Critical level policies in lost sales inventory systems with different demand classes

We consider a single-item lost sales inventory model with different classes of customers. Each customer class may have different lost sale penalty costs. We assume that the demands follow a Poisson process and we consider a single replenishment hypoexponential server. We give a Markov decision process associated with this optimal control problem and prove some structural properties of its dynamic programming operator. This allows us to show that the optimal policy is a critical level policy. We then discuss some possible extensions to other replenishment distributions and give some numerical results for the hyperexponential server case

Linear integrated location-inventory models for service parts logistics network design

We present two integrated network design and inventory control problems in service-parts logistics systems. Such models are complicated due to demand uncertainty and highly nonlinear time-based service level constraints. Exploiting unique properties of the nonlinear constraints, we provide an equivalent linear formulation under part-warehouse service requirements, and an approximate linear formulation under part service requirements. Computational results indicate the superiority of our approach over existing approaches in the literature

On two-echelon inventory systems with Poisson demand and lost sales

We derive approximations for the service levels of two-echelon inventory systems with lost sales and Poisson demand. Our method is simple and accurate for a very broad range of problem instances, including cases with both high and low service levels. In contrast, existing methods only perform well for limited problem settings, or under restrictive assumptions.\u

Using imperfect advance demand information in ordering and rationing decisions

Cataloged from PDF version of article.In this paper, we consider an inventory problem with two demand classes having different priorities. The appropriate policy of rationing the available stock, i.e. reserving some stock for meeting prospective future demand of preferred customers at the expense of deliberately losing some of the currently materialized demand of lower demand class(es), relies on the estimation of the future demand. Utilizing current signals on future demand, which we refer to as imperfect advance demand information (ADI), decreases uncertainty on future demand and may help to make better decisions on when to start rejecting lower class demand. We develop a model that incorporates imperfect ADI with inventory ordering (replenishment) decision and rationing available stock. In a two-period setting, we show some structural properties, solve the rationing problem, and propose solution methods based on Monte Carlo simulation for the ordering problem. We conduct numerical tests to measure the impact of system parameters on the expected value of imperfect ADI, and provide useful managerial insights. (C) 2009 Elsevier B.V. All rights reserved

A Single-Product Inventory Model for Multiple Demand Classes

We consider a single-product inventory system that serves multiple demand classes, which differ in their shortage costs or service level requirements. We assume a critical-level control policy, and show the equivalence between this inventory system and a serial inventory system. Based on this equivalence, we develop a model for cost evaluation and optimization, under the assumptions of Poisson demand, deterministic replenishment lead-time, and a continuous-review (Q, R) policy with rationing. We propose a computationally-efficient heuristic and develop a bound on its performance. We provide a numerical experiment to show the effectiveness of the heuristic and the value from a rationing policy. Finally, we describe how to extend the model to permit service times, and to embed within a multi-echelon setting

Finding optimal policies in the (S - 1, S ) lost sales inventory model with multiple demand classes

This paper examines the algorithms proposed in the literature for finding good critical level policies in the (S-1,S) lost sales inventory model with multiple demand classes. Our main result is that we establish guaranteed optimality for two of these algorithms. This result is extended to different resupply assumptions, such as a single server queue. As a corollary, we provide an alternative proof of the optimality of critical level policies among the class of all policies