Managing Product-Reusability Under Supply Disruptions

Abstract

We analyze product reusability, executed through refurbishment, amid supply disruptions. Consumers trade in used units, which can later be refurbished and sold. Using a three-period model, we determine the optimal reusability level, trade-in and refurbishment policies, trade-in fee, and the prices of new and refurbished units. Our analysis provides a useful framework to understand the interaction between a firm's choice of product reusability and the possibility of supply disruptions. First, we establish a threshold refurbishment policy: the firm refurbishes more as reusability increases but avoids refurbishment at low reusability. When both consumer valuation of used units and supply disruption probability are high, the firm builds a safety-stock of traded-in units, which it refrains from refurbishing when there is no supply disruption, unless the product reusability level is sufficiently high. Second, we find that it benefits to increase product reusability as the supply disruption risk increases until a certain threshold. Beyond this threshold, it is advantageous for the firm to reduce reusability and save on design costs to be profitable, contrary to popular belief. Our numerical examples reveal that the firm reduces reusability when production cost is high due to narrow margins. Finally, we demonstrate that the firm shares the benefits of higher product reusability with its consumers through higher trade-in fees and lower refurbished unit prices. This results in a “Pareto-efficient” win for the firm, its trade-in customers, and purchasers of refurbished units. Thus, our analysis offers insights for product designers on how supply disruption influences reusability choices in products.

1. Introduction

One of the Sustainable Development Goals (SDGs) established by the United Nations in 2015 is “Responsible Consumption and Production.” This goal seeks to reduce and manage waste by effectively reusing products and resources that have been returned, discarded, or disposed of at various stages of a product’s life cycle. Governments worldwide have implemented regulatory policies to promote such reuse practices, leading to their increasing adoption across various industries. Recently, there has been an increased discussion about how such reuse practices can help businesses withstand supply disruptions like the Suez Canal blockade and the COVID-19 pandemic (UNEP-report, 2020). Circular economy practices, including product and resource reuse, can help businesses build the necessary resilience towards disruptions (McKinsey & Company, 2023). There is a growing recognition that product and resource reuse practices can provide a back-up supply for manufacturers in the event of a supply disruption (Supply Chain Management Review, 2023). These practices can serve as local value-retention strategies, aiding firms in coping with and recovering from disruptive events (EIONET-report, 2021). This article analyzes how firms should manage their product-reusability decisions in the presence of supply disruptions, specifically addressing the question of how much reusability a firm should design into its products (such as through modularity or disassemblability) to support its reuse practices in the face of supply disruptions. While incorporating reusability into product design can lower a firm’s unit refurbishment cost, it incurs substantial upfront product-design costs to enhance the ease of a product’s reusability.

Supply chains frequently encounter disruptions stemming from various sources, such as natural disasters, political conflicts, economic fluctuations, and unforeseen events. These disruptions pose significant challenges to ensuring the uninterrupted flow of goods and materials along supply networks. For instance, the Coronavirus outbreak precipitated a global shortage of computer chips, colloquially termed “chipageddon,” affecting a wide array of industries, including computing, automotive, and telecommunications (Kelion, 2021). These industries continue to grapple with the repercussions of such shortages.

Existing risk mitigation strategies like order-splitting and multi-sourcing that address supply or sourcing disruptions are advantageous for securing supply (Anupindi and Akella, 1993; Tomlin, 2006). However, in the context of responsible consumption and resource availability, there is growing recognition of the role that reuse practices can play in bolstering resilience while promoting value retention. Practices such as refurbishment and remanufacturing are increasingly advocated by industry experts and organizations as a means to enhance supply chain resilience (Alicke et al., 2020; Fitzsimons, 2020). For instance, HP introduced remanufactured laptops alongside its mainstream products during the pandemic, underlining its commitment to sustainability with the slogan “We believe in reincarnation—at least when it applies to HP Notebooks” (REMATEC, 2020). Similarly, Nike launched a refurbishment program in select stores post-pandemic, reflecting a broader industry trend towards embracing reuse practices (Salpini, 2021). Recently, Simchi-Levi et al. (2023) underscore the significance of such practices in boosting resilience within semiconductor supply chains, which are particularly susceptible to disruptions.

Our interviews with senior refurbishing and remanufacturing professionals across various geographic regions, encompassing both developed and emerging economies, underscored the significance of reuse practices, particularly in the context of supply disruptions. ¹ One professional noted, “refurbishing and remanufacturing surely is playing a critical role in the recent times as we have seen imports have been banned and there was a huge supply chain disruption going on [during the COVID pandemic]. Having said that companies still have not cracked on refurbishing or remanufacturing in big way yet. It’s just a start and has a long way to go till refurbishing and remanufacturing become an everyday norm. Recent supply chain disruptions has given it a big boost though.” Another professional emphasized, “This [i.e., using reuse practices as a tool to address supply disruption] is true but only possible for a short to medium term fix.” These varied opinions from industry practitioners served as compelling motivations to explore how firms can effectively manage product reusability amidst supply disruptions and potentially alleviate the impacts of supply shortage risks resulting from disruptive events.

Drawing from both industrial practice and academic literature, we broadly classify reuse practices into two categories: (1) refurbishment, and (2) remanufacturing & recycling. The primary distinction between these two categories is the product quality after processing of the used units returned (or traded-in) by consumers. Refurbished units typically exhibit inferior quality compared to the original, leading to decreased consumer willingness to pay for such units. Conversely, in remanufacturing and recycling, the quality of used units is restored to that of newly manufactured units of the product (Chen and Chen, 2019; Thierry et al., 1995). Nevertheless, refurbishing remains one of the most widely used methods to efficiently reuse products and resources, with the market for refurbished products experiencing substantial growth post the COVID-19 pandemic (Allied-Market-Research, 2023; Rawuf, 2022). Consequently, this article focuses on refurbishment practices.

A well-designed product enables a firm to derive greater value from used units during reuse operations (Gershenson et al., 2003; Souza, 2017). This is often achieved by enhancing key product characteristics such as “disassemblability,” “modularity,” and “reusability.” Some examples of firms’ “product reusability” choices include the following. Dell’s product-design methodology emphasizes the role of modular product design in providing “easy access and disassembly” to facilitate their circular economy initiatives (Shrivastava and Schafer, 2018). Another example is Cisco’s sustainability initiatives that incorporates circularity in their products. Cisco’s product design strategy is to “design for reuse, repair & recycling,” so that the products are engineered to be quickly assembled and disassembled (Seward and Doran, 2024). Likewise, our interactions with industry professionals revealed a significant importance for “design for reuse.” One respondent commented, “surely if a firm is going for refurbishing or remanufacturing process they need to think on the designs right away.” However, it is crucial to acknowledge that while product-design techniques such as modularization aid a firm’s reuse operations, they typically entail substantial design process costs. Hence, such costs should be carefully considered in any analysis of product reusability, particularly in the context of supply disruptions.

In this article, we address the following questions when a firm faces potential supply disruptions:

Can managing product reusability be an effective strategy to manage the risk of supply disruptions, and, if yes, under what conditions?

How should a firm operationalize its product reusability strategy through pricing and trade-in inventory management decisions?

Does product reusability lead to “responsible consumption and production,” which is the United Nations’ twelfth sustainability development goal (UN SDGs, 2024)?

To the best of our knowledge, ours is the first paper that studies product-reusability in the context of reuse practices (executed via refurbishment), in the presence of supply disruptions. Our analysis can provide crucial managerial insights on the interplay between the risk of supply disruptions and the optimal level of product reusability. These insights can assist firms in designing efficient products for reuse when there are supply disruptions.

To address the above questions, we develop a three-period model with periods denoted as 0, 1, and 2. The following events and actions occur in each of these three periods:

Period 0: The firm determines the reusability level to be integrated into its product design.

Period 1: Based on the reusability level decided in period 0, the firm produces the product if there is no supply disruption in this period. The firm decides the price of the new units along with the trade-in fee, which determines the volume of trade-ins. The customers buy the new units, use them through the period, and choose to trade-in these used units for new ones towards the end of period 1. On the other hand, if the supply is disrupted, the firm cannot produce new units during this period. Consequently, there will be no new items for customers to buy during the period and trade-in at the end of the period.

Period 2: If there is no supply disruption during this period the firm produces new units, along with the refurbished ones that are obtained by carefully utilizing the trade-in inventory collected in period 1. The firm decides the prices of new and refurbished units along with trade-in fee for period 2. The customers choose between new and refurbished units, and those who purchase the new ones use them through the period, and could potentially trade them in towards the end of period 2. However, if the supply is disrupted during period 2 the firm cannot produce new units but could refurbish the trade-ins collected in period 1. Consequently, the firm only decides the price of refurbished units.

Figures 1 and 2 in Section 3 provide the states and the firm’s decisions in each period in greater detail. Following are some key findings of our analysis:

1. As the risk of supply disruption increases, increasing product reusability can be advantageous up to a certain extent. However, when the risk of supply disruption increases beyond this threshold, increasing product reusability hurts the firm’s profits due to elevated design costs and diminished revenues.

2. When consumers’ value for refurbished units is low, the firm always accepts trade-ins and adopts a threshold based refurbishment policy. That is, the firm does not refurbish when the reusability level is low, increasingly refurbishes the trade-ins as reusability increases, and refurbishes all trade-ins when reusability is sufficiently high.

