce ergonomic stress and developing a systematic understanding of the associated economic implications is important.

Figure 1.

Four steps of crop production.

Figure 2.

Stacks of mushroom beds in a farm.

Figure 3.

A worker’s posture during harvesting.

Given the consequential economic and ergonomic considerations at stake, our work examines managerial decision making in harvesting operations. This involves answering two important questions: (i) When to harvest? and (ii) how much produce to harvest? Typically, managers view these questions through the lens of harvesting protocols that offer guidance in terms of when to start harvesting, what produce to collect based on characteristics such as color or size, and how much to harvest. Different harvesting protocols have varying economic and ergonomic impacts. To assist firms in quantifying these impacts and evaluate alternative harvesting protocols, we develop models that characterize the performance of such protocols along three key performance metrics: (i) The firm’s profitability, (ii) workers’ monetary welfare captured by their earnings, and (iii) workers’ ergonomic welfare captured by a metric, namely the Hand Activity Level (HAL), which we describe in detail in Section 3.2. Following the analytical characterization, we discuss the implementation of these models at one of the largest mushroom producers in North America. Below, we describe the collaboration that provides the motivating context for our study.

1.1. Industry Motivation

This research is in collaboration with TMG (The Mushroom Grower, a name we use for our industry collaborator to preserve their identity), a collective of several mushroom producers. This collective is one of the largest mushroom producers in North America, both in terms of volume and revenues generated. The collective sells more than 225 million pounds of fresh mushrooms annually, with a corresponding revenue of over $250 million. Our research questions are motivated by three contextual factors relevant to this industry: Crop characteristics, the labor-intensive nature of harvesting, and the harvesting protocol utilized.

1.1.1. Crop Characteristics

Fresh mushrooms are a major product category within TMG’s offerings and they are particularly challenging to harvest for two reasons: (1) Their quick-to-perish nature, and (2) the heterogeneity in their maturity time. Figure 4 delineates the monetary value evolution of a representative mushroom over its lifetime. Typically, this evolution comprises of three phases. In the germination (or “vegetative”) phase, the mycelium (akin to a plant body) grows and the mushroom (which is a fruiting body) appears and begins to grow at a negligible rate with an insignificant monetary value. Next, in the growth phase, the mushroom starts to increase in size, with a commensurate increase in monetary value. We refer to the time when the mushroom enters the growth phase as the Pop-up time. The mushroom reaches its peak monetary value at the end of the growth phase, referred to as the Peak time. Finally, in the deterioration phase, the monetary value of a mushroom degrades drastically due to decay and eventually reduces to zero at the end of this phase.

Figure 4.

Evolution in the monetary value of a mushroom (fruit) over three phases.

The variation in the monetary value across the different phases in Figure 4 suggests that it is in the firm’s financial interest to pick each mushroom as close to its peak value as possible. However, this task is particularly challenging for two reasons. First, unlike crops suitable for mass production and synchronous harvests such as soybeans and corn, mushrooms within and across beds (physical structures where mushrooms are grown) do not mature at the same time. This is because the pop-up times of individual mushroom units often vary and are unpredictable. Consequently, at any given moment in time, even mushrooms that are in close proximity can be at different levels of maturity. Second, searching for and identifying mushrooms that are close to their peak value can be time-consuming for harvesters, resulting in lower harvesting speed and productivity. Furthermore, the harvester may not be able to reach all the mushrooms before they enter the deterioration phase and start losing value rapidly. In essence, harvesting operations involve a time-quality trade-off: If left unharvested for too long, the mushroom loses a majority or entirety of its monetary value; if harvested too early, a portion of the potential value is lost due to a lack of opportunity for the mushroom to reach its peak value.

1.1.2. Labor-intensive Nature of Harvesting

The harvesting operation in agriculture tends to be repetitive: A harvester pulls out a mushroom, cuts its stem with a small knife, and puts the cut mushroom in a tray. The harvester repeats the same sequence of steps several thousand times each shift. Another challenge with mushroom harvesting is that they are grown in expensive, climate-controlled rooms. To maximize the use of these facilities, firms in this industry use a layout consisting of stacks of bunk beds placed next to each other, as shown in Figure 2. Each bunk structure has six beds stacked vertically. Harvesters need to climb up a ladder or crouch down to pick mushrooms from the top and bottom beds respectively, as shown in Figure 3. Performing repetitive tasks in this constrained posture is physically taxing, resulting in bodily stress. Hence, it is of significant interest to our partner firm to evaluate if alternative harvesting protocols can alleviate the ergonomic stress.

1.1.3. Harvesting Protocols

Firms in this industry typically use a harvesting protocol called “Harvest-all.” As mentioned before, mushrooms grow in stacks of beds (see Figure 2) and each mushroom bed can be thought of as consisting of multiple “bins.” For example, a sixty feet long bed may have fifteen bins, each four feet long (and five feet wide). For managerial purposes, each bin maps on to a small enough area that a worker can harvest the entire bin standing in one spot. Under the Harvest-all protocol, the harvester would start picking mushrooms from a bin in one corner of a bed. They would pick all the mushrooms in that bin and then move on to the next one. After harvesting all the bins in a bed, they move to the next bed. The worker repeats this process until all mushrooms in the beds assigned to them are harvested. This harvesting protocol is prominent in the industry for two reasons: (i) It is easy to implement and (ii) it is highly efficient since workers do not waste a lot of time moving around—they essentially stand in one spot and harvest all the mushrooms in a bin before going to the next one. An additional advantage of the Harvest-all protocol is that workers have a high pick rate since they pick all viable crop units (that can be sold to customer) instead of carefully identifying the best produce to harvest. Notwithstanding the above benefits, the Harvest-all protocol suffers from two main drawbacks.

First, from a monetary perspective, when a firm uses the Harvest-all protocol, many mushrooms might be harvested at lower-than-peak values, resulting in the firm not realizing the full monetary potential. This is because mushrooms within a bin germinate at different times and when they are all harvested together around the same time, a portion of the mushrooms may still be in the growth phase when picked while others may be past-peak. Consequently, picking mushrooms of varying sizes and monetary values under the Harvest-all protocol negatively impacts the firm’s profit potential. Second, from an ergonomic perspective, the Harvest-all protocol puts stress on workers’ bodies due to the prolonged time spent standing in one spot, performing repetitive harvesting motions within a bin before moving to the next one. Such consistent, high-level ergonomic stress can have a detrimental impact on workers’ health and potentially also hurt the firm’s profit in the long run due to absences.

Given the above concerns, managers at TMG were interested in evaluating alternative harvesting protocols, specifically to understand if switching to a different harvesting protocol (as opposed to Harvest-all) would enable the firm to pick mushrooms of higher monetary value, leading to increased profitability while simultaneously improving workers’ economic and ergonomic welfare. Towards this end, we analyzed an alternative harvesting protocol proposed by our partner firm, namely Selective Harvesting. Under this protocol, a harvester picks only a fixed proportion of the mushrooms within a bin during each visit (e.g., the 20 best (i.e., highest value) out of 100 mushrooms growing in a bin in each round), before moving on to the next bin. Since the harvester picks only a fraction of the mushrooms within each bin during a visit, they need to visit each bin multiple times to harvest all the mushrooms in the bins assigned to them.

From a monetary perspective, a worker utilizing the Selective Harvesting protocol would pick fewer mushrooms per unit time relative to the Harvest-all protocol (because they spend more time in moving around the room) but the value per mushroom harvested is higher on average. The net impact of picking fewer but more valuable mushrooms per unit time on firm profitability and worker earnings was not readily apparent. From an ergonomic standpoint, the Selective Harvesting protocol lowers stress on workers’ bodies since they move around more relative to Harvest-all, resulting in a lower frequency of repetitive hand movements carried out in tightly constrained physical spaces. However, it is not as efficient and productive as the Harvest-all protocol, highlighting potential trade-offs at play between firm profitability and workers’ economic and ergonomic welfare in implementing the Selective Harvesting protocol.

1.2. Research Focus and Contributions

Given the relative strengths and weaknesses of Harvest-all vis-a-vis Selective Harvesting, it is not clear which of the two protocols is better in terms of firm profitability and worker welfare, and under what conditions? Consequently, we investigate the following questions in our work:

From the firm’s perspective, what are the optimal operational decisions under Harvest-all (harvest start time) and Selective Harvesting (harvest start time and proportion to harvest) protocols?

How do the two harvesting protocols compare in terms of firm profits and worker welfare (economic and ergonomic)?

Do higher firm profits and improved worker welfare go hand-in-hand or are there trade-offs between the two? More importantly, are there win–win scenarios where both the firm and workers are better-off with Selective Harvesting when compared to Harvest-all?

In this paper, we develop mathematical models to analyze the two harvesting protocols. In analyzing the protocols, we take the perspective of a profit-maximizing firm and examine how the firm’s decisions impact not only its profitability but also the workers’ economic and ergonomic welfare. We provide a complete analytical characterization of the optimal managerial decisions under each protocol, which includes the optimal harvest start time in the Harvest-all protocol, as well as the optimal start time and proportion to selectively pick under the Selective Harvesting protocol. Furthermore, we investigate how these decisions are influenced by three important groups of contextual factors: The biological characteristics of the crop, worker compensation structure, and worker efficiency.

This analysis yields several interesting and nuanced insights, including the following: (i) With respect to the biological characteristics, we find that for crops with faster growth rates and/or slower deterioration rates, it is optimal to start harvesting later relative to crops with slower growth rates and/or faster deterioration rates. (ii) With respect to the worker compensation structure, we find that it has no bearing on the optimal harvest start time under both harvesting protocols. However, an increase in either the time-based compensation or performance-based compensation (tied to the value of mushrooms harvested) results in a decrease in the proportion of produce the firm should selectively pick under the Selective Harvesting protocol. (iii) With respect to worker efficiency, we find that under both protocols, it is optimal to delay the harvest start time as workers become more efficient. However, the impact of worker efficiency on the optimal proportion to selectively pick is non-monotone, exhibiting a V-shaped pattern. These nuanced, and in some cases, non-linear effects of the contextual factors highlight the importance of using a rigorous analytical framework to support decision making in harvesting operations.

