Production, Manufacturing, Transportation and Logistics
Optimal postponement contracting decisions in crowdsourced manufacturing: A three-level game-theoretic model for product family architecting considering subcontracting

https://doi.org/10.1016/j.ejor.2020.09.049Get rights and content

Highlights

  • Our game-theoretic model finds optimal solutions for crowdsourced manufacturing.

  • The net profits of a manufacturer, distributors, and subcontractors are maximized.

  • We formulate a postponement contracting with subcontracting (PCS) problem.

  • A novel virtual postponement structure is introduced to optimize the PCS problem.

  • We verify the model using an electric vehicle company case study.

Abstract

Crowdsourced manufacturing enables companies to outsource and share manufacturing resources based on demand and capacity across the value chain. A postponement strategy is well recognized as an effective means to deal with supply chain risks and uncertainties of producing customized products. However, coordinated decision-making among product design, postponement contracting and subcontracting is a challenging problem area that requires innovative modeling and decision support. This study develops a model that emphasizes interactive decisions within a three-level non-cooperative game that determines the optimal solutions for a single manufacturer, multiple distributors, and multiple subcontractors by maximizing their net profits. This study formulates a postponement contracting with subcontracting (PCS) problem for product family architecting to interact with postponement contracting and subcontracting decisions based on optimal planning of crowdsourced manufacturing activities. The PCS problem differs from traditional postponement design models that assume a (fixed) product architecture is given at the outset. In this study, interaction among different stakeholders is modeled as a non-linear, mixed-integer, three-level game-theoretic model based on the Stackelberg game theory. A novel virtual postponement structure is introduced to concretize optimization of the PCS problem and to justify which product module(s) should be postponed. Analytical solutions are developed incorporating a nested genetic algorithm. A practical case study of postponement contracting decisions in an electric vehicle company is reported to verify the feasibility and potential of the proposed approach for product family architecting. The optimal product family design, the types of postponed product modules, some parts in the postponed product modules that need to be further subcontracted, and other decision results are determined simultaneously in the case study. The sensitivity analyses on the proposed postponement cost and demand parameters indicate that the changes of their values greatly influence the decision makers’ net profit, and the net profit situation of each decision maker in different regions is obtained by the sensitivity analysis of the union of the two parameters. Thus, the PCS problem for product family architecting in crowdsourced manufacturing provides a more complete solution for the current implementation of the postponement strategy, and our proposed three-level game-theoretic model can handle well the coordination among the PCS problem.

Introduction

With the advance of information and communication technologies, manufacturing enterprises are confronted with unprecedented competition and challenges. Simultaneously, there has been widespread emergence of new technologies and innovative ideas, such as smart manufacturing and the Internet of Things, to satisfy increased customer demand for personalization (Wang, Ma, Yang & Wang, 2017). Increasing number of enterprises have advocated an open approach to their entire business model (Kortmann & Piller, 2016). One revolutionary example is crowdsourced manufacturing (Kaihara, Katsumura, Suginishi & Kadar, 2017), which essentially transfers product fulfillment to a crowdsourcing process to enable new value–based movements (Ramsden, 2015). Crowdsourced manufacturing promotes collaboration across firms and uses an open, collaborative, and distributed network to support sharing and exchange of manufacturing knowledge and services throughout the product fulfillment value chain (Li et al., 2018).

A popular trend in crowdsourced manufacturing is toward customized and personalized products (Yang et al., 2017). As multiple products have to be produced, customer demand becomes less predictable, resulting in higher supply chain risks and uncertainties (Gupta, Maranas & McDonald, 2000). Product differentiation through modular configuration of product families can accommodate increasing product variety across diverse markets (Sundgren, 1999). Crowdsourced manufacturing enterprises must cooperate with external partners in different aspects of manufacturing product families (Li et al., 2017). Crowdsourcing manufacturing mode indicates a promising open design paradigm for product family design in a form of co-creation, where the end products are fulfilled by multiple stakeholders across the value chain (Wu, Du & Jiao, 2020). It leads to the fact that more product modules can be postponed in the fulfillment process for the product family, which will inevitably lead to the postponement structure (containing the type of the postponed product module and the optimal attribute levels for each postponed module) that is undefined in advance. This facilitates a delayed product differentiation or postponement strategy (Blecker & Abdelkafi, 2006) that enables quick response to effectively manage the risks associated with final products and uncertain sales (Cavusoglu, Cavusoglu & Raghunathan, 2012).