3. On the other hand, when consumers’ value for refurbished units is high, the firm accepts trade-ins if the reusability level is sufficiently high (i.e., above a threshold). Next, the firm refurbishes all the trade-ins in period 2 if the risk of supply disruption is low. On the other hand, if the risk is high, the firm adopts a threshold policy similar to 2 above in the absence of supply disruption, but refurbish all trade-ins during supply disruption.

4. The cost saving in refurbishment due to product reusability enables the firm to encourage trade-ins and offer refurbished units at reduced prices. Thus, firm can promote value retention in alignment with the United Nations’ sustainability goal of “Responsible Consumption and Production.”

Figure 1.

Possible outcomes in different periods $t=0,1,2$ in the three-period horizon.

Figure 2.

Sequence of events and decisions.

This article is organized as follows. In Section 2, we discuss the literature related to our work. In Section 3, we present the model preliminaries capturing the consumer-behavior and the firm’s operational context. In Section 4, we develop and formulate the model that captures the firm’s production, refurbishment, and pricing activities. In Section 5, by assuming that the firm accepts trade-ins that are at most one-period old, we draw insights on firm’s optimal trade-in policy, optimal pricing of new and refurbished units, trade-in fee, and product-design choice in terms of reusability level. In Section 6, we analyze and discuss the impacts of risk of supply disruption and production cost on the firm’s choice of reusability level. Then, in Section 7, we relax the restriction on the age of trade-ins and extend our model to draw additional insights. In the concluding Section 8, we summarize our work and suggest directions for future research. We provide auxiliary results in Appendix. Auxiliary Results and the proofs of all our results in the electronic companion.

2. Literature Review

This article resides at the intersection of two research domains: “closed loop supply chains” (CLSC) and “supply disruption.” CLSC can be defined as “the strategic management of a system aimed at maximizing value creation throughout a product’s life cycle, including the dynamic recovery of value from various types and volumes of returns over time” (Guide and Van Wassenhove, 2009). To structure the literature review, we adopt the five-phase framework proposed by Guide and Van Wassenhove (2009). Our study aligns with phases four and five of this framework. Phase four addresses CLSC issues such as product design decisions throughout the entire product life cycle, encompassing both forward and reverse logistics. Phase five deals with market dynamics, such as cannibalization between new and refurbished units, and product valuation, including prices of remanufactured/refurbished products. Given that our paper focuses on a firm’s decisions regarding product design (for reusability) and pricing, we examine existing CLSC literature that addresses these topics.

We introduce Table 1 to summarize significant studies within phases four and five of the CLSC domain, highlighting the context of our work. Table 1 underscores that existing CLSC literature has not explicitly addressed the joint decisions concerning product design and pricing in the presence of supply disruption along three primary dimensions:

product’s ease of reusability for refurbishment,

pricing mechanism of new and refurbished units depending on the risk of supply disruption, and

trade-in fee to regulate trade-in inventory and its usage.

Table 1.

Positioning our research in the extant CLSC literature (analytical studies).

Paper	CLSC setting	SD	PM	RPP	TF
Guide et al. (2003)	Remanufacturing	N	N	N	N
Mukhopadhyay and Setoputro (2005)	Recycling	N	Y	N	N
Ray et al. (2005)	Remanufacturing	N	N	Y	Y
Ferrer and Swaminathan (2006)	Remanufacturing	N	N	Y	N
Vorasayan and Ryan (2006)	Refurbishing	N	N	Y	N
Geyer et al. (2007)	Remanufacturing	N	N	N	N
Zikopoulos and Tagaras (2007)	Refurbishing	N	N	N	N
Wu (2012)	Remanufacturing	N	Y	Y	N
Subramanian et al. (2013)	Refurbishing	N	Y	N	N
Wang et al. (2017)	Remanufacturing	N	N	Y	N
Raz and Souza (2018)	Recycling	N	N	N	N
Alev et al. (2020)	Recycling	N	N	N	N
Borenich et al. (2020)	Refurbishing	N	N	Y	Y
Gui (2020)	Recycling	N	Y	N	N
Agrawal et al. (2021)	Leasing	N	Y	N	N
Rahmani et al. (2021)	Recycling	N	Y	N	N
Liu et al. (2022)	Remanufacturing	N	N	Y	N
Hu et al. (2023)	Refurbishing	N	N	N	Y
Gao et al. (2023)	Remanufacturing	N	N	N	N
Huang et al. (2023)	Refurbishing	N	N	Y	Y
Wang et al. (2024)	Remanufacturing	N	N	Y	N
Our study	Refurbishing	Y	Y	Y	Y

CLSC = closed loop supply chains; SD = supply disruption; PM = product modularity; RPP = refurbished/remanufactured product price; TF = trade-in fee.

We now review the key studies within the CLSC domain that align with the three primary dimensions outlined above. The underlying assumption on product design in the CLSC literature is that well-crafted products can enable firms to maximize the value extracted from returned units. Mukhopadhyay and Setoputro (2005) examined the value of product modularity for firms implementing return policies for build-to-order products, weighing the trade-off between modularity costs and the salvage value of returned and recycled products. Similarly, Wu (2012) explores the role of product disassemblability in reducing remanufacturing costs, although incurring some upfront fixed costs. Subramanian et al. (2013) assessed the value of component commonality (CC) in a refurbishing setting within a multi-product context, examining the trade-off between higher production costs for low-end products and lower refurbishment costs for high-end products. Recent contributions by Gui (2020) and Rahmani et al. (2021) further investigated the impact of product design in recycling contexts.

In the context of refurbishment operations, pricing decisions regarding refurbished products vis-à-vis new products emerge as a critical factor for firms. Several studies within the CLSC literature analyze optimal pricing strategies for refurbished or remanufactured products (Borenich et al., 2020; Ferrer and Swaminathan, 2006; Huang et al., 2023; Liu et al., 2022; Ray et al., 2005; Vorasayan and Ryan, 2006; Wang et al., 2017; Wu, 2012). In their recent work, Wang et al. (2024) analyzed the social planner’s practice of levying fee on producer or consumer in the context of remanufacturing setting.

Product return is a fundamental aspect of problem settings considered in various CLSC studies (Ferrer and Swaminathan, 2006; Geyer et al., 2007; Guide et al., 2003; Vorasayan and Ryan, 2006). However, managing product design alongside trade-ins during supply disruptions is not the primary focus of most papers in the CLSC literature. Some studies (Wang et al., 2017; Zikopoulos and Tagaras, 2007) have examined the impact of the quality of returned units on a firm’s reuse practices. Similarly, a few studies have explored the role of trade-in fees in a firm’s reuse operations. Borenich et al. (2020) studied the impact of unit refund offered by a manufacturer to the retailer in lieu of providing the used units on the manufacturer’s refurbishing operations. However, the authors do not consider the unit refund as a decision variable. Conversely, Ray et al. (2005) and Hu et al. (2023) considered settings where firms optimally determine trade-in fees while managing reuse operations. In their recent work, Huang et al. (2023) explored the impact of certified pre-owned (CPO) programs on market efficiency, with trade-in discounts playing a pivotal role in the effective utilization of such programs.

It is important to note that none of the above mentioned papers in the CLSC literature have analyzed product-reusability design decisions in the presence of supply disruption, which is the topic of this article. We also consider refurbished product price and trade-in fees decisions.

Finally, without getting into specifics of supply uncertainty literature, we establish the context of supply disruption as adopted in our article. In the literature, uncertainty is categorized into two main types: (1) yield uncertainty and (2) supply disruption. For an extensive review of the literature on yield uncertainty and supply disruption, readers are directed to Fang and Shou (2015) and Kumar et al. (2018), respectively. Yield uncertainty pertains to instances where the supply is not entirely halted, yet the quantity supplied remains uncertain (Chintapalli, 2021; Dada et al., 2007). Conversely, supply disruption involves a supplier either fulfilling the entire order in the absence of disruption or providing nothing in the event of a disruption (He et al., 2020; Kumar et al., 2018; Tomlin, 2006). Out of these two types of supply uncertainties, our article focuses on the latter type, which typically carries a low occurrence probability but entails significant adverse effects when they do occur (Kleindorfer and Saad, 2005; Sheffi and Rice, 2005).

3. Model Preliminaries and Consumer Behavior

In this section, we introduce the basics of our analytical model, laying the groundwork for formulating the firm’s problem and analyzing its decisions. We adopt a three-period model indexed as 0, 1, and 2, commonly utilized in durable product contexts (Desai and Purohit, 1998, 1999).

In period 0, the firm designs its product by determining its reusability level ( $\varphi \in [0,1]$ ). Given a unit production cost $c$ , the refurbishment cost for a product with reusability $\varphi$ is $c\cdot (1-\varphi )$ . Thus, higher reusability reduces refurbishment costs. Additionally, designing product reusability incurs a cost of $t{\varphi }^2$ , with $t>0$ , before production and sale in subsequent periods.