Our analytical development provides a decision-support to assist managers in comparing the performance of the two harvesting protocols. We further analytically establish the conditions under which adopting the Selective Harvesting protocol (instead of the status-quo practice of Harvest-all) creates win–win scenarios where both the firm and workers benefit. We demonstrate the practical value of our models through a grounded study that utilizes data and relevant contextual information from TMG. Consistent with our analytical development, the calibrated study results indicate that adopting the Selective Harvesting protocol (instead of the status-quo practice of Harvest-all) does create win–win scenarios where both the firm and workers benefit (20.9% increase in firm’s profit; 20.5% increase in worker earnings and 31.6% decrease in their HAL). However, while both the firm and workers can benefit from engaging in Selective Harvesting, the optimal Selective Harvesting percentages at which the firm profit and workers’ earnings are maximized do not coincide. Specifically, the firm would have to give up 9.0% in profits (relative to the potential maximum profit it can generate) if it were to pick a Selective Harvesting percentage that would maximize the workers’ earnings, indicating that the firm’s and workers’ interests may not be in full alignment. Subsequently, we demonstrate that by making appropriate adjustments to the compensation structure—for example, by linking a greater proportion of worker compensation to the value of the harvested produce—it is possible to substantially reduce this misalignment, ensuring that the workers’ earnings are maximized while having a minimal impact on firm profitability. This is often a key concern for managers when implementing socially-responsible innovations and our results demonstrate that it is indeed possible to make a firm’s operations more people-centric without compromising profitability.

Beyond the mushroom industry context that motivated this study, our analytical development is general enough to support managerial decision making for a variety of crops such as raspberries and corn that differ from mushrooms in terms of their biological characteristics. Overall, our work highlights how incorporating ergonomic considerations into supply chain operations can contribute to a firm’s triple bottom line and result in higher wages and better working conditions for employees.

The remainder of this paper is organized as follows. In Section 2, we review the related literature. In Section 3, we present our general harvesting model framework, while in Sections 4 and 5, we describe details of the Harvest-all and Selective Harvesting protocols, and derive the optimal decisions under each protocol. In Section 6, we demonstrate the existence of a win–win region where both firms and workers benefit under the Selective Harvesting protocol and discuss its characteristics. We present the results of our grounded study based on data from TMG in Section 7. In Section 8, we summarize the paper.

2. Literature Review

Our work is related to three streams of research: (i) Agribusiness supply chain management, (ii) staff planning, and (iii) socially responsible operations.

2.1. Agribusiness Supply Chain Management

The literature on agribusiness supply chain management is vast and varied, as discussed by Lowe and Preckel (2004). Bansal et al. (2021) provide a recent comprehensive review of this literature covering different stages of crop production, as laid out in Figure 1. With respect to the seeding stage, papers in the operations literature have examined different issues including what to grow, on how much land, and when to plant (see e.g., Bansal and Nagarajan, 2017, Zhang and Swaminathan, 2020), and how market structures and government subsidies impact these decisions (Chintapalli and Tang, 2021). With respect to the plant growth management stage, Dawande et al. (2013) examines approaches to manage critical inputs such as water while Federgruen et al. (2019) show how contracts can be effective in encouraging stakeholders to invest in improving crop yields.

Focusing on the harvesting stage of crop production, some papers have examined the harvest timing decision, considering external factors such as prevailing market prices (e.g., Parker et al., 2016). However, there is limited body of work that takes into account the inherent biological characteristics of the crop when determining how much to harvest and the optimal harvest timing. Thornthwaite (1953) provides the first description (to our knowledge) of the challenges associated with determining the harvest timing when dealing with crops that have dynamically-evolving monetary value curves similar to mushrooms.

Each ( $\cdots$ manager) had the same problem: When would the harvest start,…and how could he keep up with the rate of maturing of the crop? $\cdots$ When the peas began maturing at a rapid rate the division managers tried to harvest them at a rapid rate $\cdots$ (but they risked) getting behind in the harvest so that some peas were over-mature and of poor quality. (Thornthwaite, 1953: 33-34)

This descriptive article establishes that carefully planning the harvesting operations is important for a firm’s profit, and that managerial decision support tools for harvesting can help firms extract more value from their crops. Nevertheless, with a couple of exceptions, there have been scarce efforts to develop a prescriptive, model-driven decision support for harvesting operations. Allen and Schuster (2004) study the capacity allocation problem for grape harvesting under weather uncertainty. Once the grapes in the vineyard are mature, there is a limited time window during which the grapes can be harvested close to their peak value. After this window, the grapes lose their value precipitously. The duration of the time window is uncertain—it is long in some years and short in others. The vineyard needs to determine how much harvesting capacity to acquire before the harvesting season. Investing in too much (little) capacity will lead to a wastage of resources (loss of produce value) if the harvest window turns out to be very long (very short). Lamsal et al. (2017) explore the impact of processing capacity on sugarcane harvesting. Sugarcane loses its value rapidly after harvest, and it is important to synchronize its harvesting with the available processing capacity at sugar mills.

Both these papers differ from our work in terms of the focus on a key biological detail. These articles examine scenarios where all crop units in a field mature at the same time (e.g., sugarcane) or approximately the same time (e.g., grapes). That is not the case for a large number of crops such as peas, mushrooms, berries etc. Individual units of these crops pop-up at different times in a field and reach their peak monetary value at different times. As suggested by Thornthwaite (1953), this variation in when the crop units reach their peak value poses an interesting managerial challenge. Harvesting crop units at varied maturity levels results in not only lower overall quality but also lost profits, since crop units harvested too early lose growth potential while those harvested too late lose monetary value. We develop a new class of models called “Harvesting Models” that incorporates the heterogeneity in crop maturity times as well as the human factors associated with harvesting, elements that have not been considered in the prior operations literature.

2.2. Staff Planning and Socially Responsible Operations

There is a substantial body of work related to staff planning in operational settings. This stream has mainly focused on optimizing workforce capacity, utilizing mathematical models to forecast demand and allocate resources efficiently (Bhandari et al., 2008). However, this research has often overlooked the physical and mental limitations of workers. Recently, some papers have highlighted the importance of considering worker welfare in operational planning. For example, Benjaafar et al. (2022) analyze the impact of labor pool size on worker welfare in on-demand service platforms. They show that labor welfare changes non-monotonically with contextual factors such as the size of the existing labor force. However, their paper considers worker welfare only from a monetary standpoint, that is, earnings. Some other papers Plambeck and Taylor (see e.g., 2016) study worker welfare through the lens of working conditions, and examine the effectiveness of alternative strategies including enhanced visibility and auditing in improving working conditions in supply chains. These papers, however, do not directly take into consideration the workers’ economic welfare when evaluating the impact of these strategies. Our study takes a more comprehensive view of worker welfare through its consideration of both the economic and ergonomic aspects. In doing so, we show that incorporating ergonomic considerations in supply chain operations can improve a firm’s triple bottom line and create better working conditions for employees.

3. Model Preliminaries

In this section, we present a decision-making framework for harvesting operations. This framework consists of two components: (1) Contextual details specific to harvesting operations, and (2) performance metrics. For expositional clarity, our framework description is grounded in the mushroom industry. But our analytical development is general, and it can be applied to a variety of crops, as discussed in Section 6.3. We begin by introducing the relevant aspects of harvesting operations.

3.1. Contextual Features

Our empirical observations at TMG reveal two salient aspects of harvesting operations: (i) The nature of harvester tasks, and (ii) the evolution of the monetary value of produce over time.

3.1.1. Harvester Tasks

Consider a farm where crops are grown in beds. Figure 5 shows how the beds are typically stacked in a mushroom farm. As we mentioned in the Introduction, the beds are further divided into smaller working areas known as bins (or “squares” as referred to in the mushroom industry), with each bin containing multiple units of the crop, as shown in the schematic Figure 6. In the context of the mushroom industry, each crop unit represents a single mushroom. Crop units are considered to be in the same bin if they are in close proximity for a worker to harvest all of them without having to move horizontally. Figure 6 illustrates the layout of a typical bed with multiple bins. The worker moves from one bin to the next along the $x$ -axis to harvest produce. The span of each bin, measured along the $y$ -axis, is small enough that a harvester can reach the furthest point in the bin from any given point along the $x$ -axis. The layout depicted in Figure 6 comprises $M$ bins, each containing $N$ units of produce.

Figure 5.

Stacks of mushroom beds. (Photo credit: Mark Spear)

Figure 6.

Schematic layout of the produce bed.

Harvesting commences at time $t_0$ from the leftmost bin, and the harvester moves progressively to the right, collecting produce from each bin along the way until all the $M$ bins are complete. The firm provides a time-based compensation to the workers at the rate of $c$ per unit time. In addition, the firm also offers performance-based payment, which is equal to $\alpha$ proportion of the total value of the harvested produce. We next describe how the monetary value of the produce evolves over time.

3.1.2. Monetary Value Evolution

As described earlier in the Introduction and shown in Figure 7 for the case of mushrooms, the value of a crop unit evolves in three distinct phases: Germination (from time $0$ to $t_p$ ), growth (from time $t_p$ to $t_p+P$ ), and deterioration (after time $t_p+P$ ). The pop-up time $t_p$ represents the time at which a crop unit enters the growth phase and begins to grow at a noticeable rate. The pop-up times of individual crop units vary and are unpredictable, which we assume to follow a uniform distribution between $0$ and $T$ .

Figure 7.

Piece wise linear approximation to the monetary value evolution of a crop unit.

The evolution of the monetary value of a crop unit across the three phases is shown by the dotted line in Figure 7. We approximate this value function using the piece wise linear function $v(x)$ with three parts, as represented by the solid line. In the germination phase, the value $v(x)=0$ . In the growth phase, the value increases at rate $k_1>0$ , and in the deterioration phase, the value decreases at rate $k_2<0$ . In the definition of $v(x)$ , $x$ refers to the age of the produce, where age is defined as the time elapsed since the pop-up time of the crop unit. It follows that the value of a crop unit that pops up at time $t_p$ and is picked at time $t$ equals $v(t-t_p)$ . In general, the value $v(x)$ of a crop unit of age $x$ is defined as:

$$v(x)=\{\begin{array}{rl}& k_{1}x,0\le x\le P\\ & k_{2}x+(k_1-k_2)P,P<x\le \frac{k_2-k_1}{k_2}P\\ & 0\text{otherwise}\end{array}$$

(1)

The choice of a piecewise linear structure to represent the evolution of monetary value is motivated by several factors. First, this approach allows for analytical tractability, enabling us to develop sharper insights. Second, from a practice standpoint, it is easier for managers to specify the monetary evolution of a crop unit using piece-wise linear functions that are based on a combination of historical growth/deterioration rate data and experience. Notwithstanding these theoretical and practical justifications, as a robustness check, we conducted simulations using the empirical crop value curve to validate our linear approximation. The results (see Appendix B3) show that our linear approximation preserves the optimal decision structure and managerial insights, demonstrating its practical reliability. Finally, we note that in our model development, we assume that the number of crop units in a bin $N$ is known and that the growth trajectory variables such as $P$ take the same value for all units. This model representation is consistent with the prior literature including Thornthwaite (1953), and Yang and Sowell (1981). Nevertheless, in Appendices A2 and A3, we allow for stochastic variations in $N$ and $P$ , and demonstrate that key structural properties continue to hold under the more relaxed version of the model.

