Solving quadratic assignment problems with rectangular distances and integer programming

The problem considered involves the assignment of n facilities to n specified locations. Each facility has a given nonnegative flow from each of the other facilities. The objective is to minimize the sum of transportation costs. Assume these n locations are given as points on a two-dimensional plane and transportation costs are proportional to weighted rectangular distances. Then the problem is formulated as a binary mixed integer program. The number of integer variables (all binary) involved equals the number of facilities squared. Without increasing the number of integer variables, the formulation is extended to include “site costs” Computational results of the formulation are presented.     

Toward optimal bidding strategies

In this paper we investigate a form of rational behavior in response to an oligopoly pricing problem where only one buyer is involved. We investigate the problem from the standpoint of the seller who wants to maximize his gain from the transaction. In particular, we deal with the problem of one seller's response to an invitation to submit a sealed (i. e., noncooperative) bid to a government or other dominant purchasing agency for supplying a specified bundle of goods and services for which either (1) no other demand exists, or (2) the terms or quantities involved cannot, at least in the short run, be obtained from another source. Although treated from a normative standpoint, i. e., what bid the supplier should make, the paper also has implications for the buyer's behavior and oligopoly-monopsony pricing in a more general sense.     

Multiproduct lot-size scheduling with proportional product demands

In this paper we consider the multiproduct, multiperiod production-scheduling model of Manne under the assumption that, across products, demands are interrelated over time. When demand requirements are proportional we show that the solution has a specific structure determined by the ratio of setup to production-run time of each product. This structure holds for any length horizon and may permit a substantial (time) savings for column generation solution procedures.     

A heuristic network procedure for the assembly line balancing problem

Proposed is a Heuristic Network (HN) Procedure for balancing assembly lines. The procedure uses simple heuristic rules to generate a network which is then traversed using a shortest route algorithm to obtain a heuristic solution. The advantages of the HN Procedure are: a) it generally yields better solutions than those obtained by application of the heuristics, and b) sensitivity analysis with different values of cycle time is possible without having to regenerate the network. The rationale for its effectiveness and its application to problems with paralleling are presented. Computational experience with the procedure on up to 50 task test problems is provided.     

An approximative algorithm for the fixed charge problem

This paper describes an approximate solution method for solving the fixed charge problem. This heuristic approach is applied to a set of test problems to explore the margin of error. The results indicate that the proposed fixed charge simplex algorithm is capable of finding optimal or near optimal solutions to moderate sized fixed charge problems. In the absence of an exact method, this heuristic should prove useful in solving this fundamental nonlinear programming problem.     

Statistical quality control of information

This paper was written to promote interest by management and statistical quality control personnel in the current need for statistical quality control of information of all types. By way of illustration, a step by step procedure for implementing such control on computer files is presented. Emphasis has been placed on the sequencing of the system rather than the underlying techniques.     

A deterministic inventory model for reparable items

A reparable inventory system has two distinct inventories within it—the inventory of items ready-for-issue and the inventory of carcasses available for repair. A reparable item is usually rebuilt upon failure, but the scrap rate in the repair process is generally positive. Consequently, new items must be procured from time to time to replace those item: which were scrapped. The ready-for-issue inventory has two input sources—procurement and repair, This paper develops a deterministic inbentory model for the reparable inventory system, and determines the optimal procurement and repair quantities.