In period 1, the firm can manufacture new units if there is no supply disruption (i.e., the period’s state is $N$ ) and cannot manufacture any if there is a disruption (i.e., the state is $D$ ). Disruption probability $\beta$ and conditional disruption probability $\alpha$ account for the risk of supply disruption (see Table 2). In state $N$ , the consumers purchase the manufactured new units and can choose to trade their used units in for new ones towards the end of period 1. However, if the period’s state is $D$ , consumers cannot trade-in any units at the end of period 1 as they will not have purchased any new units during the period, due to the absence of production. Therefore, in period 1, the firm decides the price of new units and the trade-in fee when the state is $N$ . Instead, if the state during the period is $D$ , there is nothing for the firm to decide during the period.

Table 2.

Summary of notation.

Variable	Definition
$N$	State of normal supply
$D$	State of disrupted supply
$V$	Consumer’s value for a new unit
$k\cdot V$	Consumer’s value for a refurbished or old unit; $k\in [0,1)$
$p_i$	Price of new unit in period $i=1,2$
$v_i$	Trade-in fee in period $i=1,2$ .
$y_i\equiv p_i-v_i$	Trade-in price in period $i=1,2$
$p_N,p_D$	Prices of refurbished units during period 2, in states $N$ and $D$ , respectively
$c$	Unit-cost of manufacturing a new unit.
$t$	Product-design cost factor (i.e., cost of designing reusability in product)
$\varphi$	Product-reusability level
$\beta$	Probability of supply disruption occurring in a period.
$\alpha$	Conditional probability of disruption given the previous period was in disruption
${\xi }_i$	Demand for new units (only in state $N$ ) in period $i=1,2$
${\xi }_N$ , ${\xi }_D$	Demand for refurbished units in second period for states $N$ and $D$ , respectively
${\xi }_{t,i}$	Number of traded-ins in period $i=1,2$
$I_i$	Initial trade-in inventory in period $i=1,2$
$f^{(z_1,\dots ,z_n)}$	= ${\mathrm{\partial }}^{n}f/\mathrm{\partial }{z}_1,\dots ,\mathrm{\partial }{z}_n$
$z^{+}$	= $max\{0,z\}$

Next, in period 2, the firm can continue to produce new units if the period’s state is $N$ , along with refurbishing some of the trade-in inventory collected in period 1 (see Figure 1). Hence, the firm decides the prices of new and refurbished units along with the trade-in fee when period 2’s state is $N$ (see Figure 2). Here, it is important to note that the firm can potentially accept trade-ins during period 2 if it is profitable to sell new units to the customers trading in their used units. However, if period 2’s state is $D$ , then the firm cannot produce any new units and can only choose to refurbish the trade-in inventory carried over from period 1. Hence, the firm decides only the price of refurbished units (we assume that the firm does not entertain trade-ins of refurbished units). We illustrate the three-period horizon with the possible states and feasible actions in Figure 1 and provide the sequence of events and the firm’s decisions in Figure 2.

Allowing for supply disruptions in period 1 introduces uncertainty regarding the availability of trade-ins that could be refurbished in period 2. Our interviews highlighted that managers often overlooked this critical aspects, which could substantially influence the effectiveness of using trade-ins to counter supply disruptions. Moreover, a potential supply disruption in period 2 further increases the firm’s reliance on refurbishing these trade-ins to meet demand during that period.

Let $p_i$ and $v_i$ , $i=1,2$ , represent the prices of new units and trade-in fees in period $i$ . As refurbished units are obtained from previous trade-ins, they are unavailable for sale in period 1. Thus, the firm’s decision on refurbished unit pricing occurs only in period 2. Denote the prices of refurbished units in period 2 as $p_N$ and $p_D$ for states $N$ and $D$ , respectively. For simplicity, we assume the salvage value of the unused trade-ins is $0$ . See Table 2 for a summary of notation.

3.1. Consumer-Choice and Product Demand

In examining consumer behavior, we consider their decisions to: (i) buy the product, (ii) choose between new and refurbished units, and (iii) trade-in their used units. Let $V$ represent a consumer’s valuation of a new unit. We assume consumer valuations are uniformly distributed between $0$ and $1$ (i.e., $V\sim U[0,1]$ ). Additionally, let $k\cdot V$ , where $k\in [0,1)$ , denote the valuation of a refurbished (or used) unit. In period 1, a consumer purchases a new unit priced at $p_1$ if and only if $V⩾p_1$ . Thus, demand for the product in period 1 is given by the following equation:

$${\xi }_1(p_1)=1-p_1.$$

(1)

In period 2, when the state is $N$ , consumers choose between new and refurbished units. A consumer selects a new unit if $V-p_2⩾[kV-p_N{]}^{+}$ , and a refurbished unit if $kV-p_N⩾[V-p_2{]}^{+}$ . However, when the state in period 2 is $D$ , only refurbished units are available at price $p_D$ , and a consumer purchases one if and only if $kV⩾p_D$ . Thus, the demands for refurbished units in period 2 for states $N$ and $D$ are:

$$\begin{array}{rl}{\xi }_N(p_2,p_N)& =\mathbb{P}(kV-p_N⩾[V-p_2{]}^{+})\\ & =\mathbb{P}(\frac{p_N}{k}⩽V⩽\frac{p_2-p_N}{1-k})=\frac{[k{p}_2-p_N]}{k(1-k)},\end{array}$$

(2)

and

$$\begin{array}{rl}{\xi }_D(p_D)& =\mathbb{P}(kV⩾p_D)=[1-\frac{p_D}{k}],\text{ respectively.}\end{array}$$

(3)

Likewise, the demand for new units during period 2 in state $N$ is given by the following equation:

$$\begin{array}{rl}{\xi }_2(p_2,p_N)& =\mathbb{P}(V-p_2⩾[kV-p_N{]}^{+})\\ & =1-max\{p_2,\frac{p_2-p_N}{1-k}\}.\end{array}$$

(4)

Next, a consumer who previously bought a new unit will opt to trade it in after using it for one period if they value their used unit less than the trade-in value, that is, $kV⩽V+v_1-p_1$ . For simplicity, let $y_i=p_i-v_i$ , $i=1,2$ , denote the net price of a trade-in, or the “trade-in price.” We assume that:

Assumption 1 (Trade-in Behavior)

The firm encourages trade-ins within one period of purchase. Consumers only trade in their used unit upon acquiring a new unit; otherwise, they retain their used unit.

In practice, firms often restrict the age of trade-ins they accept to ensure that these units are not overused and they have sufficient residual value for refurbishment. Thus, the above assumption is non-restrictive when we model product sales over a two-period horizon. We relax this assumption later in Section 7.

Therefore, by using Assumption 1, the number of trade-ins in periods 1 and 2 are:

$$\begin{array}{rl}{\xi }_{t,1}(y_1)& =\mathbb{P}(V⩾p_1,V-y_1⩾kV)\\ & =1-max\{p_1,\frac{y_1}{1-k}\},\end{array}$$

(5)

and

$$\begin{array}{rl}{\xi }_{t,2}(y_2)& =\mathbb{P}(V⩾max\{p_2,\frac{p_2-p_N}{1-k}\},V-y_2⩾kV)\\ & =1-max\{p_2,\frac{p_2-p_N}{1-k},\frac{y_2}{1-k}\},\mathrm{respectively}.\end{array}$$

(6)

4. Model Formulation

In this section, we calculate the firm’s profits for each period and derive the total profit over the three-period horizon. We then determine the optimal pricing and inventory strategies for periods 1 and 2, considering states $N$ and $D$ , to maximize the total profit starting from period 0, given any reusability level $\varphi$ . Subsequently, we analyze this total profit to identify the optimal reusability level ${\varphi }^{*}$ .

4.1. Profits and Decisions in Period 2

First, we examine the case where the state is $N$ (no supply disruption) in period 2. The firm’s profit in this state, with an initial on-hand inventory $I_2$ of trade-in units, is:

$$\begin{array}{rl}{g}_2^N(p_2,p_N,y_2;I_2,\varphi )& =(p_2-c)\cdot {\xi }_2(p_2,p_N)\\ & +(p_N-c(1-\varphi ))\cdot {\xi }_N(p_2,p_N)\\ & +(y_2-c)\cdot {\xi }_{t,2}(y_2).\end{array}$$

(7)

The first term represents profit from sales of new units during the period, with a unit margin of $(p_2-c)$ and total demand ${\xi }_2(p_2,p_N)$ . The second term is profit from refurbished-unit sales, with a unit margin of $(p_N-c(1-\varphi ))$ and demand ${\xi }_N(p_2,p_N)$ . The last term represents profit from trade-ins, with a net margin per unit of $(y_2-c)$ . As mentioned earlier, the salvage value of unused trade-ins is 0. The firm maximizes the profit in (10) in period 2 when the state is $N$ . Additionally, the firm should satisfy the following constraints when maximizing its profit:

1. Non-negative demand: The demand for refurbished units given in (3) is non-negative:

   $${\xi }_N(p_2,p_N)⩾0\iff k{p}_2⩾p_N.$$

   (8)
   By using (11), the demand for new units given in (5) can be rewritten as follows:
   $${\xi }_2(p_2,p_N)=1-\frac{p_2-p_N}{1-k}.$$

   (9)

2. Trade-in feasibility: The number of trade-ins cannot exceed the number of new units sold earlier in that period. Therefore, in period 2 we require:

   $${\xi }_{t,2}(y_2)⩽{\xi }_2(p_2,p_N)\iff y_2⩾p_2-p_N.$$

   (10)

3. Non-negative trade-ins: The number of trade-ins ${\xi }_{t,2}(y_2)$ is non-negative. Since, as per (8) and (10), ${\xi }_{t,2}(y_2)=0$ whenever $y_2⩾(1-k)$ , the following is true in period 2:

   $${\xi }_{t,2}(y_2)⩾0\iff y_2⩽1-k.$$

   (11)
   Thus, using (8), (10), and (11), we can rewrite the number of trade-ins given in (6) as follows:
   $${\xi }_{t,2}(y_2)=1-\frac{y_2}{1-k}.$$

   (12)
   Note that when $y_2⩾1-k$ , it is evident that the profit in (7) becomes independent of $y_2$ . Thus, it suffices to analyze the case $y_2⩽1-k$ to determine the optimal value of $y_2$ .

