راه‌اندازی سیستم کنترل موجودی با شروع تقاضا در زمان معین

This paper considers a single-echelon, continuous review, inventory system with a warehouse facing compound Poisson customer demand. The replenishment lead-time is constant. Demand that cannot be met directly is backordered. There are standard linear holding and backorder costs but no set-up or ordering cost. It is assumed that the demand process starts at a certain given time. Consequently, before the demand starts, the lead-time demand is lower than in steady state. This affects the optimal ordering policy. We derive the optimal ordering policy under these assumptions.

A standard assumption in stochastic inventory models is that we have reached steady state. The optimal policy is therefore only directly applicable under this assumption. However, there is normally also an initiation problem when starting to sell a new item. It may be that the company announces officially that it starts to sell a new item at a certain date. Then there is no demand before that date. In this paper we consider such a situation. The stochastic demand in the form of a compound Poisson process starts at a certain time denoted time 0. Otherwise all assumptions are standard. There are holding and backorder costs per unit and unit time. There is no set-up or ordering cost so there is no advantage to order in batches. The replenishment lead-time is constant. Several previous papers have dealt with related initiation problems in connection with inventory control. One such situation, considered in several papers, is when demand cannot be satisfied until a batch is delivered, there is no initial stock, and the production rate is finite. It is then, in general, optimal to use smaller initial batch quantities so that demand can be satisfied earlier. Examples of models dealing with this aspect are Axsäter (1988), Ding and Grubbström (1991), and Grubbström and Ding (1993). Axsäter (in press) considers a related situation where the forecasts are improving. It turns out that this will also affect the initial batch quantities. Other reasons to use different initial batch quantities can be learning and forgetting effects, which change the production rate. See e.g., Elmaghraby (1990) and Klastorin and Moinzadeh (1989). This paper is organized as follows. Section 2 describes the considered problem in detail. We derive the optimal policy in Section 3. Finally, we give a few concluding remarks in Section 4.

In this paper a transient inventory control problem has been considered. The stochastic demand process starts at a certain given time. Otherwise all assumptions are standard. There is a given replenishment lead-time. The costs considered are holding and backorder costs but no set-up or ordering cost. It is rather obvious that the order-up-to level should be lower before the demand starts. We have demonstrated that the optimal ordering policy is a time-varying order-up-to policy, which is easy to determine.