• We model the supply chain with form postponement as two-stage queuing network.• CODP position and base-stock level are jointly optimized.• We propose a normal distribution approximation for the objective function.• We give a quick algorithm for finding the optimal policy of the supply chain.The form postponement (FP) strategy is an important strategy for manufacturing firms to utilize to achieve a quick response to customer needs while keeping low inventory levels of finished products. It is an important and difficult task to design a supply chain that uses FP strategy to mitigate the conflict between inventory level and service level. To this end, we develop a two-stage tandem queuing network to model the supply chain. The first stage is the manufacturing process of the undifferentiated semi-finished product, which is produced on a Make-To-Stock basis: the inventory is controlled by base-stock policy. The second stage is the customization process based on customers’ specified requirements. There are two types of order: ordinary order and special order. The former can be met by customizing from semi-finished product, while the latter must be entirely customized beginning from the first stage. The customer orders arrive according to a Poisson process. We first derive the inventory level and fill rate, and then present a total cost model. It turns out that the model is intractable due to the Poisson distribution in the objective function. To analytically solve the problem, we use normal distribution as an approximation of the Poisson distribution, which works well when the parameter of the Poisson distribution is quite large. Finally, some numerical experiments are conducted and managerial insights are offered based on the numerical results.
Nowadays, more and more companies are enlarging product varieties in order to fulfill demand from increasingly different types of customers. Favorably, information techniques make the diversification of product feasible by providing companies with low cost platforms to interact with their customers and realize mass customization. However, product variety has a significant impact on inventory level and service performance (Lee & Tang, 1997). To offer a large variety of products in highly efficient ways, various supply chain structures have been previously explored. Most of them can be divided into two strategies (Zinn & Bowersox, 1988): One is the time postponement (TP) strategy which delays delivery until customer orders arrive. The other is the form postponement (FP) strategy which delays the differentiation of the product until the detailed specification is confirmed.
Form postponement is one of the most popular and successful strategies in mass-customizing supply chains (Lampel and Mintzberg, 1996 and Ahlstrom and Westbrook, 1999). In practice, many companies have successfully implemented the FP strategy, e.g., Dell computer, Toyota’s “Build your Toyota”, Amazon’s “Built your own ring”, and Nike’s “Design your shoes”, etc. For maximizing efficiency of the FP strategy, companies are showing increasing interest in incorporating the customer order decoupling point (CODP) as an important input to the strategic design of manufacturing operations as well as supply chains. CODP is defined as the point in the value-adding chain that separates the decision based on forecast from the decision based on the detailed product specification of the order. In other words, CODP divides the material flow that is forecast-driven (upstream of the CODP) from the flow that is customer order-driven (downstream of the CODP). It is also referred to as “the point of differentiation” (Lee & Tang, 1997).
Since Buclin (1965) first introduced the term “postponement”, there have been a large number of researches on the postponement strategy. We do not attempt to cite and discuss every significant contribution in this area. Instead, we refer readers to van Hoek, 2001, Swaminathan and Lee, 2003 and Yang and Burns, 2003 for a comprehensive review. More recently, Leung and Ng (2007) use a goal programming model to optimize production planning in a perishable supply chain with postponement. Kumar, Nottestad, and Murphy (2009) investigate the effect of product postponement on distribution network supply chains by using simulation models. Trentin, Salvador, Forza, and Rungtusanatham (2011) develop an operational procedure to identify and quantify the opportunities for applying the FP strategy to a given product family. Wong, Potterb, and Naimb (2011) show that the postponement strategy can improve the performance of the soluble coffee supply chain. Sharda and Akiya (2011) investigate the inventory management policy for a specific chemical plant by using a postponement strategy simulation.