4. Refurbishment feasibility: The total number of refurbished units sold cannot exceed the initial inventory of trade-ins in a period. Thus, utilizing (8), we need:

   $${\xi }_N(p_2,p_N)⩽I_2\iff \frac{k{p}_2-p_N}{k(1-k)}⩽I_2.$$

   (13)

Finally, by substituting the demands and trade-ins from (2), (9), and (12) in the firm’s profit (7), the firm’s optimization problem during period 2 in state $N$ is given as follows:

$$\begin{array}{rl}{\pi }_2^N(I_2,\varphi )& =\underset{p_2,p_N,y_2}{max}\{g_2^N(p_2,p_N,y_2;I_2,\varphi )\}\\ & \mathrm{s}.\mathrm{t}.(8),(10),(11),(13).\end{array}$$

(14)

Similarly, the profit when state $D$ is realized in period 2 is

$$g_2^D(p_D;I_2,\varphi )=(p_D-c(1-\varphi ))\cdot {\xi }_D(p_D),$$

(15)

since only refurbished units are sold in state $D$ , in period 2, with no new units sold and no trade-ins accepted. Furthermore, since the total number of refurbished units sold is at most the trade-in inventory carried from period 1, we require:

$${\xi }_D(p_D)⩽I_2\iff 1-\frac{p_D}{k}⩽I_2.$$

(16)

Hence, the firm’s problem in period 2 under state $D$ with an initial inventory of $I_2$ is

$${\pi }_2^D(I_2,\varphi )=\underset{p_D}{max}\{g_2^D(p_D;I_2,\varphi )\}\mathrm{s}.\mathrm{t}.(16).$$

(17)

Now that we have finished formulating period 2, we will move on to formulate the firm’s problem for period 1 in the next subsection.

4.2. Profits and Decisions in Period 1

First, we derive the firm’s profit under state $N$ during period 1. Since the firm can only produce and sell new units and accept trade-ins of these purchased units during the period, its profit is

$$g_1^N(p_1,y_1;\varphi )=(p_1-c)\cdot {\xi }_1(p_1)+(y_1-c)\cdot {\xi }_{t,1}(y_1),$$

(18)

where ${\xi }_1(p_1)$ and ${\xi }_{t,1}(y_1)$ are defined in (1) and (5), respectively. Furthermore, to ensure that the number of trade-ins in period 1 is lower than the number of new units sold earlier in the period, we need

$${\xi }_{t,1}(y_1)⩽{\xi }_1(p_1)\iff y_1⩾(1-k)p_1.$$

(19)

Thus, the firm’s profit over periods 1 and 2 under state $N$ in period 1 is

$$\begin{array}{rl}{V}_1^N(p_1,y_1;\varphi )& =g_1^N(p_1,y_1;\varphi )+\beta \cdot {\pi }_2^D({\xi }_{t,1}(y_1),\varphi )\\ & +(1-\beta )\cdot {\pi }_2^N({\xi }_{t,1}(y_1),\varphi ).\end{array}$$

(20)

Therefore, the firm’s optimization problem in period 1 is

$${\pi }_1^N(\varphi )=\underset{p_1,y_1}{max}{V}_1^N(p_1,y_1;\varphi )\mathrm{s}.\mathrm{t}.(19).$$

(21)

Similarly, the profit in state $D$ in period 1 is

$${\pi }_1^D=(1-\alpha )[{\left(\frac{1-c}{2}\right)}^2+\left(\frac{1}{1-k}\right){\left(\frac{1-k-c}{2}\right)}^2].$$

(22)

In state $D$ , the firm cannot earn profit during period 1 due to supply disruption. However, in period 2, it can earn profit by selling new units and accepting trade-ins with a probability of $(1-\alpha )$ . Thus, the total expected profit across periods 1 and 2, given state $D$ in period 1, is as in (22). Since there is no benefit of reusability level $\varphi$ in period 2, when there is supply disruption in period 1, the profit ${\pi }_1^D$ is independent of $\varphi$ . Next, we backtrack to formulate the problem in period 0.

4.3. Profit and Product-Design Decision in Period 0

The total profit in period 0, considering the probability of disruption as $\beta$ and accounting for the cost of product design, is given by the following equation:

$$V_0(\varphi )=(1-\beta )\cdot {\pi }_1^N(\varphi )+\beta \cdot {\pi }_1^D-t{\varphi }^2.$$

(23)

The firm selects the product reusability ${\varphi }^{*}$ that maximizes the above expected total profit over the three-period horizon.

In the subsequent section, we analyze the firm’s problem described above and determine: (i) optimal pricing and trade-in decisions, (ii) inventory-carryover and refurbishment policies, and (iii) the optimal reusability level ${\varphi }^{*}$ .

5. Model Analysis

To solve (14), we formulate the following Lagrangian by relaxing (8), (10), and (13):

$$\begin{array}{rl}& {\mathcal{L}}_2^N(p_2,p_N,y_2,{\lambda }_1,{\lambda }_2,{\lambda }_3;I_2,\varphi )=g_2^N(p_2,p_N,y_2)\\ & +{\lambda }_1[k{p}_2-p_N]+{\lambda }_2[y_2-(p_2-p_N)]+{\lambda }_3[I_2-\frac{k{p}_2-p_N}{k(1-k)}].\end{array}$$

(24)

Likewise, to solve (17), we form the following Lagrangian:

$${\mathcal{L}}_2^D(p_D,\mu ;I_2,\varphi )=g_2^D(p_D)+\mu [I_2-(1-\frac{p_D}{k})].$$

(25)

In our analysis, we consider two cases that influence both consumers’ and firm’s behaviors:

• Case 1 ( $c+k⩽1$ ): The consumers’ value of used unit is low, that is, $k⩽1-c$ .

• Case 2 ( $c+k>1$ ): The consumers’ value of used unit is high, that is, $k>1-c$ .

We address each of the above cases separately.

5.1. Case 1: Value of Used Units Is Low ( $k⩽1-c$ )

By solving the Lagrangian (24), we obtain the following firm’s decisions for prices $p_2$ and $p_N$ of new and refurbished units, and the trade-in price $y_2$ during period 2 in state $N$ :

Lemma 1 (Period 2 Decisions in State $N$ )

When $k⩽1-c$ , the firm sets the price of new units as $p_2^{*}=(1+c)/2$ and the trade-in price as $y_2^{*}=(1+c-k)/2$ . However, the price of refurbished units depends on the reusability $\varphi$ and the initial inventory $I_2$ :

$$\begin{array}{r}{p}_N^{*}=\{\begin{array}{ll}{\displaystyle \frac{k(1+c)}{2}}& \text{if }\varphi ⩽1-k,\\ {\displaystyle \frac{c(1-\varphi )+k}{2}}& \text{if }(1-k)<\varphi ⩽(1-k)[1+{\displaystyle \frac{2k{I}_2}{c}}],\text{ and}\\ {\displaystyle \frac{k(1+c)}{2}}-k(1-k)I_2& \text{if }(1-k)[1+{\displaystyle \frac{2k{I}_2}{c}}]<\varphi ⩽1.\end{array}\end{array}$$

(26)

The firm chooses to refurbish if, and only if, $\varphi >1-k$ (i.e., reusability is sufficiently high).

The refurbished-unit price $p_N^{*}$ depends on $\varphi$ and $I_2$ (as in equation (26)). If $\varphi$ is low (i.e., $\varphi <1-k$ ), indicating a high refurbishment cost $c(1-\varphi )$ , the firm does not refurbish any units. For moderate $\varphi$ , the firm sets a lower price for refurbished units to increase their sales. For high $\varphi$ , the firm further decreases the refurbished-unit price due to lower refurbishment cost and refurbishes all past trade-ins $I_2$ . Thus, the firm increasingly refurbishes more trade-ins and progressively decreases the price of refurbished units as the product’s reusability level increases (as evident from (26)). Moreover, in this scenario, it benefits the firm to choose a higher price $p_2^{*}=(1+c)/2$ for new units while charging a slightly lower price $p_N^{*}=k(1+c)/2-k(1-k)I_2$ for refurbished ones, as described in Lemma 1. Certainly, the total number of new units sold ( ${\xi }_2(p_2^{*},p_N^{*})$ by using (9)) is lower when the trade-in inventory $I_2$ is higher, due to cannibalization. Next, in the following result, we address the firm’s decisions in state $D$ during period 2:

Lemma 2 (Period 2 Decisions in State $D$ )

Suppose the consumers’ value for refurbished units is low (i.e., $k⩽1-c$ ). The optimal price of refurbished units when supply is disrupted (i.e., state $D$ ) during period 2 and the initial trade-in inventory is $I_2$ is as follows:

$$p_D^{*}=\{\begin{array}{ll}{\displaystyle \frac{c(1-\varphi )+k}{2}}& \text{if }\varphi ⩽1-{\displaystyle \frac{k(1-2I_2)}{c}},\text{ and}\\ k(1-I_2)& \text{otherwise.}\end{array}$$

(27)

The firm exhausts the total initial trade-in inventory $I_2$ if $\varphi$ is high (i.e., $\varphi ⩾1-\frac{k(1-2I_2)}{c}$ ). It is easy to verify from Lemmas 1 and 2 that the firm sets a lower refurbished-unit price when the initial trade-in inventory $I_2$ is high (i.e., $p_D^{*(I_2)}⩽0$ ), as expected. Additionally, we can conclude:

Corollary 1

The firm never refurbishes (in both $N$ and $D$ states) when $\varphi ⩽1-\frac{k}{c}$ .