3.2. Performance Metrics of Interest

3.2.1. Firm’s Expected Profit

Consider a worker who is assigned $M$ bins to harvest. The expected profit generated by this worker for the firm, denoted by $\mathrm{\Pi }$ , can be written as:

$$\mathrm{\Pi }=\mathbb{E}[(1-\alpha )V]-cD$$

(2)

The first term on the right-hand side represents the company’s revenues, where $V$ denotes the total value of crop units harvested by the worker, and $(1-\alpha )$ is the fraction of this value retained by the firm after making performance-based payments $\alpha V$ to the harvester. The expectation in this term is taken over $t_p$ , the stochastic pop-up time of individual crop units. The second term represents the time-based payment to the worker, where $D$ is the total time the worker spends in harvesting and $c$ is the per unit time payment. Next, we look at performance measures from the workers’ perspective.

3.2.2. Workers’ Monetary Welfare

We quantify the workers’ monetary welfare in terms of their earnings as follows:

$$S=\mathbb{E}\left[\alpha V\right]+cD$$

(3)

The right-hand side of equation (3) includes two terms representing different components of the workers’ earnings. The first term is the performance-based component that is directly linked to the value of the harvested produce. The second term represents payment to the worker that is not directly tied to the value of the harvested produce, but is instead time-based.

3.2.3. Workers’ Ergonomic Welfare

In addition to the workers’ monetary welfare, agribusiness firms are also concerned with workers’ ergonomic welfare and the associated health implications. Harvesting involves repetitive hand movements, and if not properly designed and managed, it can result in physical stress for workers.

A metric commonly used to quantify ergonomic stress in such repetitive work environments is the HAL. This metric was originally proposed by Latko et al. (1999). It employs a 10-point visual-analog scale (see Figure 8) to quantify repetitive motion, ranging from idle hand activity (0) to rapid steady motion with difficulty keeping up (10). Various approaches have been proposed in the ergonomics literature to quantify HAL, such as by Akkas et al. (2015), Chen et al. (2013), and Radwin et al. (2015). The differences between these formulations are negligible in our context. Hence, we adopt the formulation proposed by Radwin et al. (2015) as our metric for evaluating the workers’ ergonomic welfare:

$$HAL=4.31-0.637\frac{1}{f}+3.4G$$

(4)

Figure 8.

10-point scale of hand activity level (HAL) developed by Latko et al. (1999) to quantify ergonomic stress.

In equation (4), $f$ denotes the repetition frequency of the hand activity, and $G$ represents the duty cycle defined as $G=\frac{\text{time spent on activities involving hand movements}}{\text{total time spent working}}$ . Equation (4) indicates that an increase in either the hand activity frequency $f$ or duty cycle $G$ will result in a higher HAL and correspondingly, lower ergonomic welfare for workers. In the subsequent sections, we describe how HAL maps onto the mushroom context and use this metric to evaluate the workers’ ergonomic welfare under different harvesting protocols.

3.3. Performance Metrics Trade-offs

Our performance metrics of interest have some inherent trade-offs. For example, in case of the Harvest-all protocol, a worker spends less time moving around the farm and is able to complete the assigned harvesting tasks in a shorter time duration. This results in lower time-based labor costs. However, the average value of the harvested crop units tend to be lower. This is due to the simultaneous harvesting of crop units at different maturity levels, some pre-peak and some post-peak. Furthermore, this harvesting protocol also induces a higher HAL, placing physical strain on workers. In contrast, under the Selective Harvesting protocol, workers’ HAL tends to be lower and the average quality of the harvested produce is higher. However, the main downside is that workers spend a considerable amount of time moving around, escalating the firm’s time-based costs, potentially compromising profitability. Given these trade-offs, it is not clear which of the two harvesting protocols is better and under what conditions. Hence, a rigorous analysis of the protocols is required to unravel the trade-offs at play. We begin with the Harvest-all protocol.

4. Base Case: Harvest-all Protocol

We next present the analytical development and results for the Harvest-all protocol, which serves as the base case in our analysis. We focus on this harvesting protocol for two main reasons: First, the Harvest-all protocol is the dominant approach used in the agribusiness industry, including by TMG. Optimizing this protocol is of significant importance and relevance to firms in this industry. Second, the tractability of the Harvest-all protocol allows us to develop insights into the underlying trade-offs related to harvesting operations.

4.1. Model Formulation

Consider a worker who is tasked with harvesting $M$ bins of crops. The worker starts harvesting at time $t_0$ from the left-most bin (see Figure 6 for a layout of the harvesting area), picks all the crop units in that bin, then proceeds to the next one. The worker repeats this process until all crop units in the allocated bins have been harvested. We denote the time taken to harvest one crop unit by ${\epsilon }_y$ . Hence, for a bin with $N$ crop units, the worker spends $N{\epsilon }_y$ units of time harvesting the crop units in that bin. After harvesting a bin, the worker takes ${\epsilon }_x$ time units to reach the next bin along with their tools and harvesting trays. Therefore, the total time spent on each bin is $N{\epsilon }_y+{\epsilon }_x$ . This process is repeated for all $M$ bins, resulting in the following expression for the total harvest duration $D^{HA}$ :

$$D^{HA}=M(N{\epsilon }_y+{\epsilon }_x)$$

(5)

We next characterize the total value of crop units harvested by the worker, denoted by $V^{HA}$ . As stated in Section 3.1.2, the economic value of a crop unit changes based on its age (i.e., time since pop-up). We are interested in calculating the monetary value at the time of harvesting of a focal crop unit in bin $i$ that popped up at time $t_p$ . The harvest time of the focal unit depends on three factors: (i) The time at which the worker started harvesting crops, (ii) the duration needed for the harvester to arrive at bin i, and (iii) the time lag between arriving at bin $i$ and picking the focal crop unit. As stated earlier, we denote the harvest start time by $t_0$ . For (ii), the time spent by the worker on the previous $i-1$ bins equals $(i-1)(N{\epsilon }_y+{\epsilon }_x)$ . For (iii), we assume that the worker harvests the focal crop unit half way through bin $i$ , that is, the worker will harvest the focal crop unit at $\frac{N{\epsilon }_y}{2}$ time units after arriving at bin $i$ . This approximation is motivated by the fact that in practice, workers tend to use different heuristics (smallest first, largest first, random picking and so on) when harvesting crops within each bin. The intermediate time point represents a good approximation for such dispersed routines. From (i) to (iii), we obtain the harvest time of the focal crop unit to be $t=t_0+(i-1)(N{\epsilon }_y+{\epsilon }_x)+\frac{1}{2}N{\epsilon }_y$ . The age of the focal crop unit is the time difference between the harvest time and pop-up time, that is, $t_0+(i-1)(N{\epsilon }_y+{\epsilon }_x)+\frac{1}{2}N{\epsilon }_y-t_p$ , and its monetary value is equal to $v(t_0+(i-1)(N{\epsilon }_y+{\epsilon }_x)+\frac{1}{2}N{\epsilon }_y-t_p)$ . For $M$ bins, each with $N$ crop units, the total monetary value of the produce harvested by a worker equals:

$$V^{HA}=\sum _{i=1}^{M}Nv(t_0+(i-1)(N{\epsilon }_y+{\epsilon }_x)+\frac{1}{2}N{\epsilon }_y-t_p)$$

(6)

Substituting equations (5) and (6) into (2), we obtain the firm’s expected profit as:

$$\begin{array}{rl}{\mathrm{\Pi }}^{HA}(t_0)& =\mathbb{E}[(1-\alpha )V^{HA}]-c{D}^{HA}\\ & =\mathbb{E}[(1-\alpha )\sum _{i=1}^{M}Nv(t_0+(i-1)(N{\epsilon }_y+{\epsilon }_x)+\frac{1}{2}N{\epsilon }_y-t_p)]\\ & -cM(N{\epsilon }_y+{\epsilon }_x)\end{array}$$

(7)

The expectation operation in equation (7) is over the pop-up time $t_p$ and can be divided into two partitions. Consider a particular time instant $t$ during a worker’s harvesting process. At that time, the worker will harvest a crop unit that is either in its growth phase or deterioration phase, as determined by the crop unit’s age $x=t-t_p$ . If $x\le P$ , the crop unit is in the growth phase; otherwise, it is in the deterioration phase, with the demarcation condition being $t-t_p=P$ . We denote the pop-up time that meets this condition as $t_c$ . This implies that crop units with a pop-up time in the range $(0,t_c)$ will be harvested in their deterioration phase. Based on equation (1), we can write the value of crop units harvested in their deterioration phase as $k_2(t_0+(i-1)(N{\epsilon }_y+{\epsilon }_x)+\frac{1}{2}N{\epsilon }_y-t_p)+(k_1-k_2)P$ . The second partition accounts for crop units that popped up late, that is, in the time window $t_c$ to $T$ , which are harvested during their growth phase. Based on equation (1), the value of these crop units can be expressed as $k_1(t_0+(i-1)(N{\epsilon }_y+{\epsilon }_x)+\frac{1}{2}N{\epsilon }_y-t_p)$ . Taking expectation over these two partitions with respect to pop-up time $t_p$ , we obtain the firm’s profit as:

$$\begin{array}{rl}{\mathrm{\Pi }}^{HA}\left(t_0\right)& =(1-\alpha )\sum _{i=1}^{M}N\{{\int }_{t_c}^T{k}_1(t_0+\frac{1}{2}N{\epsilon }_y+(i-1)(N{\epsilon }_y+{\epsilon }_x)-t_p)\frac{\mathrm{d}{t}_p}{T}\\ & +{\int }_0^{t_c}[k_2(t_0+\frac{1}{2}N{\epsilon }_y+(i-1)(N{\epsilon }_y+{\epsilon }_x)-t_p)+(k_1-k_2)P]\frac{\mathrm{d}{t}_p}{T}\}-cM(N{\epsilon }_y+{\epsilon }_x)\end{array}$$

(8)

where $t_c=t_0+\frac{1}{2}N{\epsilon }_y+(i-1)(N{\epsilon }_y+{\epsilon }_x)-P$ . Next, we analyze this profit function.