The implementation of a postponement strategy often involves multiple stakeholders. Supply contracting in crowdsourced manufacturing can coordinate the material and information flow of these stakeholders over a long horizon and organize them into a supply chain network (Jiao, You & Kumar, 2006). It has been identified as an incentive alignment scheme for the application of postponement (Qrunfleh & Tarafdar, 2013). To concentrate on the core competing activities, postponement contractors often subcontract the peripheral activities to external suppliers or partners to reduce operation costs and improve efficiency (Feng & Lu, 2013). Our motivation for subcontracting the partial postponement activities in this study is to provide more complete supporting productions for the parts of postponed product modules or certain postponed product modules in the postponement contracting activities. In fact, the manufacturing process of products often involves multi-level contracting processes in today's crowdsourcing manufacturing mode, which has become an inevitable trend in this manufacturing environment (Shen, Choi & Minner, 2019). For a typical postponement contracting and further subcontracting example, like Honda, postponing some components manufacturing activities of the automobiles and contracting them to contract manufacturer or original design manufacturer at a regional distribution center, the latter often in turn subcontracts the peripheral components to specialized lower-tier suppliers (Choi & Hong, 2002). Subcontracting part of their workload is a common practice among contractors in many industries (Pun & Heese, 2015). In the aerospace industry, up to 70% of product components are outsourced, and it is fairly common for first-tier contractors to subcontract a portion of their work to lower-tier subcontractors (Bales, Maull & Radnor, 2004). To reduce the risk and uncertainty associated with product variants in a crowdsourced manufacturing environment, it is necessary for contracting with subcontracting strategies to be implemented in accordance with the strategic mechanisms of postponement (Jiang, 2012).

Crowdsourced manufacturing enterprises need to make trade-offs between maximally satisfying customers’ customization demands and minimizing their own operating costs in the implementation of the postponement strategy (Granot & Yin, 2008), which means that dynamic postponement design is necessary for enterprises to achieve trade-offs (Weskamp, Koberstein, Schwartz, Suhl & Voß, 2019; Xiong, Du & Jiao, 2018). Dynamic postponement design is geared towards optimal product family architecting, such that the postponed product modules are determined by optimization of interactive decisions with external partners (Adkins & Paxson, 2013; Wu et al., 2020). In fact, successful implementation of a postponement contracting strategy must incorporate its concept as early as in the product design stage (Yang, Burns & Backhouse, 2004). For instance, a modular product family architecture and configuration in the product development and production process play a very important role in determining the selection of the most appropriate postponed product modules (Ernst & Kamrad, 2000). The implementation of a postponement contracting strategy in turn affects the optimal product family architecture and configuration (Xiong et al., 2018). The postponement contractors decide on different outsourced postponed product modules that will influence the selection of the most appropriate subcontractors (Saghiri & Barnes, 2016), and in turn, that subcontractors changed decisions will also affect the selection of outsourced postponed product modules for the contractors (Liu, Du & Jiao, 2017). However, existing studies on postponement have paid limited attention to the interactive influence of product design, postponement contracting, and subcontracting decisions in a crowdsourced manufacturing environment (Choi, Narasimhan & Kim, 2012). This study emphasizes such an interactive decision-making process and refers to it as a postponement contracting with subcontracting (PCS) problem, which considers an underlying product architecture to interact with postponement contracting and subcontracting decisions according to the optimal planning of crowdsourced manufacturing activities.

This research focuses on the three-level optimization problem of PCS for product family architecting in crowdsourcing manufacturing environment, in which the interaction between product family architecting and postponement contracting is mainly realized by selecting postponed product modules and the interaction between postponement contracting and subcontracting is realized by choosing the parts of postponed product modules or certain postponed product modules for further subcontracting. In the process of interactive optimization of PCS decisions for product family architecting, the optimal design of product family and the types of postponed product modules, as well as the optimal decisions of postponement contractors and subcontractors are determined by the three-level game-theoretic model. Therefore, our proposed the PCS problem for product family architecting in crowdsourced manufacturing provides a more complete solution for the current implementation of the postponement strategy and established the three-level game-theoretic model can handle well the coordination among the PCS problem. Different from the existing literature, key technical challenges of the PCS problem can be observed as the following:

  • (1)

    Dynamic postponement contracting: To obtain the optimal solution of the PCS problem, it is necessary to identify the types of product modules (i.e., generic versus delayed modules) in the product design phase. As decisions about certain product modules to be delayed to a later stage of the supply chain or some parts of postponed product modules to further subcontracting will impact a priori combination of modules for product family configuration (Wu et al., 2020), the optimization process of PCS becomes very complicated correspondingly. However, the prevailing practice of postponement practice often assumes that a (fixed) product architecture is given in advance (Jewkes & Alfa, 2009; Li, Wang & Cheng, 2008). These studies on postponement based on the supply chain perspective mainly concentrate on optimal inventory policies in accordance with a postponement strategy (Aviv & Federgruen, 2001; Tang, 2011), or positioning of the late customer order decoupling point (Lee & Tang, 1997), or emphasizing how to select appropriate suppliers for the fixed postponed product modules (Ngniatedema, Fono & Mbondo, 2015). Compared with the existing studies on postponement, the optimization process of PCS for product family architecting involves dynamic postponement contracting regarding the following questions. (a) Which product modules should be postponed for production by which external contractors? (b) Which subcontractors should be selected by which contractors for the production of which outsourced postponed modules? (c) How should the postponed and outsourced activities be fulfilled by contracting and subcontracting in what crowdsourced manufacturing activities? These uncertainties make PCS for product family architecting an uncertainty-to-uncertainty interactive influence process of different levels in the supply chain, and its optimal solution is obtained by the dynamic postponement contracting process. As product family architecting involves the product module domain (Jiao, Simpson & Siddique, 2007) and postponement activities involve the supply chain domain (Cvsa & Gilbert, 2002), cross-domain decisions lead to a more complex implementation for dynamic PCS decisions for product family architecting.