After solving period 2, we backtrack to solve the problem (21) in period 1 under state $N$ .

5.1.1. Trade-in Inventory and Refurbishment Policies

The firm’s trade-in inventory policy in period 1 under state $N$ is as follows:

Lemma 3 (Trade-in and Refurbishment)

In period 1, if the state is $N$ and $k⩽(1-c)$ , the firm’s trade-in inventory and refurbishment policies for any reusability level $\varphi$ are as follows:

Firm always accepts trade-ins during period 1.

If the state in period 2 is $D$ , then the firm will:

not refurbish if $\varphi ⩽1-\frac{k}{c}$ ,

refurbishes some of the trade-in inventory $I_2$ if $\varphi \in [1-\frac{k}{c},\frac{1-2k}{1-k}]$ , and

refurbishes all traded-in units (i.e., all $I_2$ ) if $\varphi ⩾\frac{1-2k}{1-k}$ .

On the other hand, if the state in period 2 is $N$ , the firm will:

not refurbish if $\varphi ⩽1-k$ ,

refurbishes some of $I_2$ if $\varphi \in [1-k,{\varphi }_{\lambda }(\beta )]$ , where ${\varphi }_{\lambda }(\beta )=\frac{(1-k)[c(1-k)+k(1-c)-k^2(1-\beta )]}{c[1-k(1-k\beta )]}$ , and

refurbishes all $I_2$ if $\varphi ⩾{\varphi }_{\lambda }(\beta )$ .

Lemma 3 states that the firm accepts trade-ins in period 1 when the state is $N$ , capitalizing on consumers’ increased inclination to trade in due to lower valuations of old units ( $k⩽1-c$ ). This strategy helps mitigate potential supply disruptions thereby boosting sales in period 2 in the event of supply disruption, because the firm can sell refurbished units although it cannot produce new units during period 2.

The firm employs a strategic threshold policy for refurbishing trade-in inventory during both states $N$ and $D$ in period 2. In state $D$ , the firm refrains from refurbishing when reusability is low ( $\varphi ⩽1-\frac{k}{c}$ ), as refurbishment costs exceed refurbished-unit price $p_D^{*}$ , which is given in (27). However, at moderate reusability levels ( $\varphi \in [1-\frac{k}{c},\frac{1-2k}{1-k}]$ ), the firm profits from refurbishment-unit sales. When reusability is sufficiently high ( $\varphi ⩾\frac{1-2k}{1-k}$ ), the firm consumes all trade-in inventory for refurbishment.

Similarly, in state $N$ , the firm strategically refrains from refurbishing, although it collects trade-ins in period 1, if $\varphi <(1-k)$ to avoid high refurbishment costs and protect its profits earned from new unit sales. However, with higher $\varphi$ , refurbishment becomes increasingly profitable. If $\varphi$ is sufficiently high ( $\varphi >{\varphi }_{\lambda }(\beta )$ ), the firm refurbishes all the trade-in inventory. Comparing statements 2(a) and 3(a) of Lemma 3, the firm refurbishes trade-ins in state $D$ but not in $N$ when $1-\frac{k}{c}⩽\varphi ⩽1-k$ , indicating a stronger inclination to refurbish in state $D$ .

Note that earlier in Lemmas 1 and 2 we obtained the firm’s optimal decisions for any given trade-in inventory $I_2$ in period 2. Next, in Lemma 3 we described (i) the firm’s trade-in inventory policy in period 1 that determines $I_2$ and (ii) its refurbishment policy in period 2 for the determined $I_2$ . Now, in Lemma 4, we obtain the firm’s optimal decisions $p_1^{*}$ and $y_1^{*}$ in period 1, and we later simplify $p_N^{*}$ and $p_D^{*}$ of period 2 by substituting the optimal trade-in inventory level $I_2={\xi }_{t,1}(y_1^{*})$ in (26) and (27), respectively.

Lemma 4 (Optimal Decisions in Periods 1 and 2)

Let ${\varphi }_{\lambda }(\beta )$ be as defined in Lemma 3, and $k⩽1-c$ . The firm’s pricing decisions in periods 1 and 2 are as follows:

Period 1 decisions: If the state is $N$ , the firm sets the new-unit price at $p_1^{*}=(1+c)/2$ . The trade-in price $y_1^{*}$ depends on the reusability level $\varphi$ as follows: ²

$y_1^{*}=y_{1,low\varphi }^{*}\equiv \frac{1+c-k}{2}$ for $\varphi \in [0,\frac{1-2k}{1-k}]$ ,

$y_1^{*}=y_{1,med\varphi }^{*}\equiv y_{1,low\varphi }^{*}-\left[\frac{c\beta (1-k)}{2(1-k(1-\beta ))}\right][\varphi -\frac{1-2k}{1-k}]$ for $\varphi \in [\frac{1-2k}{1-k},{\varphi }_{\lambda }(\beta )]$ , and

$y_1^{*}=y_{1,high\varphi }^{*}\equiv y_{1,med\varphi }^{*}-\left[\frac{c(1-k)(1-\beta )(1-k(1-k\beta ))}{2(1-k(1-\beta ))(1-k^2(1-\beta ))}\right][\varphi -{\varphi }_{\lambda }(\beta )]$ for $\varphi \in [{\varphi }_{\lambda }(\beta ),1]$ .

Period 2 decisions: The firm sets the optimal new-unit price $p_2^{*}=(1+c)/2$ and the trade-in price $y_2^{*}=(1+c-k)/2$ . The refurbished-unit prices are:

in state $N$ :

$$p_N^{*}=\{\begin{array}{ll}k\left({\displaystyle \frac{1+c}{2}}\right)& \text{if }\varphi ⩽1-k,\\ {\displaystyle \frac{c(1-\varphi )+k}{2}}& \text{if }1-k<\varphi ⩽{\varphi }_{\lambda }(\beta ),\text{ and}\\ {\displaystyle \frac{k[2k(1-[k(1-\beta )+\left(\frac{1-c}{2}\right)\beta ])+c(1-k)(3-\varphi )]}{2[1-k^2(1-\beta )]}}& \text{if }{\varphi }_{\lambda }(\beta )<\varphi ⩽1;and\end{array}$$

(28)

in state $D$ :

$$p_D^{*}=\{\begin{array}{ll}k& \text{if }\varphi ⩽1-{\displaystyle \frac{k}{c}},\\ {\displaystyle \frac{c(1-\varphi )+k}{2}}& \text{if }1-{\displaystyle \frac{k}{c}}<\varphi ⩽{\displaystyle \frac{1-2k}{1-k}},\\ {\displaystyle \frac{k(1-k(1-\beta )+c(1+\beta (1-\varphi )))}{2(1-(1-\beta )k)}}& \text{if }{\displaystyle \frac{1-2k}{1-k}}<\varphi ⩽{\varphi }_{\lambda }(\beta ),\\ {\displaystyle \frac{k[2k(1-[k(1-\beta )+\left(\frac{1-c}{2}\right)\beta ])+c(1-\varphi )+(1+c)(1-k)]}{2[1-k^2(1-\beta )]}}& \text{if }{\varphi }_{\lambda }(\beta )<\varphi ⩽1.\end{array}$$

(29)

Lemma 4 illustrates that the trade-in price $y_1^{*}$ in period 1 decreases as reusability level $\varphi$ increases. The reduction in refurbishment costs due to higher $\varphi$ allows the firm to offer a higher trade-in fee to its customers, leading to a lower trade-in price $y_1^{*}$ . These decisions align with the refurbishment policy outlined in Lemma 3. Specifically, when $\varphi$ is low, the firm prices refurbished units sufficiently high to discourage their purchase, and gradually lowers their price as the reusability level increases.

5.1.2. Optimal Reusability Level

In this section, we determine the optimal reusability choice for the firm’s product design by solving:

$${\pi }_0=\underset{\varphi \in [0,1]}{max}{V}_0(\varphi ),$$

(30)

where $V_0(\varphi )$ (from (23)) is the firm’s total profit-to-go in period 0. To define $V_0(\varphi )$ , we initially derive ${\pi }_1^N(\varphi )$ by substituting the optimal decisions from Lemma 4 into (20), as shown in (21). Then, by using ${\pi }_1^N(\varphi )$ and ${\pi }_1^D$ (from (22)) we obtain $V_0(\varphi )$ that is defined in (23).

