Comments and clarifications about paper [Wilbrecht, J. K., W. B. Prescott. 1969. The influence of setup time on job shop performance. Management Sci. 16 (4, December).].

A multi-stage linear program is defined with linking variables that connect consecutive stages. Optimality conditions for the composite problem are partitioned into local and linking conditions. When the Dantzig-Wolfe decomposition scheme is applied with the first stage as the master, the subproblem is also a MLP with one' less stage. The same decomposition is then applied to the subproblem, giving rise to a nested decomposition scheme, in which each stage acts as a master for the following stage and a subproblem for the preceding. Optimizing a single stage problem results in satisfying the “local” optimality conditions. A very general rule is given for selecting the next subproblem to optimize, and finite convergence to a solution satisfying all linking conditions is demonstrated. Procedures for extracting the optimal primal solution at the end of the main algorithm and for initialization are given. Particular rules for selecting the next subproblem and for generating additional proposal vectors are discussed. Finally, it is shown how a variety of problems may be restructured as multi-stage linear programs to which this algorithm may be applied, and some computational experience is reported.

This paper attempts to provide an economic framework in which various job shop dispatching rules can be evaluated. It shows the relative advantage of shortest processing time rules in gaining increased utilization of the shop facilities and the relative advantage of minimum slack rules in meeting promise commitments. The paper graphs each of four kinds of costs (costs of long promises, costs of missed promises, costs of idle resources, and costs of carrying inventory) against two independent variables, the amount of work-in-process inventory and the tightness of the promises. It demonstrates the kind of cost structure which causes a minimum slack rule to be superior to a shortest processing time rule.

This paper presents results of research into computer simulation of a mixed-model assembly line. The problem to be solved is described and the mathematical model of the line is presented. Algorithms that provide acceptable sequences of product models in various conditions are given, and results of simulator experiments are analysed and discussed. In the final section of the paper conclusions are drawn from the results of the work, and the general usefulness of simulation for assembly work is considered.

In Part I of this paper, we develop an algorithm for finding planning horizons for the deterministic production smoothing problem when all demand must be met from regular production, under rather general assumptions for the production, production smoothing, and holding cost functions. (In Part II, planning horizons will be developed when the model is extended to include backlogging and overtime.) The techniques developed here are essentially forward-looking and marginal-cost-balancing in nature, rather than total-cost-minimizing and backward-looking such as dynamic programming, or total-cost-minimizing and omni-looking in nature such as linear programming. The fact that the planning horizon theorems do not depend on having discount rates less than one illustrates that the approach developed here is fundamentally different from ordinary infinite horizon dynamic programming techniques. The algorithm is “user oriented” in the sense that only a small amount of forecasting work and computation ordinarily must be done to determine the horizon; the nature of the algorithm also makes the exact dependence of the horizon on the forecast clear for sensitivity analysis. Firms facing a seasonal demand pattern will often find that the horizon occurs within the first several periods after the peak period if there is a sufficient enough drop in demand afterwards. This result complements the findings of Modigliani and Hohn and provides insight into the nature of the optimal policy for stochastic planning problems.

Most of the procedures that have been developed to find solutions to the single-machine, multi-product lot scheduling problem depend on judgment to define the desirable frequencies of production for the products. In this paper we describe an iterative procedure for directly determining near optimal frequencies of production for the products and the associated fundamental cycle time which, in many cases, can be used directly for constructing production schedules. In cases where feasible schedules cannot be constructed using the values from the iterative procedure, the procedure provides a basis for changing the production frequencies and the fundamental cycle time to obtain feasible schedules.

In this paper we are concerned with imposing constraints directly on the admissible majority decisions so as to insure transitivity without restricting individual preference orderings. We demonstrate that this corresponds to requiring that majority decisions be confined to the extreme points of a convex polyhedron. Thus, transitive majority decisions can be characterized as basic solutions of a set of linear inequalities. Through the use of a majority decision function (which is not restricted to be linear) it is shown that constrained majority rule is equivalent to an integer programming problem. Some special forms of majority decision functions are studied including the generalized l p norm and an indicator function. Implications of an integer programming solution, including alternate optima and post optimality analysis, are also discussed.

The paper describes a method of supplementing network analysis by taking a global view of project planning. The sequencing constraints normally found in a project are condensed into restrictions on the quantity of work performed by any stage in its duration. The objective is to minimise cost, where cost is considered to vary both with project duration and with the instantaneous rate of change of resource. Variational methods are used to produce optimal work-time and resource-time project profiles. The form of some constraints likely to arise in a project is considered, and the best profiles subject to certain constraints are derived and discussed. The techniques have been used to obtain a lower bound to project cost and to estimate ideal project duration.

A maximum entropy approach leads to a truncated normal distribution for the activity time in PERT analysis. Three different methods of fit are discussed, and a comparison with the standard assumption of a Beta distribution is made. The results suggest new ways of performing the PERT analysis.

A new test for suboptimal actions in discounted Markov decision problems is proposed. The test is discussed in relation to that of MacQueen and Porteus and preferred computational schemes are given.