Solving the Installation Scheduling Problem Using Mixed Integer Linear Programming

for installing a large number of sizes and types of items (e.g., machines) over time so as to optimize some measure (e.g., initial capital investment), subject to various resource constraints. Examples of this problem are scheduling the installation of point-of-sale terminals in supermarket and retail chains, and teller terminals in banks. We have formulated the installation scheduling problem as a mixed integer linear program and developed a computer code for solving the model. By using techniques for exploiting the special structure of the model, our formulation allows rather quick solution times. The installation scheduling problem is often a difficult aspect of capital investment programs. Simply stated, the installation scheduling problem involves finding an orderly schedule for installing a large number of systems of different sizes and types over time so as to optimize some measure (e.g., initial capital investment), subject to various resource constraints. Examples of this problem are scheduling the installation of point-of-sale terminals in supermarkets and retail stores, and teller terminals in banks. We have formulated the installation scheduling problem as a mixed integer linear program and developed a computer program, the Installation Optimization System (IOS), for solving the model. IOS uses IBM'S mixed integer linear programming system MIPi370 as a subroutine. Because of special structure in the model, our formulation allows rather quick solution times, thus avoiding the usual criticism of integer linear programs that they require excessive computational effort. We will first give a detailed description of the installation scheduling problem. Next we will present our mixed integer programming formulation of the problem. We will then show how the Copyright 1978 by International Business Machines Corporation. Copying is perrnit-ted without payment of royalty provided that (1) each reproduction is done without alteration and (2) theJournal reference and IBM copyright notice are included on the first page. The title and abstract may be used without further permission in computer based and other information-service systems. Permission to republish other excerpts should be obtained from the Editor.