تصمیمات موجودی و سفارش معوق تاکتیکی برای سیستم های با عملکرد تولید قابل پیش بینی

We consider a manufacturing system with stochastic demand and predictable production yield. The manufacturer has predetermined prices and limited production capacity in each period. The manufacturer also has the option to save some inventory for future periods even if there is demand in the current period. The demand that is not met is lost or may be backordered for only one period. Our objective is to maximize the expected profit by choosing optimal produce-up-to level View the MathML source(Yt¯⁎), save View the MathML source(St⁎) and backorder quantities View the MathML source(Bt⁎) in each period t . We formulate this problem as a Markov Decision Process where the state of the system is represented by the net inventory and the yield rate. We show that a modified order-up-to policy View the MathML source(Yt¯⁎,St⁎,Bt⁎) is optimal in each period t. We also perform computational analysis to examine the effects of production yield on the optimal decisions.

In modern production systems, due to highly competitive markets, it is extremely essential to follow and optimize all stages of production. From raw material procurement to customer delivery, all processes have to be designed and carried out very carefully. Hence, a vast number of studies were conducted on supply chain systems, many of which are about inventory control systems. Inventory related costs constitute a significant portion of total supply chain costs explaining the particular interest in inventory problems. Demand uncertainty is one of the main problems faced in inventory systems, and the prevalent tradeoff is between lost (or backordered) sales and inventory holding costs. Almost all inventory management strategies are developed to minimize costs by controlling this tradeoff. In traditional inventory control systems, the manufacturer meets the demand with all products at hand. However, sometimes it may be more profitable not to sell all items available and allow lost sales. That is especially true for systems with varying prices and production costs. Rationing policies have been introduced as alternative inventory control policies to consider this fact. With these policies, the manufacturer has the option to reserve some of the products for future periods even if it is possible to sell these items in the current period. In this study, we consider a manufacturer with production capacity restrictions that produces a single item to serve a single customer class. The manufacturer has the option to save some inventory for future use and backorder some demand to be met in the following period. The prices for all periods are set at the beginning of the time horizon. However, these prices are not known by the customers beforehand. Hence, the customers do not act tactically. This is a general assumption considered in recent studies on rationing such as Federgruen and Heching (1999), Chan et al. (2006), and Duran et al. (2007). Different than the previous studies, there is a predictable production yield rate in each period in our study. In each period, the manufacturer has to decide how much to produce, save and backorder. Our policies may be adopted successfully by a manufacturer introducing a new genuine product to the market. In such a system, the manufacturer is the sole monopolistic supplier and can decide prices over a time horizon. There are no substitutes and customers may accept backordering for a limited time. Also, the firm may reserve products for future use if there are restrictions such as capacity deficiency. Change in the production yield and production costs can be forecasted as they are affected by the learning effect and seasonality. In this framework, we focus on the characterization of the optimal inventory policy and the corresponding production quantities. As a real life example, we can consider the time Apple introduced iPhone to the market. Before the product launch, the introductory price and probably prices for the following few months were already decided by the firm. Introductory price was planned to be a bit higher than the following period prices since people had waited for the product for months already and they were much more eager to buy initially. Also, they easily accepted backordering. It is obvious that customers will accept backordering up to a specific time, for example one month. Last, the firm probably had a production yield trend affected by the learning effect as we have in our model. Our findings indicate that using tactical instruments that we discuss (saving inventory for future demand and backordering demand to satisfy in the future) may provide substantial benefits to the companies, especially when the prices are nonstationary, and the capacity is limited due to physical constraints and imperfect production processes. In such settings, firms should allocate their limited production to customers considering the effects of changes in their costs and prices through time. We believe that such environments are frequently observed, especially in new product launches. Our computational analysis reveals that the improvement due to these instruments may exceed 25% when compared to the traditional inventory management policies. However, it should be noted that the success of tactical inventory management depends heavily on the firm's ability to forecast the prices/costs and production capabilities for the planning horizon. The remainder of this study is organized as follows. In Section 2, we review the related literature and discuss recent studies about rationing and yield. We introduce and analyze our model in Section 3. In 4 and 5, we discuss save-inventory and backlog-demand models, respectively. We discuss our findings from computational analysis in Section 6 and share some insights. Finally, we present our findings briefly and present some extension ideas in Section 7.

In this study we focused on a single-item, multi-period production system with limited capacity and predictable production yield. The manufacturer has the option to refuse part of the demand even when there is inventory on hand. This strategy is referred as discretionary sales and is beneficial when costs and prices are variable throughout the planning horizon. The manufacturer also has the option to backlog demand for one period. Demand across periods is assumed to be independent and unsatisfied demand that is not backlogged is lost. Prices are assumed to be predetermined and not known by the customers before each period. The manufacturer has to decide optimal production, reserve and backorder amounts in each period. We analyze the profit-to-go functions and show that the optimal policy is of a modified order-up-to type. This optimal policy is characterized by three parameters View the MathML source(Y¯t⁎,St⁎,Bt⁎) where View the MathML sourceYt¯⁎ is the produce-up-to level, View the MathML sourceSt⁎ is the reserve-up-to and View the MathML sourceBt⁎ is the backlog-up-to levels in period t. We prove that the reserve and backlog decisions cannot be positive at the same period. Hence, we have two candidate policies to be optimal; save-inventory policy and backlog-demand policy and in each period the better one is chosen. We analyze and present how the optimal policy is affected by changes in the production yield. The production yield of the current period is shown to have no impact on the optimal policy for the current period. On the other hand, in the save-inventory strategy the optimal reserve decision is non-increasing while in the backlog-demand strategy the optimal backlog decision is non-decreasing in the production yield of the following period. The production decision is non-increasing for both strategies. There are some potential extensions we suggest for future research. One may consider random production yield and analyze how the policies are affected. Random capacity limits may be included to the model as some industries have unpredicted capacities due to production line problems. Another extension of our study may allow backlogged items to be satisfied until the end of the time horizon. Finally, dynamic pricing decisions may be incorporated into the model as well.