The impact of manufacturing flexibility on inventory investments in a distribution network consisting of a central depot and a number of local stockpoints is investigated. The lead time of outstanding orders in the pipeline of the central depot can be shortened by the use of flexibility. Stock levels are controlled by a periodic review echelon-order-up-to-policy under service level constraints.

1. Introduction

In this paper we consider the impact of manufacturing flexibility on inventory investment in a distribution network consisting of a central depot and a number

of local stockpoints. In practice manufacturing flexibility is exploited by planners that reduce the manufacturing throughput time of a particular production order in case the actual need date is earlier than was initially planned for. Such a reduction in throughput time can be realized by giving this order priority at bottleneck work stations. The rescheduling of orders by giving some orders priority may lead to the delay of other orders unless some excess capacity is available to prevent this happening. The amount of excess capacity needed to maintain due dates depends, among other things, on the frequency of rescheduling. In practice often implicit or explicit information is available about the frequency of rescheduling orders for particular products. Thereby, it is possible to make a trade-off between the frequency of rescheduling orders, which is a measure for manufacturing flexibility, and the capital investment in end products inventory.

To investigate the impact of this type of flexibility we consider a single-product/two-echelon model consisting of a central depot and multiple retailers. The retailers face stochastic demand. The demand for the product at the retailers in subsequent time periods is i.i.d. The lead time of orders from the retailers at the depot is constant, but may be different for different retailers. The lead time of orders from the depot at the manufacturer of the product is a constant [L.sub.0] but may be shortened as explained below. Both the depot and the retailers order according to periodic review echelon-order-up-to-policies. The review period is the same for both depot and retailers.

After ordering of both depot and retailers the situation may occur that the depot has insufficient stock to satisfy the retailer orders. In that case the depot attempts to make outstanding orders available immediately. This speeding up of orders already in the pipeline is exploited until the depot is able to satisfy the retailer orders or further speeding up is impossible. However, how many orders can effectively be made available without any time delay depends on an exogenous stochastic process. The assumption that the extent to which orders can be speeded up is governed by an exogenous stochastic process can be motivated as follows. The opportunity for expediting manufacturing orders depends on the overall workload, the available capacity, and agreements with other customers/depots. In reality a planner at the manufacturer must solve a complex multi-product, multi-period, finite capacity production planning and scheduling problem. The outcome of this planning process is neither observable nor controllable by the individual depot. Therefore, from an individual product's point of view, the outcome of this planning process seems to generate random opportunities for use of manufacturing flexibility. Based on past experience, i.e., historical data, the depot determines the probability that the order to arrive at the beginning of the next period can be made available instantaneously, the probability that the next two outstanding orders can be delivered instantaneously, etc. It is interesting to note that our description of the stochastic process governing manufacturing flexibility can be used to describe different strategies for allocating flexibility to individual products at the manufacturer.