Marcel Kleijn

Inventory rationing in an ( s, Q ) inventory model with lost sales and two demand classes

Whenever demand for a single item can be categorised into classes of different priority, an inventory rationing policy should be considered. In this paper we analyse a continuous review (s, Q) model with lost sales and two demand classes. A so-called critical level policy is applied to ration the inventory among the two demand classes. With this policy, low-priority demand is rejected in anticipation of future high-priority demand whenever the inventory level is at or below a prespecified critical level. For Poisson demand and deterministic lead times, we present an exact formulation of the average inventory cost. A simple optimisation procedure is presented, and in a numerical study we compare the optimal rationing policy with a policy where no distinction between the demand classes is made. The benefit of the rationing policy is investigated for various cases and the results show that significant cost reductions can be obtained.

An overview of inventory systems with several demand classes

In this chapter we discuss inventory systems where several demand classes may be distinguished. In particular, we focus on single-location inventory systems and we analyse the use of a so-called critical level policy. With this policy some inventory is reserved for high-priority demand. A number of practical examples where several demand classes naturally arise are presented, and the implications and modelling of the critical level policy in distribution systems are discussed. Finally, an overview of the literature on inventory systems with several demand classes is given.

Stock Rationing in a Continuous Review Two-Echelon Inventory Model

In this paper we consider a 1-warehouse, N-retailer inventory system where demand occurs at all locations. We introduce an inventory model which allows us to set different service levels for retailers and direct customer demand at the warehouse. For each retailer a critical level is defined, such that a retailer replenishment order is delivered from warehouse stock if and only if the stock level exceeds this critical level. It is assumed that retailer replenishment orders, which are not satisfied from warehouse stock, are delivered directly from the outside supplier, instead of being backlogged. We present an analytical upper bound on the total cost of the system, and develop a heuristic method to optimize the policy parameters. Numerical experiments indicate that our technique provides a very close approximation of the exact cost. Also, we show that differentiating among the retailers and direct customer demand can yield significant cost reductions.

The break quantity rule's effect on inventory costs in a 1-warehouse, N-retailers distribution system

Abstract In this paper the effect of the break quantity rule on the inventory costs in a 1-warehouse, N -retailers distribution system is analyzed. The break quantity rule is to deliver large orders from the warehouse, and small orders from the nearest retailer, where a so-called break quantity determines whether an order is small or large. Under the assumptions that the stock at the warehouse can only be used to satisfy large orders, and that demand during the lead times is normally distributed, an expression for the inventory costs is derived. The objective of this paper is to provide insight into the effect of the break quantity rule on the inventory holding costs, and therefore we present extensive computational results, showing that in many cases the rule leads to a significant cost reduction.

Using break quantities for tactical optimisation in multistage distribution systems

In this chapter we discuss a tactical optimisation problem that arises in a multistage distribution system where customer orders can be delivered from any stockpoint. A simple rule to allocate orders to locations is a break quantity rule, which routes large orders to higher-stage stockpoints and small orders to end-stockpoints. A so-called break quantity determines whether an order is small or large. We present a qualitative discussion on the implications of this rule for the marketing process, and a qualitative and quantitative analysis on the implications for the transportation and inventory costs. Furthermore, we present a case study for a company that implemented a break quantity rule. Finally, in the last section the main results are summarised.

On the newsboy model with a cutoff transaction size

In this paper we analyse the effect of a cutoff transaction size on the average inventory cost in a simple newsboy setting. It is assumed that customers with an order larger than a prespecified cutoff transaction size are satisfied in an alternative way, against additional cost. For compound Poisson demand with discrete order sizes, we show how to determine the average cost and an optimal cutoff transaction size. Because the computational effort to calculate the exact cost is quite large, we also consider an approximate model. By approximating the distribution of the total demand during a period by the normal distribution one can determine an expression for the average cost function that solely depends on the cutoff transaction size. A significant advantage of this approximation is that we can solve problems of any size. The quality of using the normal approximation is evaluated through a number of numerical experiments, which show that the approximate results are satisfactory.

On the marginal cost approach in maintenance

In this paper we investigate the conditions under which the marginal cost approach of Refs. 1–3 holds. As observed in Ref. 4, the validity of the marginal cost approach gives rise to a useful framework of single-component maintenance optimization models, which covers almost all models used in practice. For the class of unimodal finite-valued marginal cost functions, we show that these optimization models are easy to solve.