A Dynamic Programming Approach to Sustainability

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. INTRODUCTION Many interesting and important optimization problems require the determination of a best order of performing a given set of operations. This paper is concerned with the solution of three such sequencing problems: a scheduling problem involving arbitrary cost functions, the traveling-salesman problem, and an assembly-line balancing problem. Each of these problems has a structure permitting solution by means of recursion schemes of the type associated with dynamic programming. In essence, these re-cursion schemes permit the problems to be treated in terms of combinations, rather than permutations, of the operations to be performed. The dynamic programming formulations are given in ?1, together with a discussion of various extensions such as the inclusion of precedence constraints. In each case the proposed method of solution is computationally effective for problems in a certain limited range. Approximate solutions to larger problems may be obtained by solving sequences of small derived problems, each having the same structure as the original one. This procedure of suc-cessive approximations is developed in detail in ?2 with specific reference to the traveling-salesman problem, and ?3 summarizes computational ex-perience with an IBM 7090 program using the procedure.