The following result describes the structure of the firm’s profit $V_0(\varphi )$ :

Lemma 5

$V_0(\varphi )$ is a smooth continuous function. Therefore, the optimal reusability level is a stationary point, denoted as ${\varphi }^{*}$ , satisfying $V_0^{(\varphi )}({\varphi }^{*})=0$ and $V_0^{(\varphi ,\varphi )}({\varphi }^{*})<0$ .

Next, before examining the impact of the risk of supply disruption $\beta$ on the firm’s optimal choice of reusability ${\varphi }^{*}$ , we analyze the scenario when consumers value for used units is high ( $k>1-c$ ) in the subsequent section.

5.2. Case 2: Value of Used Units Is High ( $k>1-c$ )

In this section, we discuss the firm’s decisions during period 2 when the state is $N$ . From Lemma 1 in Section 5.1, it is evident that setting the trade-in price $y_2=(1+c-k)/2$ is infeasible due to (11). Therefore, the firm sets $y_2^{*}=1-k$ , dissuading consumers from trading in during period 2. By substituting $y_2=1-k$ into (24) and solving the problem, we obtain the optimal prices in periods 1 and 2. We provide the detailed result in Lemma 7 in Appendix. Auxiliary Results, and summarize the firm’s pricing and trade-in inventory policy below:

The firm discourages trade-ins during period 2 by setting $y_2=1-k$ , prompting consumers to opt out of trade-ins.

Let

$${\beta }_0\equiv \frac{c+k-1}{k(1-c)}.$$

(31)

If the risk of supply disruption is low (i.e., $0⩽\beta ⩽{\beta }_0$ ), the firm encourages trade-ins in period 1 if and only if reusability is sufficiently high (i.e., $\varphi >\widehat{{\varphi }_I}(\beta )$ ). ³ Moreover, all trade-ins are refurbished in period 2 in both $N$ and $D$ states.

On the other hand, when the risk is high (i.e., $\beta >{\beta }_0$ ), the firm encourages trade-ins in period 1 if and only if reusability is sufficiently high (i.e., $\varphi >{\varphi }_I(\beta )$ ). Additionally, all trade-ins are refurbished during supply disruptions (i.e., state $D$ ) in period 2. However, when there is no disruption (i.e., state $N$ ) in period 2 and $\beta >{\beta }_0$ , the firm’s refurbishment policy is as given in statement 3 in Lemma 3. That is,

do not refurbish if $\varphi ⩽(1-k)$ ,

refurbish some trade-ins if $(1-k)<\varphi <{\varphi }_{\lambda }(\beta )$ , and

refurbish all trade-ins if $\varphi ⩾{\varphi }_{\lambda }(\beta )$ .

When consumers’ value for used units is high (i.e., $k>1-c$ ), the firm needs to offer a higher trade-in fee in period 2 to encourage trade-ins, which reduces the unit margin from trade-ins. Hence, the firm discourages trade-ins during period 2. However, during period 1, the magnitude of the risk of supply disruption $\beta$ and reusability level $\varphi$ jointly influence the firm’s decisions. Trade-ins are encouraged only if reusability is sufficiently high to ensure sizable margins from refurbished units sold later (in period 2).

It is noteworthy that the optimal trade-in policy (formally discussed in Lemma 7 in Appendix. Auxiliary Results) ensures that the firm never accepts more trade-ins in period 1 than the number of refurbishments it plans during disruptions (state $D$ ) in period 2, because any additional trade-ins always remain unused without refurbishment (in both states $N$ and $D$ ) in period 2. Hence, by appropriately adjusting the trade-in fee $v_1$ during period 1, the firm can avoid overstocking trade-ins and boost profits.

Next, the greater the risk of supply disruption, the lower the reusability level at which the firm begins to encourage trade-ins. This is evident from the decreasing nature of $\widehat{{\varphi }_I}(\beta )$ and ${\varphi }_I(\beta )$ with respect to $\beta$ . Consequently, when the risk is higher, especially when $\beta >{\beta }_0$ , the firm refrains from refurbishing units in period 2 when there is no supply disruption (state $N$ ), unless product reusability is sufficiently high (i.e., $\varphi >1-k$ ). Thus, the firm’s traded-in inventory acts as a safety stock against supply disruption in period 2 under state $D$ , while remaining optional for use when there is no disruption (state $N$ ), contingent on the reusability level $\varphi$ . The following result describes the optimal reusability level ${\varphi }^{*}$ when $k>(1-c)$ :

Lemma 6

When used units are highly valued ( $k>1-c$ ):

For low risk ( $\beta ⩽{\beta }_0$ , where ${\beta }_0$ is defined in (31)), the firm abstains from trade-ins and refurbishment, choosing ${\varphi }^{*}=0$ .

With high risk ( $\beta >{\beta }_0$ ), ${\varphi }^{*}$ is a stationary point of $V_0(\varphi )$ satisfying $V_0^{\mathrm{″}}({\varphi }^{*})<0$ . ⁴

When consumers highly value used units ( $k>1-c$ ), offering a high trade-in fee to facilitate trade-ins can hurt the firm’s profits. Additionally, the trade-in inventory is less advantageous when the risk of supply disruption is low ( $\beta ⩽{\beta }_0$ ). Therefore, when $k>1-c$ and $\beta <{\beta }_0$ , the firm chooses not to accept trade-ins and refrains from investing in reusability ( ${\varphi }^{*}=0$ ), as it never refurbishes trade-ins.

However, when the risk of supply disruption is high ( $\beta >{\beta }_0$ ) and the design costs are affordable (i.e., $t<t_{[(1-k),{\varphi }_{\lambda }(\beta )]}\equiv \frac{c^2(1-\beta )(1-k-\beta +\beta k(2-\beta k))}{4(1-k)k(1-(1-\beta )k)}$ ), the firm encourages trade-ins in period 1 through a high trade-in fees to mitigate the impact of supply disruptions in period 2. The optimal choice of reusability when the risk of supply disruption $\beta >{\beta }_0$ is described in the second statement of Lemma 6.

Finally, we analyze the impact of the risk of supply disruption $\beta$ on the firm’s choice of reusability level ${\varphi }^{*}$ in the next section.

6. Impact of Risk of Supply Disruption and Production Cost on Reusability Choice

After establishing the optimal reusability level ${\varphi }^{*}$ , we explore the effects of two key factors: (i) risk of supply disruption $\beta$ , and (ii) production cost $c$ , which are crucial considerations for product design decisions. Later, we discuss the broader advantages of the firm’s reusability decision.

6.1. Impact of Risk of Supply Disruption

We now address the key question: “Does increasing product reusability benefit the firm as the risk of supply disruption rises?” This question gains relevance amid growing risk of supply disruptions in many supply chains and the widespread belief that more reusable products help tackle such disruption risks. Our answer is outlined in the following result:

Proposition 1

Reducing product-reusability ( ${\varphi }^{*}$ ) benefits the firm as the risk of supply disruption ( $\beta$ ) rises, when the risk is high (i.e., ${\varphi }^{*(\beta )}<0$ when $\beta$ is sufficiently high).

While the common belief suggests increasing a product’s reusability as the risk of supply disruption rises, Proposition 1 highlights that such a strategy is only advantageous when the risk is low. Conversely, when the disruption risk is notably high, the firm opts against designing more reusable products to save on design costs, as indicated in Proposition 1. This change in the firm’s reusability strategy is due to the increased likelihood of being unable to produce new units, which limits the availability of trade-ins, thus diluting the benefits of higher reusability through refurbishment. Consequently, the firm chooses to design a less reusable product to decrease its design costs.

6.2. Impact of Production Cost

In this section, we explore a numerical example and discuss additional managerial implications. Alongside the risk of supply disruption $\beta$ , firms also consider the production cost $c$ as a crucial factor when determining the reusability level ${\varphi }^{*}$ . With higher production costs, the refurbishment cost $c(1-\varphi )$ also rises for any reusability level $\varphi$ . One might assume that, as production cost increases, it is advisable to increase product reusability to contain refurbishment costs. To investigate this, we present optimal reusability levels for various production costs and the risks of supply disruption in Figure 3 (for the plots, we focus on the scenario when supply disruptions in periods 1 and 2 are identical and independent; i.e., $\mathrm{\alpha }=\beta$ ).

Figure 3.

Optimal reusability ${\varphi }^{*}$ for different production cost $c$ and risk of supply disruption $\beta$ values: (a) optimal reusability level ${\varphi }^{*}$ when $\beta ⩽0.6$ ; and (b) optimal reusability level ${\varphi }^{*}$ when $\beta ⩾0.7$ .

Both Figure 3(a) and (b) demonstrate that, for any given $\beta$ , the firm indeed increases ${\varphi }^{*}$ as $c$ rises, provided $c$ remains low below a threshold. This allows the firm to limit its refurbishment cost $c(1-{\varphi }^{*})$ despite the increase in $c$ . Conversely, when $c$ is higher than the threshold, it benefits the firm to reduce reusability ${\varphi }^{*}$ . The higher cost $c$ that leads to narrower margins prompts the firm to cut down on its design costs by reducing ${\varphi }^{*}$ . This trend in ${\varphi }^{*}$ with respect to $c$ holds true across different $\beta$ values. Furthermore, a higher risk $\beta$ that negatively impacts the firm’s revenues increases the need for lower refurbished costs. Hence, we observe in Figure 3 that the firm opts for ${\varphi }^{*}>0$ over a broader range of $c$ values as $\beta$ increases.

