Inventory Rationing in a Make-to-Stock Production System with Several Demand Classes and Lost Sales

Abstract

This paper considers the stock rationing problem of a single-item, make-to-stock production system with several demand classes and lost sales. For the case of Poisson demands and exponential production times, we show that the optimal policy can be characterized by a sequence of monotone stock rationing levels. For each demand class, there exists a stock rationing level at or below which it is optimal to start rejecting the demand of this class in anticipation of future arrival of higher priority demands. A simple queueing model is analyzed to compute the operating cost of a rationing policy. In a numerical study, we compare the optimal rationing policy with a first-come first-served policy to investigate the benefit of stock rationing under different operating conditions of the system.inventory/production, inventory rationing, dynamic programming/optimal control, applications

Technical Note—Optimal Structural Results for Assemble-to-Order Generalized M-Systems

“…Also, because component orders are not part of our system state, these can in effect be cancelled upon transition to a new state. Both of these assumptions are standard in the literature (see, for example, Ha 1997, Benjaafar and ElHafsi 2006, ElHafsi et al 2008.…”

“…Many papers dealing with the optimal policy characterization for Markovian inventory systems assume unitary component usage rates for products and unitary replenishment quantities for components, and therefore Assumption 1 is satisfied in these papers. See, for instance, Ha (1997Ha ( , 2000, de Véricourt et al (2002), Benjaafar and ElHafsi (2006), ElHafsi et al (2008), ElHafsi (2009), and Gayon et al (2009a, b). Even when replenishment batch sizes are different from individual product sizes, we believe that batch sizes could often be adjusted to be individual product sizes by negotiating with suppliers.…”

A Threshold Inventory Rationing Policy for Service-Differentiated Demand Classes

“…Our model formulation also differs from theirs in that we do not require their simplifying assumption that not more than one order is outstanding at any point in time. Ha (1997aHa ( , 1997b considers a similar rationing policy in the context of a single-item, maketo-stock, production system with two or more demand classes. Assuming Poisson demand and exponential production times, the optimal policy is characterized by a sequence of monotone and stationary rationing levels.…”

A Single-Product Inventory Model for Multiple Demand Classes

“…He shows that a stationary critical level policy is optimal. Ha (1997b) extends the study in Ha (1997a) by allowing backorders to occur. Vericourt et al (2000Vericourt et al ( , 2002 consider the multiple-demand class extension of the two-demand class study in Ha (1997a).…”

“…Ha (1997b) extends the study in Ha (1997a) by allowing backorders to occur. Vericourt et al (2000Vericourt et al ( , 2002 consider the multiple-demand class extension of the two-demand class study in Ha (1997a). They develop a characterization of the optimal policy for the backorders case with zero set-up costs and exponential lead-times.…”