4.2. Concavity and Comparative Statistics

We first highlight some structural properties of the firm’s profit function. Then, we present results regarding how managerial decisions under the Harvest-all protocol are impacted by several key factors using a comparative statics analysis.

Proposition 1

The firm’s profit under the Harvest-all protocol is concave in the harvest start time $t_0$ . Furthermore, the optimal start time is given by

$$t_0^{*}=\frac{k_1}{k_1-k_2}T+P-\frac{1}{2}(M(N{\epsilon }_y+{\epsilon }_x)-{\epsilon }_x)$$

(9)

Proposition 1 establishes the existence of an optimal start time that balances the trade-off between starting the harvesting process too early vs. too late. Starting earlier than $t_0^{*}$ would lead to harvesting more crop units that are still in their growth phase, negatively impacting the firm’s profit. On the other hand, delaying the harvest start time beyond $t_0^{*}$ would result in more crop units being harvested when they are deteriorating in value, which would also compromise the firm’s profitability.

Using Proposition 1, we examine how various contextual factors impact the optimal harvest start time. These factors include the crop’s biological characteristics, compensation structure, and worker efficiency.

Proposition 2

• (a)

(Impact of Biological Characteristics) It is optimal to start harvesting later, that is, $t_0^{*}$ increases, as $(k_1,T,P)$ increase while it optimal to start earlier as $|k_2|$ increases.

(b)

(Impact of Compensation Structure) The optimal start time is not impacted by $c$ or $\alpha$ .

(c)

(Impact of Worker Efficiency) It is optimal to start harvesting earlier as ${\epsilon }_y$ and ${\epsilon }_x$ increase.

Proposition 2(a) offers three insights regarding the impact of a crop’s biological characteristics on the optimal start time: First, an increase in the growth rate parameter $k_1$ leads to a delay in the optimal harvest start time. While $k_1$ is often interpreted as the speed of growth, in our model it also determines the slope of the growth curve, meaning that crops not only grow faster but also attain higher maximum monetary value (as represented by the prime notations in Figures 9(a)). The impact of a higher $k_1$ is visually illustrated by the widening gap between the value trajectories with slopes $k_1$ and $k_1^{\prime }$ , which highlights the increasing benefits from delaying the harvest start time. In practice, a higher value of $k_1$ may reflect improvements in growth management—such as better nutrition, optimal humidity, or advanced cultivation techniques—that result in mushrooms that are larger and more valuable.

Figure 9.

Impact of changes in biological characteristics on the monetary value curves. (a) Impact of higher growth rate, $k_1^{\prime }>k_1$ , (b) Impact of slower deterioration rate, $|k_2^{\prime }|<|k_2|$ , (c) Impact of longer pop-up time window, $T^{\prime }>T$ and (d) Impact of longer time to peak, $P^{\prime }>P$ .

Second, a lower deterioration rate $k_2$ similarly delays the optimal harvest start time. A smaller $k_2$ implies a slower decline in value post-maturity (see Figure 9(b)), thereby reducing the urgency to harvest immediately, which in turn allows more crop units to reach their peak value. This is particularly relevant for crop varieties that maintain their value longer, either naturally or through improved climate control practices.

Third, increases in either the pop-up window $T$ or the growth duration $P$ also support a delayed harvest start time. A larger $T$ reflects greater variability in crop readiness, while a higher value of $P$ implies a longer duration over which crops accumulate value (see Figures 9(c) and (d) respectively). Both imply a more staggered and extended crop maturity timeline, and harvesting later allows the firm to take advantage of the extended timeline to harvest more crop units closer to their peak value.

Collectively, the insights from Proposition 2(a) have important practical implications. Specifically, the results offer guidelines in terms of how firms should adjust their harvest start time as they engage in performance-enhancing initiatives such as improved cultivar selection, environmental controls, or precision agriculture. We find that making operational adjustments (such as delaying the harvest start time) in response to these initiatives can be key to extracting maximum crop value.

With respect to the compensation parameters, we see that they have no impact on the optimal harvest start time. This is because under the Harvest-all protocol, the total time taken to harvest all the bins, and by extension, the time-based payment to the workers, remain the same regardless of when the firm starts harvesting. Finally, with respect to worker efficiency, we see that it is better for a more efficient worker to start harvesting later. A worker is more efficient either when they need less time to pick a unit of produce (i.e., a lower ${\epsilon }_y$ ) or if they are able to transition from one bin to another faster (i.e., lower ${\epsilon }_x$ ) or both. Essentially, a more efficient worker will need less total time ( $N{\epsilon }_x+{\epsilon }_y$ ) to fully harvest a bin and move to the next one. Given that it takes less time to harvest, it is better for the firm to start harvesting later so that more crop units get additional time to grow and be harvested closer to their peak value. Put differently, a more efficient worker requires less time to complete harvesting, enabling the firm to delay harvest further without risking deterioration. In essence, improved worker efficiency increases the benefit of waiting, enabling more crop units to reach a higher monetary value before being picked.

4.3. Performance Metrics

Below, we quantify the three performance metrics of interest for the Harvest-all protocol using the optimal harvest start time identified in Proposition 1.

4.3.1. Firm’s Expected Profit

The firm’s expected profit under the Harvest-all protocol is given by:

$$\begin{array}{rl}{\mathrm{\Pi }}^{HA}\left(t_0^{*}\right)& =\mathbb{E}[(1-\alpha )V^{HA}(t_0^{*})]-c{D}^{HA}\end{array}$$

(10)

4.3.2. Workers’ Economic Welfare

The workers’ earnings under the Harvest-all protocol is as follows:

$$\begin{array}{r}{S}^{HA}\left(t_0^{*}\right)=\mathbb{E}[\alpha V^{HA}(t_0^{*})]+c{D}^{HA}\end{array}$$

(11)

4.3.3. Workers’ Ergonomic Welfare

Recall from (4) that the worker’s ergonomic welfare is quantified by $HAL=4.31-0.637\frac{1}{f}+3.4G$ . In our context, the pick frequency $f=\frac{1}{{\epsilon }_y}$ and duty cycle $G=\frac{N{\epsilon }_y}{N{\epsilon }_y+{\epsilon }_x}$ . After substitutions, the HAL metric for the Harvest-all protocol is given by:

$$HAL=4.31-0.637{\epsilon }_y+3.4\frac{N{\epsilon }_y}{N{\epsilon }_y+{\epsilon }_x}$$

(12)

These three metrics underscore the trade-offs between the firm’s and workers’ interests; and also between the two metrics that characterize workers’ interests. As an example, consider the total bin harvest time $N{\epsilon }_y+{\epsilon }_x$ under the Harvest-all protocol. A decrease in this time improves the firm’s profit in (10). However, it lowers the workers’ ergonomic welfare by increasing the HAL score in (12). This illustrates the tension between the firm’s and workers’ interests. Even considering only the workers’ perspective, we see that the reduction in ergonomic welfare (due to the reduction in total bin harvest time) could be accompanied by either an increase or decrease in their earnings in (11). This illustrates the trade-offs between the three metrics under the Harvest-all protocol. These trade-offs are more nuanced under the alternative harvesting protocol namely, Selective Harvesting, that we consider in the next section.

5. Selective Harvesting Protocol

Recall that the Harvest-all protocol suffers from two main drawbacks: First, workers spend extended periods of time at the same spot, resulting in ergonomic stress; second, the quality of the harvested produce tends to be lower on average since different crop units within a bin may be at different points on the monetary value curve when they are picked. To overcome these drawbacks, our partner firm was interested in exploring an alternative harvesting protocol: Selective Harvesting. Under this protocol, workers selectively harvest a predetermined proportion of the produce within a bin during each visit. For instance, a worker may pick the “best” 20% of produce, that is, highest value crop units growing in a bin (20 out of 100 units), before proceeding to the next bin. It is important to note that under Selective Harvesting, workers must revisit each bin multiple times since they pick only a portion of the total produce during each visit.

Managers at our partner firm had also considered a slightly different protocol in which workers pick only those crop units that are larger than a threshold size. However, they deemed this protocol to be difficult to execute since precisely measuring the size of each crop unit before harvesting was not feasible. Therefore we focus on the protocol that is based on selectively picking a predetermined proportion of the produce in each round. Nevertheless, for completeness, we numerically explored the performance of the size-based protocol and found it to perform worse. Details of this analysis are in Appendix B.

As mentioned earlier, companies in the mushroom industry (including our collaborating partner) are interested in and have begun to experiment with the Selective Harvesting protocol in their operations. However, what is not apparent is how it stacks up relative to the Harvest-all protocol, given its relative strengths and weaknesses. Specifically, under the Selective Harvesting protocol, workers pick the best produce in each round and as a result, the average quality of the harvested produce tends to be higher. Furthermore, because Selective Harvesting involves more frequent transitions from one bin to another, workers are mobile, leading to lower ergonomic stress. The main downside, however, of Selective Harvesting is that it is less productive (i.e., fewer units picked per hour of work) compared to Harvest-all due to workers moving around more and spending time to identify the best produce. Consequently, the Selective Harvesting protocol requires additional time to fully pick a bin, which could elevate labor costs. Given these trade-offs, it is not clear which of the two harvesting protocols is better and under what conditions. To facilitate such comparisons, we first conduct a rigorous analysis of the Selective Harvesting protocol.

5.1. Model Formulation

The Selective Harvesting protocol encompasses two phases: A selective picking phase followed by a harvest-all phase. Each worker is assigned $M$ bins to harvest, with $X$ proportion of crop units harvested selectively $(0\le X<1)$ followed by the remaining $(1-X)$ proportion picked in a harvest-all manner.

The selective picking phase starts at time $t_0$ with the worker harvesting $X$ percent of the crop units in a bin in a selective manner in a fixed number of visits, denoted by $R>1$ . During each visit to a bin, the worker harvests $\frac{X}{R}N$ units of the crop selectively, where $N$ is the total number of crop units in a bin. The parameter $R$ represents the total number of visits to each bin during the Selective Harvesting phase and is typically an integer less than 5, based on managerial preferences and labor availability. For our purposes, we assume that $R$ is fixed since it tends to be a longer-term managerial decision at firms.