  • (2)

    Three-level Stackelberg game decisions: The PCS problem describes a typical postponement production mode in crowdsourcing manufacturing environment, it involves a three-level Stackelberg game decision in the optimization process. But the three-level optimization problem is rarely involved in the existing researches on postponement, among which there are several typical research models, for instance, the interactive optimization between manufacturers and contractors, including the researches based on the fixed and uncertain product architecture in advance (Graman, 2010; Xiong et al., 2018), the two-stage stochastic programming model for identifying optimal postponement strategies in supply chains (Weskamp et al., 2019), and the multi-objective robust optimization model of a single decision-maker (Jabbarzadeh, Haughton & Pourmehdi, 2019). In this study, the task of fulfilling product families through PCS is carried out by different enterprises in a supply chain, in which diverse stakeholders may have many different or even conflicting interests in order to maximize their own revenues. In this sense, the PCS problem entails a three-level non-cooperative Stackelberg game. As the interactive influence relationships among different levels, such as adjacent-level direct interactive influence and cross-level indirect interactive impact, are involved in the PCS problem for product family architecting, the corresponding optimization process needs to deal explicitly with a coordinated leader follower interactive decision game in the three-level supply chain. Various types of constraints exist for such a cross-domain and cross-level optimization problem, such as compatibility constraints and incompatible constraints among module instance for product family architecting (Du, Jiao & Chen, 2014) and restrictions on the selection of postponement contractors (Xiong et al., 2018). It is important to explore effective constraint-handling techniques throughout the game. In light of these considerations, it is challenging to develop a three-level game-theoretic model for the PCS problem for product family architecting. Another challenging is the solution of three-level game-theoretic models, which is much more complex than that of ordinary game-theoretic models.

Thus, compared with previous research, the major contributions of the study are as follows. (1) We further formulate the subcontracting decisions based on the dynamic postponement contracting problem in a crowdsourced manufacturing environment, which provides a more complete solution for the supporting productions of the parts of postponed product modules or certain postponed product modules in postponement contracting activities. (2) We establish a non-linear, mixed-integer, three-level game-theoretic model based on Stackelberg game theory to quantitatively optimize the decision process of the interactive postponement contracting mechanism, and address technical difficulties in constructing its mathematical expressions. (3) For the solution of the three-level game-theoretic model, we propose to firstly transform it into a bi-level game-theoretic model by analytical solutions, and then develop a nested genetic algorithm based on the inherent decision-making mechanism of bi-level programing to solve the bi-level game-theoretic model. (4) We propose postponement cost and demand parameters to analyze the benefits of the implementation of postponement strategy, find that they greatly influence the decision makers’ net profit by sensitivity analyses, and determine the net profit situation of each decision maker in different regions by the sensitivity analysis of the union of the two parameters.

Section snippets

Postponement contracting considering subcontracting

We consider a three-layer supply chain consisting of a manufacturer, multiple distributors (i.e., contractors) and multiple subcontractors with the PCS optimization problem for product family architecting in crowdsourced manufacturing. The manufacturer designs a product family consisting of multiple customized product variants and produces a generic (semi-finished) product that can be further modified at later stages before final delivery to customers in independent market segments. The

Notations and assumptions

The notations, including the definitions of parameters (Table 1), decision variables (Table 2), and functions (Table 3) are used to formulate the mathematical submodels of the manufacturer, distributors, and subcontractors. We make the following other assumptions to build the model.

  • (1)

    Each distributor is willing to produce the postponed product modules if doing so is profitable to it (Chen & Wu, 2010) and each subcontractor is willing to produce the outsourced postponed product modules if doing so

Model solution by nested genetic algorithms

This section shows how each decision variable of the player is optimally determined. In Section 5.1, the best reactions of the subcontractors for solving τckl and τcjr are analytically obtained. Then, substituting the analytical solutions of τckl and τcjr into the decision model of the distributors can transform the original three-level game-theoretic model into a bi-level game-theoretic model. To solve the bi-level game-theoretic model, a nested genetic algorithm (NGA) is developed in Section

Case study of electric vehicle supply chain postponement decisions

A case study of product family fulfillment supply chains is conducted in an electric vehicle (EV) company in Southern China. This particular case is concerned with optimizing EV product family architecture by determining which product modules to be postponed, selecting most appropriate distributors and subcontractors, as well as providing price quotations to the distributors and subcontractors. In addition to verifying the PCS problem contexts, we further validate the influence of varying

Concluding remarks

Based on the mechanism of dynamic postponement design (Wu et al., 2020), this study investigates the PCS problem for product family architecting in a crowdsourced manufacturing environment. This PCS problem is associated with an undefined product architecture interacting with postponement contracting decisions and subcontracting decisions, which is discerned from traditional postponement design models that assume a fixed product architecture is given at the outset. The game-theoretic approach

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    This research is sponsored by National Natural Science Foundation of China under Project Number 71371132.

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