No abstract

We consider the optimal lot size problem for multi-stage assembly systems where each facility may have many predecessors but only a single successor. Assumptions include constant continuous final product demand, instantaneous production, and an infinite planning horizon. Costs at each facility consist of a fixed charge per lot and a linear holding cost. Under the constraint that lot sizes remain time invariant, it is proven that the optimal lot size at each facility is an integer multiple of the lot size at the successor facility. This fact is used in the construction of a dynamic programming algorithm for the computation of optimal lot sizes. The algorithm exploits the concept of echelon stock [Clark, A. J., H. Scarf. 1960. Optimal policies for a multi-echelon inventory problem. Management Sci. 6 (4, July) 475-490; Clark, A. J., H. Scarf. 1962. Approximate solution to a simple multi-echelon inventory problem. Chapter 5. K. J. Arrow et al., eds. Studies in Applied Probability and Management Science. Stanford University Press, Stanford, California.].

A multi-stage assembly system is a special case of Veinott's general multi-facility system in that each facility may have any number of predecessors but at most a single successor. This paper presents two algorithms for computing optimal lot sizes in such systems with known time-varying demand. The first is a dynamic programming algorithm for which solution time increases exponentially with the number of time periods, but only linearly with the number of stages, irrespective of assembly structure. The second is a branch and bound algorithm intended for cases where the number of time periods is large but the structure is close to serial. Computational results are given and extensions considered.

DCPM is a method for formally considering the interaction between the scheduling and the planning phases of a project. Thus, if there are a number of competing methods of performing some of the jobs, each method having a different cost, a different time duration, and different technological dependencies, these possibilities are included in the project graph. Then in the scheduling phase, consideration is made of the effects of the alternate methods of performing tasks on the total cost of completing the project. The alternatives that minimize this cost are then selected. The same method can also be applied to the control of the project during its completion, to revise previous decisions in light of actual performance observed.

Problems having the mathematical structure of a quadratic assignment problem are found in a diversity of contexts: by the economist in assigning a number of plants or Indivisible operations to a number of different geographical locations; by the architect or industrial engineer in laying out activities, offices or departments in a building; by the human engineer in arranging the indicators and controls in an operators control room; by the electronics engineer In laying out components on a backboard; by the computer systems engineer in arranging information in drxan and disc storage; by the production scheduler in sequencing work through a production facility, and so on.In this paper we discuss several types of algorithms for solving such problems, presenting a unifying framework for some of the existing algorithms, and describing some new algorithms. All of the algorithms discussed proceed first to a feasible solution and then to better and better feasible solutions, until ultimately one Is discovered which Is shown to be optimal.In a subsequent paper we shall discuss our computational experience with a number of these algorithms.