We consider single-item (r, q) and (s, T) inventory systems with integer-valued demand processes. While most of the inventory literature studies continuous approximations of these models and establishes joint convexity properties of the policy parameters in the continuous space, we show that...

The literature on inventory control discusses many methods to establish the level of decision parameters -like reorder levels or safety factors-, necessary to attain a prescribed service level. In general, however, these methods are not easy applicable: they often use time-consuming iterations,...

This paper investigates the delay experienced by retailers in a distribution system due to shortages at the central warehouse. Simple formulae are developed to estimate the mean and variance of this delay. The formulae are based on replacing the stochastic lead-time demand with a stochastic...

The Net Present Value (NPV) approach is considered to be the right approach to study inventory and production systems. But, approximate average cost (AC) approach is widely used in both practice and theory. However, the opportunity cost interpretation of AC framework is not that straightforward...

We consider a production–inventory system with product returns that are announced in advance by the customers. Demands and announcements of returns occur according to independent Poisson processes. An announced return is either actually returned or cancelled after a random return lead time. We...

The awareness of importance of product recovery has grown swiftly in the past few decades. This paper focuses on a problem of inventory control and production planning optimisation of a generic type of an integrated Reverse Logistics (RL) network which consists of a traditional forward...

The Net Present Value (NPV) approach is considered to be the right approach to study inventory and production systems. But, approximate average cost (AC) approach is widely used in both practice and theory. However, the opportunity cost interpretation of AC framework is not that straightforward...

We study an assemble-to-order inventory system. The stocks are held for components, with final products assembled only when customer orders are realized. Customer orders form a multivariate compound Poisson process, component replenishment leadtimes are constant, and demands in excess of...

The discounted continuous-review (R,Q) inventory model with continuous and stochastic demand is investigated. New optimality conditions are derived, clarifying the difference to the average-cost case, also graphically. Supported by depreciation theory, applied to the value of a setup, the...

We study a basic (r, q) system, in which the demand is a Poisson process and the leadtimes are independent, identically-distributed random variables. The key issue is the joint effect of the leadtime variance and the lot size q on performance. We know that, under a simple base-stock policy (with...