In the Selective Harvesting phase, more time is required to pick a crop unit compared to the Harvest-all protocol since the worker must search for and identify the best units to pick. We denote the additional observation time for each crop unit as ${\epsilon }_o$ . This additional time requirement contributes to the main trade-off associated with Selective Harvesting: A worker needs more time to harvest a crop unit (due to increased movement and observation times), but on average, each unit is closer to maturity and has a higher monetary value. The assumption of a constant observation time per unit ${\epsilon }_o$ makes the analysis more tractable while providing a reasonably realistic estimation of the observation time that might be encountered in practice (especially when ${\epsilon }_0$ is picked carefully). Indeed, we show in Section 7.1 that a carefully calibrated ${\epsilon }_o$ from our time-motion study at the firm provides estimates of worker wages that are within 2% of average wages in the U.S. for the harvesting jobs. Nevertheless, we note that alternative specifications of ${\epsilon }_o$ , where the observation time may vary in a non-linear way with $X$ still captures the time–value trade-off inherent in our analyses, and consequently, the key results and insights emanating from our work are likely to hold in that setting as well.

Under a constant observation time, the total pick time per crop unit in the selective picking phase is ${\epsilon }_y+{\epsilon }_o$ . In total, the worker spends $\frac{X}{R}N({\epsilon }_y+{\epsilon }_o)$ units of time picking crops within a single bin during each visit. After selectively harvesting produce from a bin, the worker moves to the next bin, which takes ${\epsilon }_x$ time units. This process is repeated for all $M$ bins and $R$ Selective Harvesting rounds, resulting in a total duration of $XMN({\epsilon }_y+{\epsilon }_o)+RM{\epsilon }_x$ for the selective picking phase.

After the selective picking phase, the worker harvests the remaining $(1-X)N$ crop units within a bin in a single visit. Thus, the duration of the harvest-all phase is $M[(1-X)N{\epsilon }_y+{\epsilon }_x]$ . Therefore, the total time spent by the worker under the Selective Harvesting protocol is given by:

$$D^{SH}=[XMN({\epsilon }_y+{\epsilon }_o)+RM{\epsilon }_x]+M[(1-X)N{\epsilon }_y+{\epsilon }_x]$$

(13)

where the first term on the right-hand side is the time spent on selective picking in $R$ rounds, and the second term is the time spent on one round of harvest-all.

Next, we look at the total value of crop units harvested by a worker, represented by $V^{SH}$ . We start by examining the selective picking phase. As discussed above, in this phase, a worker takes ${\epsilon }_y+{\epsilon }_o$ time units to harvest a unit of produce (i.e., observation time plus picking time). The harvest timing for a focal crop unit in the $j$ th bin ( $1\le j\le M$ ) during the $i$ th round ( $1\le i\le R$ ) depends on three factors: The harvest start time $t_0$ , the time taken to reach the $j$ th bin for the $i$ th time, and the time lag between arriving at the $j$ th bin for the $i$ th time and harvesting the focal crop unit. The time taken to complete the previous $(i-1)$ rounds is equal to $(i-1)M[\frac{X}{R}N({\epsilon }_y+{\epsilon }_o)+{\epsilon }_x]$ and the time taken to visit the previous $(j-1)$ bins in the current round is $(j-1)[\frac{X}{R}N({\epsilon }_y+{\epsilon }_o)+{\epsilon }_x]$ . Finally, once the worker reaches the focal bin, it takes them $\frac{1}{2}\frac{X}{R}N({\epsilon }_y+{\epsilon }_o)$ time units on average to reach the focal crop unit. Adding the three components, we see that in round $i$ , a focal crop unit in bin $j$ will be harvested at time $t=t_0+((i-1)M+(j-1))(\frac{X}{R}N({\epsilon }_y+{\epsilon }_o)+{\epsilon }_x)+\frac{X}{2R}N({\epsilon }_y+{\epsilon }_o)$ . The corresponding monetary value of the focal crop unit is $v(t-t_{ik})$ where $t_{ik}$ is the $((i-1)\frac{XN}{R}+k)$ th order statistic of $N$ uniform random variables from $U[0,T]$ , and $k=1,\dots ,\frac{X}{R}N$ . Here, we use the order statistics to identify the set of $\frac{X}{R}N$ best crop units that will be picked in round $i$ .

After the selective picking phase, the harvest-all phase follows. The harvest-all phase begins at time $XMN({\epsilon }_y+{\epsilon }_o)+RM{\epsilon }_x$ after completing the $R$ Selective Harvesting rounds. The corresponding monetary value of a focal crop unit in the $j$ th bin picked during the harvest-all phase is given by $v(t_0+XMN({\epsilon }_y+{\epsilon }_o)+RM{\epsilon }_x+(j-1)(1-X)(N{\epsilon }_y+{\epsilon }_x)+\frac{1}{2}(1-X)N{\epsilon }_y-t_k)$ , where $t_k$ represents the pop-up time of the crop unit with the $k$ th earliest pop-up time in the $j$ th bin during the harvest-all phase, that is $t_k$ is the $(XN+k)$ th order statistic of $N$ uniform random variables from $U[0,T]$ where $k$ =1,2,… $(1-X)N$ .

Bringing the above elements together, the total monetary value of crop units harvested by the worker across the Selective Harvesting and harvest-all phases is given by:

$$\begin{array}{rl}{V}^{SH}=& \sum _{i=1}^R\sum _{j=1}^M\sum _{k=1}^{\frac{X}{R}N}v(t_0+((i-1)M+(j-1))(\frac{X}{R}N({\epsilon }_y+{\epsilon }_o)+{\epsilon }_x)+\frac{1}{2}\frac{X}{R}N({\epsilon }_y+{\epsilon }_o)-t_{ik})\\ & +\sum _{j=1}^M\sum _{k=1}^{N(1-X)}v(t_0+M(NX({\epsilon }_y+{\epsilon }_o)+R{\epsilon }_x)+(j-1)((1-X)N{\epsilon }_y+{\epsilon }_x)+\frac{1}{2}N(1-X){\epsilon }_y-t_k)\end{array}$$

(14)

where the first term on the right-hand side is the revenue from the selective picking phase and the second term is the revenue from the harvest-all phase. Note that when $X=0$ and $R=0$ , the Selective Harvesting protocol reduces to Harvest-all.

The firm’s expected profit under the Selective Harvesting protocol is:

$${\mathrm{\Pi }}^{SH}(t_0,X)=\mathbb{E}\{(1-\alpha )V^{SH}\}-c{D}^{SH}$$

(15)

where $V^{SH}$ is given by (14) and $D^{SH}$ is given by (13). In (15), the first term represents the firm’s expected revenue after sharing $\alpha$ fraction of the produce value with workers, and the second term represents the time-based labor cost.

5.2. Structural Properties and Comparative Statics

We first demonstrate that the objective function in (15) exhibits tractability properties that enable us to characterize the optimal start time $t_0^{*}$ and the optimal percentage to selectively harvest, $X^{*}$ . We then analyze how these managerial decisions depend on key contextual factors.

Proposition 3

The firm’s expected profit ${\mathrm{\Pi }}^{SH}(t_0,X)$ under the Selective Harvesting protocol is jointly concave in $t_0$ and $X$ .

Proposition 3 has two distinct implications. First, similar to Proposition 1, there exists an optimal solution, denoted by $(t_0^{*},X^{*})$ , that maximizes the firm’s profit. Selectively harvesting more crop units than the optimal percentage $X^{*}$ could result in an extended harvest duration, causing more crop units to move to the deterioration phase. Conversely, harvesting less selectively than the optimal percentage $X^{*}$ would provide insufficient time for crop units in the growth phase to accrue monetary value. The second implication of Proposition 3 is the concavity of the profit function in the individual dimensions $t_0$ and $X$ . For instance, if a firm has in place a Selective Harvesting protocol that utilizes a value of $X$ different from the optimal Selective Harvesting percentage $X^{*}$ (due to the firm’s long-term operational practices or other shorter-term considerations), it can still optimize the harvest start time $t_0^{*}$ for that value of $X$ .

Utilizing the concavity established in Proposition 3, we next explore how the firm should tailor the optimal start time $t_0^{*}$ and picking percentage $X^{*}$ to the crop’s biological characteristics, compensation structure, and worker efficiency. The comparative statics for the harvest start time $t_0^{*}$ are the same as reported in Proposition 2 for the Harvest-all protocol and we do not repeat them here. The following result highlights the comparative statics with respect to $X^{*}$ , which is a salient feature of the Selective Harvesting protocol.

Proposition 4

The optimal selective picking percentage $X^{*}$ :

• (a)

(Impact of Biological Characteristics) increases in $k_1$ and decreases in the magnitude of $k_2$ but does not change with $P$ .

(b)

(Impact of Compensation Structure) decreases in $c$ and $\alpha$ .

(c)

(Impact of Worker Efficiency) increases in ${\epsilon }_o$ when ${\epsilon }_o$ is below the threshold ${\hat{\epsilon }}_o$ , and decreases otherwise.

Proposition 4 provides insights for managers should tailor the Selective Harvesting protocol as relevant contextual factors change. Part (a) highlights the influence of biological factors on the optimal selective picking percentage $X^{*}$ . Higher rates of growth $k_1$ and lower rates of deterioration $k_2$ lead to a higher percentage of the produce being picked selectively. This is because under these conditions, the additional benefits from picking the best quality produce in each Selective Harvesting round more than offset the additional cost attributed to the extra time spent in identifying such produce. In contrast, a change in the duration of the growth phase, as captured by $P$ , does not impact $X^{*}$ . This is because for fixed $k_1$ and $k_2$ values, an increase in the duration of the growth phase also proportionally increases the time it takes for the produce to deteriorate in value. As a result, the fractions of produce harvested in the growth and deterioration phases remain unchanged, making the optimal Selective Harvesting percentage insensitive to the duration of the growth phase.

To better understand part (b), note that Selective Harvesting is more time consuming (requiring ${\epsilon }_y+{\epsilon }_o$ time for picking each crop unit instead of ${\epsilon }_y$ in the Harvest-all protocol). Therefore, as the time-based payment to the worker increases through an increase in $c$ , the firm would opt to pick a lower percentage of the produce in a selective manner. While $c$ influences the differential cost of performing Selective Harvesting, $\alpha$ dictates the share of (potentially) additional revenue the firm retains from engaging in more Selective Harvesting. An increase in $\alpha$ reduces the share retained by the firm, diminishing the attractiveness of Selective Harvesting, which in turn translates into a lower $X^{*}$ .