6.3. The Advantages of Reusability

In this section, we highlight how a firm’s choice of reusability can benefit both the firm and its consumers. First, Lemmas 4 and 7 (in Appendix. Auxiliary Results) demonstrate that a higher reusability level leads to lower trade-in prices during period 1 ( $y_1^{*(\varphi )}<0$ ). Thus, the firm shares the benefits of reduced refurbishment costs (due to higher product reusability) with its consumers who trade-in, offering them higher trade-in fees (or equivalently, lower trade-in price). Second, from equations (28) and (29), along with Lemma 7, we observe that the firm sets lower prices for its refurbished units when reusability is high ( $p_N^{*(\varphi )}<0$ and $p_D^{*(\varphi )}<0$ ), thus passing on the cost benefits of reusability to purchasers of refurbished units. Hence, the optimal reusability level ${\varphi }^{*}$ offers a three-way “Pareto-efficient” win for the firm, its trade-in customers, and purchasers of refurbished units. ⁵

Thus, for any given risk level $\beta$ , by encouraging trade-ins and offering refurbished units at reduced prices, the firm promotes value retention in alignment with the United Nations’ sustainability goal of “Responsible Consumption and Production.” This is achieved through the firm’s optimal product reusability level ${\varphi }^{*}$ in a Pareto-efficient manner.

Consequently, any activities like subsidizing or decreasing the firm’s design costs $t$ that increase reusability ${\varphi }^{*}$ are beneficial for all stakeholders involved. ⁶

7. Accepting Trade-ins Older Than One-Period

In this section, we analyze the case where the firm accepts trade-ins older than one period, thereby partially relaxing Assumption 1. However, we continue to assume that a consumer trades in their used unit only upon acquiring a new unit, as stated in the later portion of the assumption. Allowing to trade-in older units will provide more opportunities for the consumers to trade-in and for the firm to acquire used units over the product’s life.

To enable older trade-ins, we extend the base model in Section 4 by adding two new trade-in opportunities: one at the beginning and another at the end of period 2. We assume that a unit’s value diminishes to a fraction of $k\in (0,1)$ per period. So, for a unit that is purchased in period 1, its value at the start of period 2 is $k\cdot V$ (the same as at the end of period 1), and it drops to $k^2\cdot V$ at the end of period 2.

During period 2, owners can trade in at the beginning of the period after knowing the new trade-in price $y_2$ , or at the period’s end after retaining their used units through the period. Therefore, under the two additional trade-in opportunities in period 2, a rational consumer with valuation $V\in [0,1]$ finds it beneficial to trade in:

at the beginning of period 2 if and only if $kV<V-y_2\iff V>y_2/(1-k)$ , and

at the end of period 2 if and only if $k^{2}V<V-y_2\iff V>y_2/(1-k^2)$ .

Therefore, a consumer who finds it beneficial to trade in at the beginning of period 2 always finds it beneficial to do so at its end.

Furthermore, after accounting for the risk of supply disruption $\beta$ in period 2, the customers who purchase the product during period 1 ( $V>p_1$ ) will choose to trade in during period 1 at a net price $y_1$ if and only if

$$\begin{array}{rl}V-y_1& >\beta \cdot kV+(1-\beta )(V-y_2)\text{ and }\\ V-y_1& >\beta \cdot k^{2}V+(1-\beta )(V-y_2)\\ \iff V& >\frac{[y_1-(1-\beta )y_2{]}^{+}}{\beta (1-k)}.\end{array}$$

(32)

Next, we consider two cases: (i) the firm sets $y_1<y_2$ and (ii) the firm sets $y_1⩾y_2$ , and analyze each of these two cases.

Figure 4.

Trade-in behavior of period 1’s customers when the firm entertains trade-ins older than one period: (a) when $y_1<y_2$ ; and (b) when $y_1⩾y_2$ .

Firm sets higher trade-in price in period 2 ( $y_1<y_2$ ). Consider the customers who purchase the product during period 1 ( $V>p_1$ ), when its state is $N$ . The trade-in choices of these customers when the firm chooses a higher trade-in price during period 2 ( $y_2>y_1$ ) are as follows, which we also illustrated in Figure 4(a):

All customers with $V⩾\frac{y_1}{1-k}(>\frac{[y_1-(1-\beta )y_2{]}^{+}}{\beta (1-k)})$ choose to trade in at the end of period 1. Further, among these customers who trade-in, those with $V>y_2/(1-k)$ will again trade-in at the end of period 2 (since, $V-y_2>kV$ , at the end of period 2).

All customers with $(\frac{y_1-(1-\beta )y_2}{\beta (1-k^2)}<)\frac{y_2}{1-k^2}⩽V⩽\frac{y_1}{1-k}$ will trade in at the end of period 2.

Thus, period 1’s customers either trade-in at the end of period 1 or at the end of period 2 when the period 2’s trade-in price $y_2$ is higher than period 1’s $y_1$ . Therefore, the total number of trade-ins that the firm receives during period 2 when $y_1<y_2$  is

$$\begin{array}{rl}{\mathrm{\Xi }}_{t,2}(y_1,y_2)& =[{\xi }_{t,2}(y_2){]}^{+}+{[1-\frac{y_2}{1-k}]}^{+}\\ & +{[\frac{y_1}{1-k}-\frac{y_2}{1-k^2}]}^{+},\end{array}$$

(33)

where ${\xi }_{t,2}(y_2)$ are the trade-ins from the customers who buy new units during period 2, as given in (12). The trade-ins received during period 1 is ${\xi }_{t,1}(y_1)$ , as given in (5) (because it still suffices to let $y_1⩽1-k$ , as it can be shown that $y_1>1-k$ will not affect the firm’s profits).

Firm sets higher trade-in price in period 1 ( $y_1⩾y_2$ ). When the firm sets $y_1⩾y_2$ , a few of the period 1’s consumers trade-in at the beginning of period 2 as well, as shown in Figure 4(b). While the number of trade-ins during period 1 remains at ${\xi }_{t,1}(y_1)$ (given in (5)), the total number of trade-ins in period 2, including from the customers who purchased during period 2, is

$$\begin{array}{rl}{\mathrm{\Xi }}_{t,2}(y_1,y_2)& ={\xi }_{t,2}(y_2)+[1-\frac{y_2}{1-k^2}]\\ & +[\frac{y_1-(1-\beta )y_2}{\beta (1-k)}-\frac{y_2}{1-k}].\end{array}$$

(34)

Here, it can be shown that setting $y_1>\beta (1-k)+(1-\beta )y_2$ will not affect the firms profit, because the number of trade-ins during first period is 0 and the trade-ins at the beginning of period 2 is independent of $y_1$ . Hence, it is sufficient to restrict the feasible set to $y_1⩽\beta (1-k)+(1-\beta )y_2$ .

Therefore, by using ${\mathrm{\Xi }}_{t,2}(y_1,y_2)$ , which is given in (33) or (34) depending on whether $y_1<y_2$ , the total profit from trade-ins in period 2 is given by $(y_2-c)\cdot {\mathrm{\Xi }}_{t,2}(y_1,y_2)$ . Furthermore, since the total number of (first-time) trade-ins received from period 1’s customers cannot exceed the total sales in period 1, we require the firm to choose its price $p_1$ and $y_2$ such that:

$$p_1⩽\frac{y_2}{1-k^2},$$

(35)

otherwise, the firm can improve its profits by increasing $y_2$ so that the constraint is satisfied.

Since the two additional cases $y_1<y_2$ and $y_1⩾y_2$ , (33) to (35) greatly complicate the problem for obtaining an analytical solution, we opt for numerical solutions to gain useful insights. We focus on the scenario when supply disruptions in periods 1 and 2 are identical and independent; that is, $\alpha =\beta$ .

Figure 5.

Optimal reusability level and total trade-in quantity (base case refers to the scenario when trade-ins that are at most one period old are accepted): (a) optimal reusability; and (b) total trade-in quantity in two periods.

Figure 6.

Trade-in quantity and trade-in price in period 2: (a) trade-in quantity in period 2; and (b) trade-in price in period 2.

7.1. Discussion and Insights

First, it is crucial to note that the optimal product reusability ${\varphi }^{*}$ remains unimodal with respect to the risk of supply disruption $\beta$ as illustrated in Figure 5(a). The firm initially opts for higher product reusability as $\beta$ increases, up to a certain threshold of $\beta$ . Beyond this threshold, the firm reduces the reusability level as the risk $\beta$ continues to increase. Additionally, the firm accepts more trade-ins across two periods due to more trade-in opportunities when compared to the base case under Assumption 1 (Figure 5(b)).

Second, some customers of period 1 can choose to postpone their trade-ins to period 2 when the firm offers them additional trade-in opportunities in period 2 (Figure 6(a) shows an increase in period 2’s trade-ins quantity). This could decrease the trade-in inventory accrued during period 1 (Figure 7(a)) that undermines the benefit of product reusability, which eventually prompts the firm to lower product-reusability ${\varphi }^{*}$ as shown in Figure 5(a). Moreover, the firm may charge a higher trade-in price $y_2^{*}$ in period 2 (see Figure 6(b)) to exploit the customers’ trade-in postponement behavior.