Here we focus on a few studies that are the most pertinent to our own work, i.e., the joint optimization of CODP and the inventory level in a mass-customizing supply chain. Aviv and Federgruen, 2001a and Aviv and Federgruen, 2001b investigate the tradeoff between the inventory level and redesigning cost in a form postponement supply chain, but they do not consider the problems of congestion and order delay. Conversely, Su et al., 2005, Gupta and Benjaafar, 2004 and Jewkes and Alfa, 2009 all capture the impact of congestion on the FP strategy by using queuing models. Su et al. (2005) compare the TP strategy with the FP strategy based on total operational cost. In their paper, the FP supply chain is actually modeled as a two-stage Make-To-Stock (MTS) queuing network with exogenous CODP position. They assume that there are n categories of customizing processes in the downstream stage, which are also controlled by the base-stock policy. Both Gupta and Benjaafar, 2004 and Jewkes and Alfa, 2009 model the customizing process as an Make-To-Order (MTO) queue that incorporates CODP position optimization. The former assumes that the potential CODP position in a multi-stage supply chain is a discrete number. The latter constructs a two-stage tandem queuing network in which the CODP position is relaxed to be continuous number on the interval of (0, 1).
In this paper, we address the same basic question as Gupta and Benjaafar, 2004 and Jewkes and Alfa, 2009: How to optimize the CODP position and inventory level to minimize operational cost? Here, we develop a two-stage tandem queuing network to model the supply chain using an FP strategy. The first stage is the manufacturing process of the undifferentiated semi-finished product, which is produced on a Make-To-Stock (MTS) basis and the inventory is controlled by the base-stock policy. The second stage is the customization process based on customers’ specific requirements. However, our model differs from Gupta and Benjaafar, 2004 and Jewkes and Alfa, 2009 in the following ways: First of all, we assume that the processing time (both replenishment process and customizing process) are constant, instead of exponential distributed in Gupta and Benjaafar, 2004 and Jewkes and Alfa, 2009. This assumption is practicable in some cases, e.g., in automatic production lines. It is shown that the performance evaluation of two stage tandem queuing network with mixed MTS and MTO is very difficult, even in case of the exponential distributed process time. In our work, we derived the closed-form performance measures based on the results of Zipkin, 2000 and Sherbrooke, 1975, such as inventory level and unfill rate. Secondly, we consider the effect of CODP position on the capability of customization. It is clear that the further downward the CODP position, the more customer orders cannot be met based on semi-finished product. We model this situation with two categories of order: ordinary order and special order. The former can be met by using semi-finished product, while the latter must be entirely customized beginning from the first stage. Furthermore, we assume that the fraction of ordinary customer orders γ is a decreasing function of CODP position θ. Third, we involve the lead-time quotation policy and the penalty cost of tardiness for being more practical.
The rest of the paper is organized as follows. In Section 2, we present the model description. Section 3 presents the optimization problem. The approximation of the cost function by normal distribution and the solution of the approximate model are given in Sections 4 and 5, respectively. Section 6 conducts numerical experiments to demonstrate the impact of the parameters on the optimal policy. Section 7 concludes the paper.
The form postponement strategy is an efficient tool to balance the tradeoff between high customization and quick response. In this paper, we developed a two-stage tandem queuing network with constant process time to evaluate the operational performance of a form postponement supply chain. Based on Zipkin’ result and Shebrooke’s result, we derived the closed-form performance measures, such as inventory level and unfill rate. By using normal approximation of Poisson distribution, we optimized the CODP position θ and the base-stock level S to minimize the total cost. Furthermore, we developed an efficient algorithm for finding the optimal policy. Our numerical examples show that the optimal policy is not sensitive to most of the decision parameters, except the demand rate. Based on the numerical results, we can gain managerial insights: (1) As the demand commonality increases, the optimal policy delays the CODP position and keeps higher base-stock levels; (2) As the finished product’s unit holding cost increases, it is better for the supply chain to set the CODP position more closely to the finished product node of the supply chain and reduce the base-stock level; (3) For the policy of constant penalty cost, larger penalty costs causes a more forward CODP position with larger inventory levels; (4) When the system is quite less congested, the optimal policy for the supply chain is Make-To-Order, and when the utilization is moderate, the later differentiation is favored for larger load. However, when the system becomes quite congested, the CODP position decreases as the utilization increases.
Our research can be further extended along the following three lines: (1) To consider that the semi-finished product inventory is controlled by (s, S) policy; (2) To let the processing time be subject to an arbitrary distribution; (3) To relax the assumption of independent Poisson demand and allow for more complex demand structure, e.g. the demand rate depends on the price and lead-time quotation, which may be more practical.