Part (c) states that an increase in the observation time per pick ( ${\epsilon }_o$ ) has a non-monotonic impact on the optimal Selective Harvesting percentage $X^{*}$ . This is because of the two opposing and heterogeneous effects a higher ${\epsilon }_o$ has on the value of the harvested produce. An increase in ${\epsilon }_o$ slows down the harvesting of high-value crop units, which inadvertently gives more time for earlier-stage units to continue growing before they are picked in subsequent rounds. This can lead to an increase in the average value of harvested produce, especially for crop units that would otherwise have been harvested prematurely. At relatively small values of ${\epsilon }_o$ , the benefits from an increase in average crop quality outweigh the downwsides, justifying picking more crop units selectively (i.e., higher $X^{*}$ ). However, this benefit does not persist indefinitely. As ${\epsilon }_o$ becomes large, the prolonged observation times delay the collection of crop units that are already near or beyond their peak value. This increases the likelihood that some crop units will deteriorate before being harvested, thereby eroding the overall gains from Selective Harvesting. Consequently, the relationship between ${\epsilon }_o$ and $X^{*}$ is non-monotonic: for ${\epsilon }_o<{\hat{\epsilon }}_o$ , the net effect of a higher ${\epsilon }_o$ is positive, and $X^{*}$ increases; for ${\epsilon }_o\ge {\hat{\epsilon }}_o$ , the negative effects dominate, and $X^{*}$ declines.

5.3. Performance Metrics

Below, we provide expressions for the three performance metrics under the Selective Harvesting protocol.

5.3.1. Firm’s Expected Profit

The firm’s expected profit, as previously shown in (15), is:

$${\mathrm{\Pi }}^{SH}\left(t_0^{*}\right)=\mathbb{E}[(1-\alpha )V^{SH}(t_0^{*},X^{*})]-c{D}^{SH}(X^{*})$$

(16)

5.3.2. Workers’ Economic Welfare

The harvesters’ expected earning equals:

$$S^{SH}\left(t_0^{*}\right)=\mathbb{E}[\alpha V^{SH}(t_0^{*},X^{*})]+c{D}^{SH}(X^{*})$$

(17)

The expression for $V^{SH}(t_0^{*},X^{*})$ is rather involved and is presented in Appendix 3. We do not reproduce it here in the interest of expositional brevity.

5.3.3. Workers’ Ergonomic Welfare

Under the Selective Harvesting protocol, the pick frequencies and duty cycles are different in the selective picking and harvest-all phases. Specifically, in the selective picking phase, the pick frequency is $f=\frac{1}{{\epsilon }_y+{\epsilon }_o}$ and the duty cycle is $G=\frac{XN{\epsilon }_y}{XN({\epsilon }_y+{\epsilon }_o)+R{\epsilon }_x}$ . In the harvest-all phase, $f=\frac{1}{{\epsilon }_y}$ and the duty cycle is $G=\frac{(1-X)N{\epsilon }_y}{(1-X)N{\epsilon }_y+{\epsilon }_x}$ . The effective HAL is a weighted average over the percentages $X$ and $1-X$ of produce that are harvested in the selective picking and harvest-all phases, respectively. Accordingly, the HAL under the Selective Harvesting protocol is as follows:

$$\begin{array}{rl}HA{L}^{SH}& =X[4.31-0.637({\epsilon }_y+{\epsilon }_o)+3.4\frac{XN{\epsilon }_y}{XN({\epsilon }_y+{\epsilon }_o)+R{\epsilon }_x}]\\ & +(1-X)[4.31-0.637{\epsilon }_y+3.4\frac{(1-X)N{\epsilon }_y}{(1-X)N{\epsilon }_y+{\epsilon }_x}]\end{array}$$

(18)

Similar to the Harvest-all protocol, there exist trade-offs between the firm and workers’ interests; and between the workers’ financial and ergonomic welfare under the Selective Harvesting protocol. For example, the term $XN({\epsilon }_y+{\epsilon }_o)$ represents the time spent by a worker picking crop units in a bin during the Selective Harvesting phase. A decrease in this time represents a faster pace of work, which increases the firm’s profit. However, it decreases the workers’ welfare through an increase in the HAL score. Furthermore, this decrease in workers’ ergonomic welfare may also be accompanied by an increase (or decrease) in their earnings, highlighting the complex trade-offs between the three performance metrics of interest. To better articulate these trade-offs, we first note how the workers’ economic and ergonomic welfare vary with $X$ , which is a key feature of the Selective Harvesting protocol.

Proposition 5

Under Selective Harvesting: (a) Workers’ earnings $S^{SH}(t_0^{*}(X),X)$ is concave in $X$ . (b) Workers’ HAL $HA{L}^{SH}(t_0^{*}(X),X)$ decreases in $X$ .

To understand why the above result holds, note that the workers’ payment consists of two parts, one based on the total value of the harvested produce and the other based on the total harvest time. The value-based component first increases in $X$ because the worker is able to pick a larger number of mushrooms that are close to their peak value. However, beyond a threshold of $X$ , the worker spends a significant amount of time transitioning from one bin to another and as a result, a disproportionately larger number of mushrooms start to deteriorate before they are harvested. Part (a) of Proposition 5 formalizes this intuition. Part (b) indicates that workers’ ergonomic welfare improves as $X$ increases. This improvement occurs because a higher $X$ leads to a slower frequency of mushroom picking, contributing to a lower overall HAL level.

So far, we have characterized the performance of the Harvest-all and Selective Harvesting protocols in terms of three metrics: Firm’s and workers’ financial interests and workers’ ergonomic welfare. Next, we perform a comparative analysis of the two protocols based on these metrics.

6. Existence of Win–Win, Trade-off, and Lose–Lose Regions

The comparative analysis helps to address our second and third research questions, namely, how do the two protocols compare with respect to the firm’s and workers’ metrics; and are there conditions under which a transition to the Selective Harvesting protocol can benefit both the firm and the workers? With respect to our second research question, we demonstrate that there exist three potential regions of the Selective Harvesting percentage $X$ : (i) A “win–win” region where both the firm and workers benefit from Selective Harvesting vis-a-vis Harvest-all, (ii) a “lose–win” region where workers are better-off under Selective Harvesting but the firm is worse-off; and (iii) a “lose–lose” region where both parties are worse off under Selective Harvesting when compared to Harvest-all. Propositions 6 to 8 below provide the analytical basis for the characterization of the three regions.

Proposition 6

• (a)

There exist a threshold $\hat{c}>0$ such that $\mathrm{\forall }c<\hat{c}$ , the firm’s optimal expected profit is higher under the Selective Harvesting protocol than under the Harvest-all protocol.

(b)

$\mathrm{\forall }c>0$ , the worker’s maximum achievable expected earning is higher under the Selective Harvesting protocol than under the Harvest-all protocol.

From the firm’s perspective, the Selective Harvesting protocol leads harvesters to pick crop units closer to their peak value. However, this benefit comes at a higher labor cost, as the Selective Harvesting protocol requires additional time for observation and revisiting bins. The threshold $\hat{c}$ represents the point at which the marginal value gained from the harvesting a higher value crop unit is offset by the additional labor expense. When the hourly wage $c$ is below this threshold ( $c<\hat{c}$ ), the Selective Harvesting protocol creates a net gain for the firm. Conversely, when $c\ge \hat{c}$ , the additional labor cost incurred under Selective Harvesting outweighs the increase in the value of crop units, making Harvest-all the more profitable choice for the firm. The effects are somewhat different for the workers. More specifically, workers benefit from a higher average crop unit value under Selective Harvesting (due to the value-based pay component) as well as additional time-based pay. Since these two forces are in unison from the worker’s perspective, it follows that the workers’ earnings are always higher under the Selective Harvesting protocol relative to Harvest-all. This asymmetry in how the two forces described above apply to the firm and workers results in a misalignment in their interests at higher wage levels, which we elaborate further following our next result, Proposition 7. It provides a useful ordering of the values of the harvesting fraction $X$ that maximize the firm’s profits and workers’ earnings, respectively.

Proposition 7

For any positive hourly wage $c>0$ , the Selective Harvesting fraction $X^{*}$ that maximizes firm profits differs from the fraction $X_W^{*}$ that maximizes workers’ earnings, with $X_W^{*}>X^{*}$ .

The intuitive reason for Proposition 7 is similar to our discussion following Proposition 6, that is, the two forces pull in opposite directions from the firm’s perspective while they act in unison for the worker. This makes Selective Harvesting more attractive for the worker over a broader range of $X$ values. This explains why the Selective Harvesting proportion that maximizes workers earnings ( $X_W^{*}$ ) is higher than the one that maximizes firm profits ( $X^{*}$ ). Together, Proposition 6 and 7 help identify win–win, lose–win, and lose–lose regions with respect to $X$ where the interests of the firm and workers are aligned or in conflict, as formalized below:

Proposition 8

Let $\hat{c}>\tilde{c}$ be two wage thresholds. The distribution of win–win, lose–win, and lose–lose regions varies with the hourly wage $c$ as follows:

• (a)

When $0<c\le \tilde{c}$ , all three regions exist. There exist $0<X_1<X_2<1$ such that Selective Harvesting yields a win–win outcome for $X\in [0,X_1)$ , a lose–win for $X\in [X_1,X_2)$ , and a lose–lose outcome for $X\in [X_2,1]$ .

(b)

When $\tilde{c}<c<\hat{c}$ , only the win–win and lose–win regions exist. There exists $0<X_1<1$ such that Selective Harvesting yields a win–win outcome for $X\in [0,X_1)$ and a lose–win for $X\in [X_1,1]$ .

(c)

When $c\ge \hat{c}$ , only the lose–win region exists.

Figures 10(a), (b), and (c) show these three cases pictorially. In each Figure, the top panel shows the firm’s profits and worker earnings as concave functions of the Selective Harvesting proportion $X$ , consistent with Propositions 3 and 5. The bottom panel in each Figure displays the HAL values, which consistently decline with $X$ , reflecting lower ergonomic stress for workers.

Figure 10.

Regions based on selective harvesting percentage $X$ . (a) Regions when $0<c\le \tilde{c}$ , (b) regions when $\tilde{c}<c\le \hat{c}$ and (c) regions when $c\ge \hat{c}$ .

