The most commonly used penalty in branch and bound approaches to integer programming is the Driebeek--Tomlin penalty. It has been used successfully in solving fixed cost linear programs by Kennington and Unger and by Barr, Glover and Klingman. It is well known that the Driebeek--Tomlin penalty...

The branch and bound principle has long been established as an effective computational tool for solving mixed integer linear programming problems. This paper investigates the computational feasibility of branch and bound methods in solving convex nonlinear integer programming problems. The...

This paper considers the problem of optimally locating multi-activity facilities whose activity compositions are also to be determined. It is assumed that there are fixed costs associated both with establishing facilities and with including specific activities at the locations. This problem is...

Decomposable systems, decomposition and 0-1 integer programming techniques are reviewed relative to project selection problems. It is concluded that a heuristic procedure is a suitable way to handle such problems in organizational settings. A hierarchical multiperiod multidimensional model is...

This paper gives optimality conditions to obtain a priori precedence relationships among some of the jobs in a single machine scheduling problem so as to curtail the enumeration while using branch-and-bound technique. The objective is to minimize a quadratic (or generalized quadratic) penalty...

In this paper, we describe an integer programming algorithm for assigning tasks on an assembly line to work stations in such a way that the number of work stations is minimal for the rate of production desired. The procedure insures that no task is assigned to a work station before all tasks...

Given n items, each having a weight w_i, and a container of capacity W, the Subset-Sum Problem (SSP) is to select a subset of the items whose total weight is closest to, without exceeding, W. The paper presents a mixed approach (depth first search-dynamic programming) to the exact solution of the...

A new method for solving the corrugator trim problem is presented. This problem draws its name from the difficult task facing scheduling personnel in corrugator box plants each day: to determine the least-cost method of combining customer orders on the corrugator, where one of the major costs to...

An important, recurring problem in statistics involves the determination of strata boundaries for use in stratified sampling. This paper describes a practical method for stratifying a population of observations based on optimal cluster analysis. The goal of stratification is constructing a...

The conventional approach to the assembly line balancing problem assumes that the manufacturing methods to be used have been predetermined. However, in practice the design engineer has several alternatives available in the choice of processing, typically involving a trade-off between labor or...