Consider a distribution warehouse divided into reserve storage and staging areas. The warehouse stores a variety of items and receives orders for any combination of items. Goods are moved from reserve storage to staging area, where they are selected to fill the given orders. The problem is to locate items in the staging area in order to minimize the expected labor costs of order selection. Several years ago, J. L. Heskett [Heskett, J. L. 1963. Cube-per-order index—A key to warehouse stock location. Transportation and Distribution Management 3 (April) 27–31.] proposed a criterion, called the cube-per-order index (CPO) rule, for solving this problem. The criterion was justified heuristically by means of numerical examples. Recently [Kallina, C. 1976. Optimality of the cube-per-order index rule for stock location in a distribution warehouse. Working paper, American Can Company, March.], one of the authors has shown that the class of problems considered by Heskett can be formulated as a linear program, and that the CPO rule is in fact the optimal solution. In this present paper, we will (1) summarize some basic background material, (2) describe the computational steps for implementation of the CPO rule, and (3) discuss some practical conclusions gathered from experience in actually applying the rule to assist in warehouse layout.
Abstract. This paper is a survey of the principal results in the theory of linear programming in reflexive linear topological spaces. We begin with a brief review of the significant results for ordinary linear programming in Euclidean space. With this as a basis for comparison, for the general case we present a complete and self-contained account of three topics: (a) the classification scheme relating the properties of primal and dual programs, (b) the duality theory relevant to the problem of duality gaps between solutions of primal and dual programs, and (c) a "marginal cost" interpretation of solutions to the dual program.Introduction. The purpose of this paper is to give a complete and selfcontained account of the theory of linear programming in reflexive linear topological spaces. While some topological notions cannot be avoided, only those absolutely essential notions are used, and these are fairly elementary. The theory is developed from the appropriate generalization of the Farkas lemma, thereby providing an infinite-dimensional theory which closely parallels the finite-dimensional theory. The paper is written so as to facilitate this comparison.The extension of the theory of finite linear programs (finite number of variables, finite number of constraints) to the case of linear programs in more general linear spaces was initiated by Duffin in his fundamental paper in 1956 [7]. Duffin
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