Figure 10(a) shows that at low per-hour wage levels, that is $0<c\le \tilde{c}$ , all three regions—win–win, lose–win, and lose–lose—exist for different levels of the Selecting Harvesting proportion $X$ . In the win–win region $X\in [0,X_1]$ , both the firm and workers are better off under Selective Harvesting relative to Harvest All. The boundary $X_1$ is defined by ${\mathrm{\Pi }}^{SH}(X_1)={\mathrm{\Pi }}^{HA}$ . As $X$ increases beyond $X_1$ , the marginal value of harvesting closer to peak quality diminishes for the firm, while the associated increase in labor cost dominates, resulting in a lose–win situation emerging in the region $(X_1,X_2)$ . In this region, workers continue to benefit from Selective Harvesting but the firm incurs a loss relative to the status quo approach of Harvest-all. The boundary $X_2$ is defined by $S^{SH}(X_2)=S^{HA}$ . In the lose–lose region with $X\in [X_2,1]$ , engaging in too much Selective Harvesting results in many crop units deteriorating in value before they are harvested, results in monetary losses for both the firm as well as the workers, relative to simply engaging in Harvest-all.

When the time-based wage rate is in the intermediate range $\tilde{c}<c<\hat{c}$ , as shown in Figure 10(b), the lose–lose region disappears. Higher wages enhance worker compensation to the extent that even at higher Selective Harvesting intensities, their total earnings remain above the Harvest-all benchmark. However, for the firm, only modest levels of $X$ still yield higher profits than the Harvest-all approach. Hence, the win–win region $[0,X_1]$ persists, but the subsequent range $(X_1,1]$ becomes purely lose–win. The absence of the lose–lose region reflects the fact that higher wages shift more of the surplus toward workers, ensuring that their earnings do not drop below the Harvest-all benchmark.

Finally, Figure 10(c) shows that for high time-based wage rate $c\ge \hat{c}$ , the firm’s cost burden outweighs any quality gains from Selective Harvesting, rendering it less profitable than Harvest-all for all values of $X$ . In other words, the entire range of $X$ becomes a lose–win region: Workers consistently benefit from Selective Harvesting while the firm is worse-off relative to Harvest-all.

In the following section, we further extend our modeling effort and substantiate the analytical results using numerical experiments based on industry-calibrated data from TMG.

7. Industry-Calibrated Decision Support and Insights

In this section, we demonstrate the practical utility of our model, first in the context of the mushroom industry and then for other crops in the agribusiness domain. For the context of the mushroom industry, we calibrate our model parameters using data from TMG, as described in Section 7.1. Building on this foundation, in Section 7.2, we proceed to highlight the trade-offs between the three performance metrics discussed earlier, and how they compare across the two harvesting protocols. In Section 7.3, we discuss how worker compensation structure—which is at the firm’s discretion—can be used to moderate these trade-offs and increase the potential for win–win scenarios where both the firm and workers are better off. Subsequently, in Section 7.4, we discuss the application of our model to other crops beyond mushrooms.

7.1. Data Collection and Model Validation

We calibrate our model parameters using data collected from three sources: (i) Time-motion studies on harvesters at TMG, (ii) interviews with company managers, and (iii) publicly available data from the U.S. Department of Agriculture (USDA) and Bureau of Labor Statistics.

To estimate worker efficiency parameters ${\epsilon }_o$ , ${\epsilon }_y$ , and ${\epsilon }_x$ , we conducted time-motion studies on harvesters at TMG, consistent with the ergonomic literature Greene et al. (see, e.g., 2017). We recorded videos of 17 harvesters, each working for an average duration of 10 minutes. These videos captured workers picking white button mushrooms that constitute more than 65% of the business volume at TMG. In the videos, workers repeatedly performed a set of activities including observing mushrooms, picking them, and relocating to the next bin. By carefully time-stamping the different activities, we developed the following estimates of the worker efficiency parameters: Time to identify a mushroom for Selective Harvesting ${\epsilon }_o=1.02$ seconds; pick time per mushroom ${\epsilon }_y=2.03$ seconds; and time to relocate to a new bin ${\epsilon }_x=30.39$ seconds.

To estimate the biological factors, we relied on an expert at TMG who has over 37 years of experience in mushroom picking and packing operations. This expert estimated the mushroom growth curve based on images taken at 30 second intervals of specific crop units in a bin. We then converted this growth curve (quantified in terms of mushroom diameters) into a monetary value function using the mushroom wholesale price data from USDA (2018). We approximated this value function to a piecewise linear form specified in equation (1), with estimated parameter values of $P=24$ hours, $k_1=\mathrm{\$}0.004/$ hour , and $k_2=\mathrm{\$}-0.04/$ hour.

To understand the firm’s compensation practices, we interviewed managers at TMG and obtained the following values for the compensation structure: Revenue share fraction $\alpha =6.6\mathrm{\%}$ and time-based payment $c=\mathrm{\$}8.95$ per hour. At these values, the earnings of an average worker at TMG (who harvests $85$ lbs/hour) would be $\mathrm{\$}14.55$ , which is consistent with the average hourly wage of $\mathrm{\$}14.27$ (within 2% of $\mathrm{\$}14.55$ ) for agricultural workers (Bureau of Labor Statistics, 2021). Managerial interviews also provided us with values of operational parameters $M$ and $R$ . Managers at the firm typically assign each worker a stack of three mushroom beds, which translates into a workload of $M=48$ bins. TMG currently follows both Harvest-all and Selective Harvesting protocols in their farms, with a majority following the Harvest-all protocol. In farms that use the Selective Harvesting protocol, workers selectively harvest mushrooms in three rounds, implying a value of $R=3$ . For these calibrated parameters, we next explore the financial and ergonomic trade-offs associated with the two harvesting protocols.

7.2. Harvest-All Vs Selective Harvesting: Financial and Ergonomic Trade-Offs

Figures 11(a), (b), and (c) highlight how the three performance metrics (on the y-axis) namely, the firm’s profit per worker per harvest, workers’ earnings per harvest, and workers’ HAL, respectively, vary based on the proportion $X$ (on x-axis) of produce that is selectively harvested. We use equations (10) and (16) to calculate the firm’s profit under the Harvest-all and Selective Harvesting protocols, respectively; equations (11) and (17) for the workers’ earnings under the two protocols; and equations (12) and (18) for computing HAL values. As a robustness check (results reported in Appendix B1), we also conducted our analysis on an annualized basis (i.e., annual profit for the firm and annual earnings for a worker) and found that all the key insights and results emanating from the per-harvest analysis continue to hold in that setting.

Figure 11.

Impact of the selective harvesting percentage $X$ on the three performance metrics. (a) Impact on firm’s profit, (b) impact on workers’ earnings and (c) impact on hand activity level (HAL) scores.

Recall from Figure 10 that in cases where $c<\hat{c}$ , the firm’s profit first increases and then decreases in $X$ while in cases with $c\ge \hat{c}$ (see Figure 10 (c)), the firm’s profit always decreases with $X$ . For the calibrated parameters reported above, we calculated the threshold $\tilde{c}$ to be $ $-13.80/$ hour $<0$ and $\hat{c}$ to be $195.41 $/$ hour. Since TMG’s cost $c=\mathrm{\$}8.95/$ hour lies between $\tilde{c}$ and $\hat{c}$ , we would expect TMG’s profit as a function of $X$ to be structurally consistent with Figure 10(b). Figure 11(a) confirms this trend. We also make the following observations from the figure: First, the firm benefits from Selective Harvesting relative to the common practice of Harvest-all. This is evident from the fact that there are multiple values of $X>0$ that yield higher firm profits than the Harvest-all protocol. Furthermore, there is an optimal level of Selective Harvesting ( $X$ =47.8%) at which the firm’s profit is 20.9% higher than the profits under the Harvest-all protocol (optimal value of $354.04 at $X=47.8\mathrm{\%}$ vs. $292.80 at $X=0$ ). These results also demonstrate the importance of judiciously choosing the fraction to selectively harvest since aggressively pursuing Selective Harvesting (i.e., choosing very high values of $X$ ) can erode firm profits relative to Harvest-all.

Turning to workers’ earnings, we see from Figure 11(b) that the insights are qualitatively similar to that of firm profits in Figure 11(a). Specifically, workers’ earnings tend to be higher under Selective Harvesting than the Harvest-all protocol and there is an optimal Selective Harvesting percentage ( $X$ =82.3%) from the workers’ perspective that maximize their earnings. At this value of $X$ , workers’ earnings are 20.5% higher ($75.03) than under the Harvest-all protocol ($62.20). Finally, we observe from Figure 11(c) that the workers’ HAL continuously decreases from a value of 5.9 at $X=0\mathrm{\%}$ to 4.1 at $X=99\mathrm{\%}$ , confirming that the workers’ ergonomic welfare always improves with Selective Harvesting. This feature is consistent with the firm’s expectations ex-ante and as discussed earlier, was one of the main drivers for them to consider the Selective Harvesting protocol.

Consistent with the results presented in Section 6 and Figure 10(b), there are two ranges of the Selective Harvesting percentage $X$ that correspond to the win–win and lose–win regions. In the win–win region, both the firm’s profit and workers’ earnings are higher than Harvest-all. Simultaneously, the HAL is lower in this region. In the lose–win region, workers’ earnings remain higher under Selective Harvesting (see Figure 11(b)). However, this improvement in worker welfare comes at the cost of a decline in firm profits. For example, if the firm were to choose $X=82.3\mathrm{\%}$ which maximizes workers’ earnings, its profits will reduce from a peak value of $354.04 to $322.01, a decrease of 9.0%.

The analysis in this section utilizes metrics on a per-harvest basis. However, as a robustness check, we also conducted our analysis on an annualized basis (i.e., annual firm profits and annual worker earnings) and found that all the insights discussed above also carry over to the annualized setting, highlighting the robustness of our study results and the associated insights. This analysis is reported in Appendix C.

7.3. Managing the Misalignment Between Firm and Worker Interests

Note from Figures 11(a) and (b) that the Selective Harvesting percentage $X^{*}=47.8\mathrm{\%}$ that maximizes firm profit is substantially different from the one that maximizes workers’ earnings ( $X=82.3\mathrm{\%}$ ), which we denote for convenience by $X_w^{*}$ . The magnitude of the gap $X_w^{*}-X^{*}$ indicates the degree of misalignment between the firm and worker interests, and identifying ways to reduce this gap is of significant interest to the firm, given its motivation to not only boost profits but also improve worker welfare. To this end, we analyze how changes to the worker compensation structure, a key lever at the firm’s disposal, impacts the degree of misalignment.

