پذیرش متمرکز و کنترل تولید در زنجیره تامین دو مرحله ای با محصولات سفارشی و تک جزئی

This paper considers a two-stage supply chain that a make-to-stock facility produces a single component in anticipation of future demand and a make-to-order facility produces customized products using components with the option of to accept or reject each customer order. We address the problem of centralizing the admission and production control that maximizes the supply chain's profit subject to the system costs. Using a Markov decision process model, we characterize the structure of the optimal admission control and production policy and establish the monotonic impact of system parameters on the optimal policy. Two heuristics are presented and their performance is numerically compared to the optimal policy under different operating conditions of the system.

This paper considers a supply chain that consists of a make-to-stock (MTS) facility and a make-to-order (MTO) facility in successive stages. The MTS facility produces a single component in anticipation of future demand from the MTO facility. With the option of to accept or reject each incoming customer order, the MTO facility produces customized products using components. Revenue is generated if each accepted order is processed and penalty is incurred if each incoming order is rejected. Holding and backlog costs are incurred for components in inventory and outstanding customer orders, respectively. Inter-arrival times of customer orders and production times of components and customized products are stochastic. This work was motivated by a manufacturer that owns two production facilities: one for semiconductor chips and the other for printed circuit board (PCB) products. The PCB production is driven by customer orders while the semiconductor chip production is scheduled by anticipating demands on chip from the PCB production facility. Inventories of generic chips give the manufacturer a strategic advantage in reducing the component level cost and the lead time for the procurement of generic chips at the customization stage. Our work is intended to serve as a basic study to provide the manufacturer with insights on their strategic decision of selectively accepting or rejecting customer orders and determining when to start or stop production of generic chips. To address such a problem, we define a two-stage production inventory problem which centralizes the admission control at the MTO stage and the production control at the MTS stage. Compared to the classical inventory control models in multi-stage production systems, our model has a distinct feature that there is a delay between the arrival of a customer order (demand) and the time component is actually needed to process that customer order. Under this circumstance, inventory is not carried at the MTO facility and it is necessary only at the MTS facility. Consequently, production control at the MTS facility will depend on both its component inventory level and the size of outstanding customer orders at the MTO facility, instead of only its component inventory level. The primary goal of this paper is to study a centralized policy that coordinates the decisions of admission and component production control so as to maximize the supply chain's profit. Coordination of inventory and production control among supply chain members can be beneficial for the whole supply chain (Carr and Duenyas, 2000 and Saharidis et al., 2009). However, the question of what level of inventory is optimal for the supply chain is still complicated. Especially, when the supply chain produces both make-to-stock and customized products, the dilemma consists of having to deliver customized products within due dates while reducing inventories of make-to-stock products. Moreover, admission control is an additional challenge for the MTO facility because outstanding customer orders incur expensive backlog costs. There is a vast literature on production control in multi-stage production systems using queueing network modeling (see Dallery and Gershwin, 1992 for the literature survey). Veatch and Wein, 1992 and Veatch and Wein, 1994 studied the problem of production planning in a two-stage production system where unmet demands from finished goods inventory are backordered. Assuming Poisson demand and exponential production times, Veatch and Wein (1992) characterized the optimal production decisions as two monotone switching curves. Veatch and Wein (1994) found conditions that certain simple policies are optimal and showed that the base stock policy can never be optimal. Optimal controls were compared with kanban, base stock, and finite buffer control mechanisms. Li and Liu (2006) considered a (s,S) type of production control at component production such that the setup process is switched on when the component inventory reaches s and the production process stops when it reaches S. There is also a rich literature on admission control in production/inventory systems. Stidham (1985) reviews the literature on customer admission control to single class make-to-order queues. Several papers have considered integrated admission control and production decision in a single-stage production system. Carr and Duenyas (2000) considered a production system that produces MTO and MTS products and studied the problem of joint admission control and production switching. A single-stage, single product, make-to-stock system with multiple customer classes have been covered in Ha, 1997a, Ha, 1997b and Ha, 2000, Benjaafar et al. (2010), de Vericourt and Karaesmen (2002), and Ioannidis (2011). Benjaafar and ElHafsi (2006), ElHafsi (2009), and Benjaafar et al. (2011) studied joint admission control and component production policy in a single product, multi-components, assemble-to-order system with multiple demand classes. Although they considered a two-stage production system (i.e., component production stage and assembly stage), the assembly process is assumed to be instantaneous. Saharidis et al. (2009) studied a joint production and admission control in a two-stage, single component, single product, make-to-stock production system where demands for component during a stockout period should be satisfied immediately from a subcontractor. In this paper, using a Markov decision process (MDP) model, we characterize the structure of the optimal admission and production control that states when to accept incoming customer orders and when to produce components under the discounted profit criterion. We identify the properties of the optimal policy under special cases and the monotonic impact of system parameters on the optimal policy. We show that there exist certain limits on the size of outstanding customer orders and component inventory level beyond which accepting an incoming order and producing a component can be never optimal for the average profit problem. We then present two heuristics: one uses two switching functions and the other uses two fixed thresholds for the control. Finally, we present numerical results which show the performance comparison between the optimal policy and two heuristics under different operating conditions of the system. The rest of the paper is organized as follows. In Section 2 we present modeling assumptions and problem formulation. Section 3 characterizes the structure of optimal production and admission control under the discounted profit criterion. In Section 4, we study the properties of the optimal policy under special cases. Section 5 presents a sensitivity analysis on the optimal policy. In Section 6, we extend the results to the average profit criterion. Section 7 reports the results of numerical experiment and the last section states conclusions

The primary goal of this paper is to investigate a model to jointly manage production and admission control for a two-stage supply chain with make-to-order and make-to-stock facilities. Using a Markov decision process framework, we characterized the structure of the optimal production and admission control by two monotone switching curves and showed that these curves are monotonically shifted as the revenue and rejection cost are changed. In addition, we examined the optimal control under the special conditions on problem parameters and identified certain limits beyond which accepting an incoming order and producing a component can be never optimal. With a understanding of the structure of the optimal policy, we present two types of heuristics. Admission and production decisions are dynamically managed by two switching functions in the first heuristic while it is done by static thresholds in the second heuristic. Through an extensive numerical experiment, we examined how much the dynamic control is effective and under what conditions it is much more favorable over the static control. Test results showed that the first heuristic is near optimal unless unit holding cost is larger than unit backlog cost. One of the major extensions to the current model is to consider setup penalties incurred when component production is switched on and off. The other direction of the future research is to consider a problem in which the make-to-stock system produces multiple types of components and only one type component is required for the make-to-order operation. In this case, the decision on production switching should be made in addition to the admission and production controls.