(This article originally appeared in Management Science, January 1981, Volume 27, Number 1, pp. 1--18, published by The Institute of Management Sciences.) One of the most computationally useful ideas of the 1970s is the observation that many hard integer programming problems can be viewed as...

Recently there has been considerable interest in the average-case performance of heuristics. This paper pursues that interest, where it concerns sequencing and packing problems. In particular, we survey the methods that have been used to obtain formal probabilistic analyses of heuristics for...

The minimum spillage sequencing problem, which arises in real-time satellite signal data processing, requires a set of numbers to be arranged so as to minimize the "overflow" of the partial sums above an upper bound. We subject several heuristics to worst-case analysis, average-case analysis,...

We describe a family of heuristics to solve combinatorial problems such as routing and partitioning. These heuristics exploit geometry but ignore specific distance measures. Consequently they are simple and fast, but nonetheless fairly accurate, and so seem well-suited to operational problems...

A new approximate algorithm for multidimensional zero-one knapsack problems with all positive coefficients is presented. The procedure is controlled by three parameters which affect the tradeoff between solution quality and computation time and whose values are set by the users. For 48 test...

This paper addresses a nonpreemptive single machine scheduling problem where all jobs have a common due date and have zero ready time. The scheduling objective is to minimize mean squared deviation (MSD) of job completion times about the due date. This nonregular measure of performance is...

In this survey paper we discuss the development of the simple assembly line balancing problem (SALBP); modifications and generalizations over time; present alternate 0-1 programming formulations and a general integer programming formulation of the problem; discuss other well-known problems...

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...