Figure 12.

Impact of compensation parameters on the misalignment gap $X_w^{*}-X^{*}$ . (a) Impact of change in per unit time payment $c$ and (b) impact of change in revenue-share fraction $\alpha$ .

Figure 12(a) and (b) show how the gap $X_w^{*}-X^{*}$ changes as a function of the two elements of the compensation structure, namely the per unit time payment $c$ and the revenue-share fraction $\alpha$ , respectively. From Figure 12(a), we see that as $c$ increases, the gap between $X_w^{*}$ and $X^{*}$ widens. Intuitively, an increase in the time-based payment rate decreases the share of the worker compensation that is performance-based, resulting in diverging incentives for the firm and workers. The impact of the revenue-share fraction $\alpha$ on the gap $X_w^{*}-X^{*}$ is different, as evident from Figure 12(b). Specifically, we see that the gap $X_w^{*}-X^{*}$ exhibits a U-shaped pattern with respect to $\alpha$ . Intuitively, as the firm shares a larger fraction of its revenue with workers, their incentives become more aligned, resulting in a reduction in the gap $X_w^{*}-X^{*}$ . However, this pattern no longer holds at very large (and impractical) values of $\alpha$ . At such high values of $\alpha$ , the firm’s share of the generated revenues is severely curtailed and consequently, the firm turns its attention toward lowering costs (specifically, time-based compensation) by reducing the proportion of produce selectively harvested. This explains why the gap $X_w^{*}-X^{*}$ begins to widen again at higher values of $\alpha$ . Overall, this analysis shows that placing higher emphasis on the performance-based component of pay and keeping the time-based component of pay at an “acceptable” level will result in operational decisions that better align firm profits and worker earnings.

The two compensation levers, $c$ and $\alpha$ , are valuable tools in reducing the misalignment between firm and worker interests, represented by $X_w^{*}-X^{*}$ . In addition, as we discuss below, changes to the compensation structure can also be effective at obtaining managerial buy-in for adapting Selective Harvesting at scale. As the firm seeks to transition from the Harvest-all protocol to Selective Harvesting, ideally it would choose $X^{*}=47.8\mathrm{\%}$ that would maximize its profits. However, as noted above, this is not the point at which the workers’ earnings are maximized. Given the firm’s interest in improving worker welfare, if it were to pick a Selective Harvesting percentage that would maximize the workers’ earnings, it would lead to a 9.0% decline in firm profits, relative to the potential maximum profit the firm can generate (if it chooses $X^{*}=47.8\mathrm{\%}$ , see the first two rows of Table 1). This significant negative impact on profit may result in managerial pushback within the firm, making it difficult to implement such a protocol. Hence, the firm was interested in exploring other ways in which it could improve workers’ earnings without significantly impacting its own profit, as a way of obtaining managerial buy-in.

Table 1.

Impact of compensation plan parameters $c$ and $\alpha$ on workers’ earnings and firm profit.

Scenarios	$\alpha$	$c$	$X$	Firm’s profit per worker per harvest	Workers’ earnings
Firm’s optimal	6.6%	8.97	47.8%	354.04	72.79
Workers’ optimal	6.6%	8.97	82.3%	322.01	75.03
Alternate 1	7.1%	8.97	47.8%	351.79	75.03
Alternate 2	6.6%	9.42	47.8%	351.78	75.03
Alternate 3	7.6%	8.55	47.8%	351.81	75.03

To this end, we next show how by modifying the compensation structure, the firm can improve the workers’ earnings while having a minimal impact on profitability. The last three rows of Table 1 show three such alternative compensation plans among many others that are possible. In the first compensation plan, the value-share percentage is set at 7.1% (higher than the firm’s current value-share rate of 6.6%) and $c$ remains the same. Under this plan, at $X=$ 47.8%, the workers’ earnings remain at its maximum possible level of $75.03, and the firm’s profit is $351.79, which is only 0.7% lower than its maximum value of $354.04. The table also shows two other plans, one in which the per unit time payment $c$ is increased from the current value of $8.97 but $\alpha$ is kept constant (see row 4 of Table 1), and a second one in which both $c$ and $\alpha$ values are modified (see row 5 of the table). Under both plans, the workers’ earnings match the maximum possible value of $75.03, while the firm experiences only a small reduction in its profit, compared to the maximum value of $354.04. These results show that compensation structures can be particularly effective at creating win–win scenarios in agriculture harvesting operations where both the firm and workers stand to benefit.

7.4. Towards a General Decision Support for Harvesting Operations

This work was motivated by our interactions with managers at TMG for mushroom production but our analytical development is fairly general and can be used to support managerial decision making for a variety of crops that differ from our motivating context in terms of biological characteristics, compensation structure, and worker efficiency. We provide some illustrative examples to this end.

First, consider the impact of biological factors, specifically the crop deterioration rate. Figure 13 illustrates the monetary value evolution for different types of crops with varying deterioration rates. Figure 13(a) corresponds to our base motivating case of white button mushrooms. Within the context of mushroom production, Figure 13(b) corresponds to organic mushrooms that tend to deteriorate faster since they are not treated with chlorine, resulting in a more rapid growth of decay organisms. Beyond the context of mushrooms, Figure 13(b) is representative of raspberries that tend to rot quickly; and Figure 13(c) corresponds to grain crops such as corn that have very slow deterioration rates in the field (except for extreme weather events).

Figure 13.

Monetary value curves for different crops. (a) White button mushrooms, (b) raspberries and (c) corn.

Figure 14 shows the firm’s profit under the Harvest-all and Selective Harvesting protocols for these crops. As illustrated by the figure and as is evident from our extensive numerical results reported in the previous subsection, transitioning from Harvest-all to Selective Harvesting is clearly more profitable in case of white button mushrooms. For crops with higher deterioration rates such as organic mushrooms and raspberry, the benefit of moving from the status-quo practice of Harvest-all to Selective Harvesting is even more acute. In contrast, for crops with markedly slower deterioration rates such as corn, transitioning to the Selective Harvesting protocol does not bring any additional benefits.

Figure 14.

Comparison of firm’s profit per harvest per worker under two harvesting protocols for different crops.

In addition to biological characteristics, the choice of the optimal harvesting protocol and the benefits derived from transitioning to Selective Harvesting also change based on prevalent labor costs and worker efficiency, both of which may differ across geographical regions and the availability of labor within those regions. For example, seasonal agricultural workers tend to be more readily available in some U.S. states such as Texas and Arizona when compared to, say, the Midwestern states. Figures 15(a) and (b) illustrate the impact of these factors on the firm profit under the Harvest-all and Selective Harvesting protocols. Figure 15(a) shows that when the per unit time labor cost is low, it is beneficial for the firm to transition to Selective Harvesting. However, the benefits of adopting the Selective Harvesting protocol decreases with the labor cost and beyond a certain threshold, transitioning to Selective Harvesting brings no additional benefits. This suggests that the firm should consider adopting Selective Harvesting when labor is abundant and cheaper, but maintain the status-quo practice of Harvest-all when labor is scarce and expensive. Figure 15(b) illustrates the impact of worker efficiency on firm profitability under the two protocols. From the figure, we see that the benefits of adopting the Selective Harvesting protocol are substantial when workers are less efficient (or equivalently at higher values of ${\epsilon }_y$ ) but the benefits become progressively lower as workers become more efficient. In fact, at very high efficiency levels (or low values of ${\epsilon }_y$ ), the firm does not benefit as much from transitioning to the Selective Harvesting protocol.

Figure 15.

Impact of per hour wages and worker efficiency on the firm’s profit per harvest per worker. (a) Impact of per hour wages on firm’s profit and (b) impact of worker efficiency on firm’s profit.

In summary, by highlighting how the benefits of adopting the Selective Harvesting protocol vary depending on a number of factors, our analytical development provides a direct way for managers to choose the harvesting protocol that is likely to be the most beneficial, given the type of crop and their operating context.

8. Summary

In this study, we examine the redesign of agribusiness, specifically, harvesting operations to enhance firm performance and worker well-being. To this end, we analyze two harvesting protocols, namely Harvest-all, the dominant status-quo practice, and an alternative approach, Selective Harvesting. For each of these two harvesting protocols, we provide a full analytical characterization of the optimal managerial decisions and offer insights into how those decisions are impacted by relevant contextual factors such as the biological characteristics of the crop, compensation structure, and worker efficiency.

Using a grounded study that leverages industry data from TMG, we demonstrate that there does exist a win–win region where a transition to Selective Harvesting results in higher firm profitability and improved worker welfare. However, the Selective Harvesting percentage that maximizes the firm’s profit is not the same as the one that maximizes workers’ earnings, indicating that the firm’s and workers’ interests may not be in full alignment. Subsequently, we highlight an effective way for the firm to reduce this misalignment. We show that by modifying the performance-based vs. time-based components of worker compensation, the firm can ensure that the workers’ earnings match the maximum potential value without compromising its own profitability. This is critical to obtaining managerial buy-in within the firm necessary to make the transition from the status-quo Harvest-all approach and adopt Selective Harvesting at scale.

Our research is motivated by the agribusiness context of the mushroom industry, but our analytical findings are more broadly applicable and have implications for other crops and industries with similar characteristics, such as perishability and heterogeneity in maturity time. Future research should consider the interplay between the three metrics developed in this paper for other crops and explore their implications for the choice of the harvesting protocol that would enhance a firm’s triple bottom line. Another promising avenue for future work is to extend the model to capture firms that explicitly incorporate social objectives into their decision-making—such as social enterprises or mission-driven organizations. In these contexts, the firm’s objective may go beyond profit maximization to include worker earnings and ergonomic well-being. This could be modeled through a multiobjective framework in which harvesting protocols are evaluated based on a weighted combination of financial and social outcomes.

Supplemental Material

sj-pdf-1-pao-10.1177_10591478251395431 - Supplemental material for Redesigning Harvesting Processes andImproving Working Conditions in Agribusiness

Supplemental material, sj-pdf-1-pao-10.1177_10591478251395431 for Redesigning Harvesting Processes andImproving Working Conditions in Agribusiness by Dongsheng Li, Saurabh Bansal, Phillip S Coles and Karthik Natarajan in Production and Operations Management