Many manufacturing firms produce component parts both for assembly into new products and to meet orders for spare parts. An inventory model for this situation would involve two types of demands: probabilistic demand as spares and deterministic (or scheduled) withdrawals as components for...

In this paper we present a heuristic method, based on Lagrangian relaxation, for multilevel lot-sizing when there is a single bottleneck facility. A series of Lagrangian relaxations (one for each item in the product structure) is imbedded in a branch and bound procedure. The objective is to find...

In this Note we present an alternative formulation to the MRP lot sizing model of Steinberg and Napier (SN) (Steinberg, E., H. A. Napier. 1980. Optimal multi-level lot sizing for requirements planning systems. Management Sci. 26 (2) 1258--1271.). The alternative is more parsimonious and the...

In this Note, we address the issue of safety stock considerations in an MRP environment through the use of a single identical component as a replacement for a set of multiple components. We indicate where the results reported by Collier (Collier, David A. 1982. Aggregate safety stock levels and...

Customer service has assumed strategic importance in most manufacturing environments. Corporate reputations often depend on how reliably promised lead times are met. A goal of filling orders within a service window of T time units is often encountered in practice. This goal ignores the...

This paper introduces a line of research on capacity-constrained multi-stage production scheduling problems. The first section introduces the problem area as it arises from a failure of MRP systems. Then a review of the literature and an analysis of the type of problems that exist are presented...

This research focuses on the effect of setup time on lot sizing. The setting is the Capacitated Lot Sizing Problem (the single-machine lot sizing problem) with nonstationary costs, demands, and setup times. A Lagrangian relaxation of the capacity constraints of CLSP allows it to be decomposed...

This paper concerns the modeling of low inventory lines. Currently, most models assume that processing times are independent. We consider the differences in behavior of workers in low- and high-inventory production lines. Using a laboratory experiment we show that workers speed up when they are...

In practice, most multi-echelon inventory systems are managed using adaptations of single location methods. This paper shows that such methods can be dramatically inferior to methods designed to take advantage of a system's structure. This is especially true in repair parts inventory systems...

This paper investigates a multi-item, multi-level production scheduling problem with linear costs and production and inventory constraints at one key facility. Two multi-item problems---one in which the constraint was on shipping capability and one in which there was a final stage bottleneck...