On the (R,s,Q) inventory model when demand is modelled as a compound Bernoulli process

In this paper we present an approximation method to compute the reorder point s in an (R, s, Q) inventory model with a service level restriction. Demand is modelled as a compound Bernoulli process, i.e., with a fixed probability there is positive demand during a time unit; otherwise demand is zero. The demand size and the replenishment leadtime are random variables. It is shown that this kind of modelling is especially suitable for intermittent demand. In this paper we will adapt a method presented by Dunsmuir and Snyder such that the undershoot is not neglected. The reason for this is that for compound demand processes the undershoot has a considerable impact on the performance levels, especially when the probability that demand is zero during the leadtime is high, which is the case when demand is lumpy. Furthermore, the adapted method is used to derive an expression for the expected average physical stock. The quality of both the reorder point and the expected average physical stock, calculated with the method presented in this paper, rum out to be excellent, as has been verified by simulation

Setting planned leadtimes in customer-order-driven assembly systems

We study an assembly system with a number of parallel multistage processes feeding a multistage final assembly process. Each stage has a stochastic throughput time. We assume that the system is controlled by planned leadtimes at each stage. From these planned leadtimes the start and due times of all stages can be derived. If a job finishes at a particular stage and has to wait before the start of the next job(s), a holding cost proportional to the waiting time is incurred. A penalty cost proportional to the lateness is incurred when the last stage of the final assembly process finishes after its due time. The objective is to determine planned leadtimes for each individual stage, such that the expected cost of a customer order is minimized.\u3cbr/\u3e \u3cbr/\u3eWe derive the recursive equations for the tardiness and earliness at all stages and an exact expression for the expected cost. We discuss the similarity between these expressions and those for serial inventory systems. Based on this observation and a conjecture related to the generalized Newsvendor equations, we develop an iterative heuristic procedure. Comparison with a numerical optimization method confirms the accuracy of the heuristic. Finally, we discuss an application of the model to a real-life case, showing the added value of a system-wide optimization of planned leadtimes compared to current practice.\u3cbr/\u3

Approximations for the waiting time in (s,nQ)-inventory models for different types of consolidation policies

In many practical situations the coordination of transportation management and inventory management may lead to considerable cost reductions. Transportation management includes the application of different types of shipment consolidation policies. Shipment consolidation takes into account the logistics strategy of combining two or more shipment orders to optimize transportation. When the shipment consolidation policy changes, the shipment lead time changes as well and if the lead time changes, the inventory policy needs to be re-evaluated, since changing lead times affect customer service. In this paper the lead time comprises two elements: waiting time due to order consolidation and the shipment time. The lead time is an important parameter for inventory management. We derive approximations for the lead time behaviour in (s,nQ) models where the items are consolidated according to different types of consolidation policies