Corrigendum to “Analysis of the performance of inventory management systems using the SCOR model and Batch Deterministic and Stochastic Petri Nets”

Jamal Fattah, Latifa Ezzine, Haj El Moussami, and Abdeslam Lachhab. Analysis of the performance of inventory management systems using the SCOR model and Batch Deterministic and Stochastic Petri Nets. International Journal of Engineering Business Management, first published online 28 November 2016. DOI: 10.1177/1847979016678370

A number of references to the following three sources were omitted from this article:

Chen H, Amodeo L, and Chu F. Batch deterministic and stochastic Petri nets. A tool for modeling and performance evaluation of supply chain. In: Proceedings 2002 IEEE international conference on robotics and automation (Cat. No.02CH37292), vol. 1, 2002, pp. 78–83. DOI: 10.1109/ROBOT.2002.1013342.

Kersten W and Saeed MA. A SCOR analysis of simulation in supply chain management. In: Squazzoni F, Baronio F, Archetti C, et al. (eds) 2014 proceedings of the 28th European conference on modelling and simulation, 2014. DOI: 10.7148/2014-0461.

Hwang YD. The performance evaluation of SCOR sourcing process—the case study of Taiwan’s TFT-LCD industry. Int J Prod Econ 2008. DOI: 10.1016/j.ijpe.2007.09.014.

The authors apologize to the readers. The following corrections apply (revisions are identified in bold).

On page 2:

Original

In this section, we will introduce the BDSPNs as a new class of SPNs, which is an extension of DSPNs by introducing batch places and batch tokens. Systems such as SCs, purchasing, production, and distribution are usually performed in a batch way with customer orders playing an important role, which justify the motivation for using the BDSPNs. In this last, we can distinguish between two types of places: discrete places and batch places. For the discrete places, tokens (which are the same as those in standard PNs) are viewed indifferently, while tokens in a batch places (which have sizes) are viewed as different individuals, called batch tokens.²⁶

BDSPNs are characterized by:

They may have inhibitor arcs and marking dependent weights of arcs.

If a transition has an inhibitor arc, it is enabled only if the number of tokens in the input place of the arc is less than the weight of the arc and the firing of the transition does not remove any token from the place.

They have three types of transitions: immediate transitions, deterministically timed transitions, and stochastic transitions with exponentially distributed firing time.

For an immediate transition, tokens will be created in their output places as soon as it is fired, while tokens will be created either after a deterministic time or a time randomly generated according to an exponential distribution.

The transition firing conditions and the state evaluation of BDSPNs are similar to those of DSPNs except in BDSPNs where the transitions may be fired in a “batch” way when batch tokens are involved.

Revised

In view of the fact that systems such as SCs, procurement, production, and distribution are usually performed in a batch mode, and in order to respond to supply chain modeling needs, where inventory replenishment and distribution operations are usually performed also in a batch mode, a new class of SPN has been introduced in the form of Deterministic and Stochastic Petri Nets (DSPN), namely Batch Deterministic and Stochastic Petri Nets (BDSPN), which is an extension as a result of introducing batch places and batch tokens.^26,43

The BDSPN model is characterized by:

The BDSPN model has two types of places: discrete places and batch places.

It may have inhibitor arcs and marking-dependent weights of arcs.

It has three types of transitions: immediate transitions, deterministically timed transitions, and stochastic transitions.

A transition that has an inhibit arc is activated only if the number of input tokens is less than the weight of the arc.

In the case where there is an immediate transition, tokens will be created in their output places as soon as it is fired.

For an immediate transition, tokens will be created either after a deterministic time or a time randomly generated.

When batch tokens are involved the transitions can be fired in a “batch” way.

On page 4:

Original

Every business process has different characteristics. Thus, a good understanding of the SCM processes is necessary before developing a simulation model.³⁴ In the past, different metrics were used to measure performance at different SC levels, and models for decision making at strategic level were scarce.³⁵ It is not achievable to have a model that perfectly represents SCM but a closely adapted model^36,37 SCOR is achievable. In 1996, the SCC has developed and released a structured framework model SCOR for SCM systems and practices.³⁸ SCOR model is the first cross-industry framework for evaluating and improving SC performance and management.^35,39 The benefit of the SCOR model is the provision of a standard format and a comprehensive methodology to facilitate communication and to improve SC operations.^36,40 In order to achieve the desired performance in the internal and external levels, upper management of a company is highly recommended to use SCOR to design and reconfigure its SC, as it constitutes a common language and a flexible framework.³⁵ SCOR is widely used in academia and practice. For these reasons, we use the SCOR framework as a base of our analysis. SCOR is a business process framework that spans from the supplier’s supplier to the customer’s customer.¹⁹ SCOR 11.0 describes an SC by four levels of details. Level 1 is a top level that defines the scope and high-level configuration by six core processes, that is, plan, source, make, deliver, return, and enable. Level 2 is a configuration level and processes at this level, along with their positioning, determine the SC strategy. Level 3 is a process element level and describes the steps that need to be performed to execute all the processes of the level 2. Level 4 is the implementation level and describes industry-specific activities that are required to perform level 3 processes.