Figure 7.

Trade-in quantity in period 1 and refurbished unit prices during disruption in period 2: (a) trade-in quantity in period 1; and (b) refurbished unit prices in period 2 in state D.

Finally, the fewer trade-ins in period 1 (Figure 7(a)) due to customers’ trade-in postponement to period 2 can lead to a higher price for refurbished units during disruption, as shown in Figure 7(b).

In summary, while the firm adapts its decisions to handle the increased trade-ins when it accepts trade-ins of all ages, our main insight on optimal product-reusability remains valid. It is beneficial to increase product reusability as the risk of supply disruption rises, but only up to a certain threshold. Beyond this threshold, it is more advantageous for the firm to reduce reusability to save on its design costs (as illustrated in Figure 5(a) when $\beta >0.6$ ). High disruption risk limits the firm’s ability to produce a sufficient number of new units, which in turn affects the availability of trade-ins. If the design cost is high due to high product-reusability, the firm may struggle to remain profitable when the risk of supply disruption is high.

8. Conclusions

In this article, we examine how a firm determines its product’s reusability amidst potential supply disruptions. We develop a three-period model. In period 0, the firms determines the optimal level of reusability and designs the product. In period 1, if there are no supply disruptions, the firm produces new units and accepts their trade-in at the end of the period. Finally, in period 2, the firm undertakes production of refurbished units if inventory is available from the trade-ins from period 1. Further, if there are no supply disruptions, the firm will continue to produce new units and accept their trade-ins at the end of this period.

We analyze consumer behavior regarding the choice between new and refurbished units and when to trade in their used units. Our analysis yields the optimal degree of product reusability, trade-in and refurbishment policies, trade-in fee, and the prices of new and refurbished units chosen by the firm. The following managerial insights can be drawn from this work.

We demonstrate that the firm adopts a threshold refurbishment policy: it does not refurbish trade-ins with low reusability, increases refurbishment with higher reusability, and refurbishes all trade-ins when reusability is sufficiently high. Additionally, under high risk of supply disruption and a high consumer valuation of used units, the firm accepts trade-ins to create a safety stock to hedge against supply disruption. However, the firm refrains from refurbishment in the absence of supply disruption when the reusability level is not sufficiently high.

Contrary to common belief, we find that the firm decreases reusability to save on design costs when (i) the risk of supply disruption is high, due to the increased likelihood of being unable to produce new units, or (ii) the production cost is high, due to lean margins.

We then discuss how the firm’s reusability choice generates a Pareto-efficient benefit for (i) the firm, with reduced refurbishment costs, (ii) trade-in consumers, with higher trade-in fees, and (iii) refurbished-unit purchasers, with lower prices. Consequently, initiatives to lower design costs for increased reusability can consistently be advantageous for all stakeholders.

Our work initiates the exploration of product reusability amid supply disruptions, relevant for sustainable operations. Further studies could explore the impact of other reuse practices such as remanufacturing, reuse practices in multi-product setting, and competition on firms’ refurbishment strategies. Future research could extend our two-period framework to analyze the infinite-horizon version of the problem and its variants to assess the impact of end-of-horizon effects more comprehensively. Finally, despite being motivated by events like COVID-19, our findings are relevant in a wider context, especially when a firm sources from suppliers who face shared upstream supply chain risks, which could impact all the suppliers simultaneously. Understanding how supply disruptions influence product designs is crucial for sustainable operations across various contexts.

In conclusion, we believe that our work provides a useful framework to understand how supply disruptions can influence product reusability design decisions.

Appendix. Auxiliary Results

Lemma 7

Let ${\beta }_0=\frac{c+k-1}{k(1-c)}(>0)$ , ${\varphi }_I(\beta )\equiv \frac{\beta (c-k)-(1-c-k)}{c\beta }(<1-k)$ , and $\widehat{{\varphi }_I}(\beta )\equiv {\varphi }_I(\beta )\cdot \beta +(1-k)\cdot (1-\beta )$ . When the used units are valued highly, that is, $k>1-c$ , the firm always sets $y_2^{*}=1-k$ , so that it discourages trade-ins in period 2. Furthermore, the other decisions in periods 1 and 2 are determined by the reusability level $\varphi$ and the magnitude of risk $\beta$ as follows:

If the risk is low, that is, $\beta ⩽{\beta }_0$ , then:

if $\varphi \in [0,\widehat{{\varphi }_I}(\beta )]$ , then $p_2^{*}=(1+c)/2$ , $p_N^{*}=k(1+c)/2$ , $p_D^{*}=k$ , $p_1^{*}=(1+c)/2$ , and $y_1^{*}=1-k$ , where $\widehat{{\varphi }_I}(\beta )\in [(1-k),{\varphi }_I(\beta )]$ .

if $\varphi \in (\widehat{{\varphi }_I}(\beta ),1]$ , then $p_2^{*}=(1+c)/2$ , $p_N^{*}=\frac{k[2k(1-[k(1-\beta )+\left(\frac{1-c}{2}\right)\beta ])+c(1-k)(3-\varphi )]}{2[1-k^2(1-\beta )]}$ , $p_D^{*}=\frac{k[2k(1-[k(1-\beta )+(\frac{1-c}{2})\beta ])+c(1-\varphi )+(1+c)(1-k)]}{2[1-k^2(1-\beta )]}(<k)$ , $p_1^{*}=(1+c)/2$ , and $y_1^{*}=\frac{(1-k)(1-(1-\beta )k(2k-1)+c(2-k(1-\beta )-\varphi )}{2(1-(1-\beta )k^2)}(<1-k)$ .

Thus, the firm discourages trade-ins in period 2 but encourages them in period 1 if, and only if, the reusability is high (i.e., $\varphi >\widehat{{\varphi }_I}(\beta )$ ). Moreover, the firm refurbishes all the trade-in inventory during period 2 (in both states $N$ and $D$ ).

On the other hand, if the risk is high, that is, $\beta >{\beta }_0$ , then:

if $\varphi \in [0,{\varphi }_I(\beta )]$ , then $p_2^{*}=(1+c)/2$ , $p_N^{*}=k(1+c)/2$ , $p_D^{*}=k$ , $p_1^{*}=(1+c)/2$ , and $y_1^{*}=1-k$ .

if $\varphi \in ({\varphi }_I(\beta ),(1-k)]$ , then $p_2^{*}=(1+c)/2$ , $p_N^{*}=k(1+c)/2$ , $p_D^{*}=\frac{k(1-k(1-\beta )+c(\beta (1-\varphi )+1))}{2(1-k(1-\beta ))}$ , $p_1^{*}=(1+c)/2$ , and $y_1^{*}=\frac{(1-k)(1-k(1-\beta )+c(1+\beta (1-\varphi )))}{2(1-(1-\beta )k)}$ ( $=y_{1,med\varphi }^{*}$ , which is defined in Lemma 4).

if $\varphi \in (1-k,{\varphi }_{\lambda }(\beta )]$ , then $p_2^{*}=(1+c)/2$ , $p_N^{*}=(k+c(1-\varphi ))/2$ , $p_D^{*}=\frac{k(1-k(1-\beta )+c(\beta (1-\varphi )+1))}{2(1-k(1-\beta ))}$ , $p_1^{*}=(1+c)/2$ , and $y_1^{*}=\frac{(1-k)(1-k(1-\beta )+c(1+\beta (1-\varphi )))}{2(1-(1-\beta )k)}$ ( $=y_{1,med\varphi }^{*}$ , which is defined in Lemma 4).

if $\varphi \in ({\varphi }_{\lambda }(\beta ),1]$ , then $p_2^{*}=(1+c)/2$ , $p_N^{*}=\frac{k[2k(1-[k(1-\beta )+\left(\frac{1-c}{2}\right)\beta ])+c(1-k)(3-\varphi )]}{2[1-k^2(1-\beta )]}$ , $p_D^{*}=\frac{k[2k(1-[k(1-\beta )+\left(\frac{1-c}{2}\right)\beta ])+c(1-\varphi )+(1+c)(1-k)]}{2[1-k^2(1-\beta )]}(<k)$ , $p_1^{*}=(1+c)/2$ , and $y_1^{*}=\frac{(1-k)(1-(1-\beta )k(2k-1)+c(2-k(1-\beta )-\varphi )}{2(1-k^2(1-\beta ))}$ ( $=y_{1,high\varphi }^{*}$ , which is defined in Lemma 4).

Thus, the firm discourages trade-ins in period 2 but encourages them in period 1 if, and only if, the reusability is sufficiently high (i.e., $\varphi >{\varphi }_I(\beta )$ ). Moreover, while the firm refurbishes all trade-ins in stated $D$ in period 2, in state $N$ it strategically uses trade-ins for refurbishment as follows:

• i.

it does not refurbish any trade-ins if $\varphi ⩽(1-k)$ ,

ii.

it refurbishes a few trade-ins if $(1-k)<\varphi <{\varphi }_{\lambda }(\beta )$ , and

iii.

it refurbishes all trade-ins if $\varphi ⩾{\varphi }_{\lambda }(\beta )$ .

Lemma 8

Firm lowers reusability whenever the design cost $t$ is higher (i.e., ${\varphi }^{*(t)}<0$ ).