Revised

To develop a simulation model of SC, a good understanding of each SC process is very necessary, since each business process has different characteristics.³⁴ To measure the performance at different levels of SC, several metrics of measurements were used, but the strategic decision-making models were scarce,³⁵ and there was no model that perfectly represented SCM, but a closely adapted model^36,37 SCOR is achievable. The Supply Chain Operations Reference (SCOR) model has been developed and endorsed by the Supply Chain Council (SCC) in 1996 as a structured framework model for SCM systems and practices.³⁸ SCOR model is the first cross-industry framework for evaluating and improving SC performance and management.^35,39,44 First of all, the SCOR model provides a standard format and a complete methodology to facilitate communication among supply chain actors and improve SC operations.^36,40 To design and reconfigure the SC, upper management of a company is highly recommended to use the SCOR model to achieve the desired performance in the internal and external levels.³⁵ Due to these advantages, the SCOR model is widely used in academic and industrial environments. For these reasons, we use the SCOR to model and analyze the performance of the inventory management system. SCOR and its corresponding performance metrics span supply chains from the supplier’s supplier to the customer’s customer.^{19, 44} SCOR provides four-levels of process detail. Level 1 (strategic) is the most aggregated and defines the supply chain by six core processes that, plan, source, make, deliver, return, and enable. Level 2 (tactical) allows, in accordance with the company strategy, to configure the supply chain from a set of sub-processes. At level 3 (operational), companies can specify the activities of sub-processes, best practices, disruptions of flows, functionalities of existing software packages, and tools. Level 4 is not in the reference model. It is appropriate for each company to define the basic tasks of the activities.

On page 5:

Original

The sourcing processes at level 2 include source stocked product (S1), source make-to-order product (S2), and source engineer-to-order product (S3). There are 17 process elements at level 3, including S1.1, S1.2, S1.3, S1.4, S1.5, S2.2, S2.3, S2.4, S2.5, S3.1, S3.2, S3.3, S3.4, S3.5, S3.6, and S3.7. This research selects level 2 of the SCOR sourcing process “source make-to-order product (S2)” to modeling, evaluation, and analysis of the performance of our inventory management systems.

Revised

SCOR sourcing process. For most companies, the sourcing processes are critical and very important. The industrial company is looking for this process to expect deliveries (receiving, inspection, storage/transfer payment); to identify and select its sources; to define and organize the supply management rules (both in terms of evaluation of supplier performance as maintenance supplies data); and to manage its product arrivals, stocks, infrastructure network providers, export–import constraints, and supplier contracts.⁴⁵

The detailed codes of the SCOR sourcing processes at level 2 are as follows:

Source stocked product S1

Source make-to-order product S2

Source engineer-to-order product S3

In this article, we will focus on “source make-to-order product (S2)” to model, evaluate, and analyze the performance of inventory management systems that will be the subject of our case study. The detailed codes of the SCOR sourcing processes source make-to-order product (S2) at level 3 are as follows:

Schedule product deliveries S2.1

Receive product S2.2

Verify product S2.3

Transfer product S2.4

Authorize supplier payment S2.5

The reference list has been updated to include the following:

43. Chen H, Amodeo L, and Chu F. Batch deterministic and stochastic Petri nets. A tool for modeling and performance evaluation of supply chain. In: Proceedings 2002 IEEE international conference on robotics and automation (Cat. No.02CH37292), vol. 1, 2002, pp. 78–83. DOI: 10.1109/ROBOT.2002.1013342.

44. Kersten W and Saeed MA. A SCOR analysis of simulation in supply chain management. In: Squazzoni F, Baronio F, Archetti C, et al. (eds) 2014 proceedings of the 28th European conference on modelling and simulation, 2014. DOI: 10.7148/2014-0461.

45. Hwang YD. The performance evaluation of SCOR sourcing process—the case study of Taiwan’s TFT-LCD industry. Int J Prod Econ 2008. DOI: 10.1016/j.ijpe.2007.09.014.