This note considers two single-machine multi-product scheduling problems with deterministic demand that have appeared in the management science literature: the economic lot scheduling problem and the joint replenishment problem. These problems are shown to be closely related. In addition, they are shown to be nearly identical to a one-warehouse, several-retailer inventory problem. As a consequence, any algorithm which solves one of the problems also solves the other two problems.

An algorithm is given for computing the serial correlations of the waiting time, and of the time in system, for successive customers in a GI/G/1 queue. The method depends on representing the inter-arrival time distribution in terms of a process in class K r (i.e., distributions with a rational Laplace transform). Thus Erlang, hyperexponential and weighted sum-of-Erlang arrivals are treated exactly, and approximate results can be found for other distributions. Computed correlation functions for some Erlang/Erlang systems are presented as examples.

In Ohio, as well as several other states, annual unemployment compensation payments paid by a corporation can be minimized by solving a set partitioning problem which has all possible nonzero binary columns. The scenario, along with the model and an illustration are given. Some solution techniques and actual results, taken from a consulting effort, for a few Northeast Ohio corporations are also mentioned.

In this paper we show that for a finite Markov decision process an average optimal policy can be found by solving only one linear programming problem. Also the relation between the set of feasible solutions of the linear program and the set of stationary policies is analyzed.

Comments about Gitlow, H. S. 1976. A methodology for determining the optimal design of a free standing abortion clinic. Management Sci. 22 (12, August) 1289–1298.

Stochastic Dominance (SD) rules are playing an increasingly prominent role in the theory of choice under uncertainty. Its application areas include stock selection, capital budgeting, etc. The theory is important because it generates decision rules which are more generally applicable to these problems than are the traditional two parameter (mean-variance) rules employed in much of financial decision making. While they are theoretically sound, the SD rules are, until now, hard to implement because they require comparisons of probability distributions over their entire ranges. In this paper, we develop an algorithm that should remedy this situation. It exploits recent theoretical results from the Stochastic Dominance literature as well as several computational techniques to efficiently determine the SD admissible set of alternatives, which contains the optimal choices for all decision makers whose preferences satisfy reasonable economic criteria. As compared with the fastest code currently available, an implementation of our algorithm significantly reduces the computational time required to solve a problem of considerable size. These results indicate that, as a management tool, this algorithm can be applied to choice problems not previously thought solvable. For example, in the portfolio choice problem, which has an infinite choice set, the algorithm can provide reasonable approximations to the true set of optimal choices via the use of a suitably fine enough grid on the space of portfolios.

A general model of participation in a transfer program is developed and applied to data obtained from housing allowance programs in Brown County, Wisconsin and St. Joseph County, Indiana. Estimates of the parameters of the model are obtained from pooled data for the two sites, and the fitted model is used to estimate the equilibrium level of participation and the time required to reach it. The model predicts that the participation rate three years after the housing allowance program's start-40 percent-will rise to a maximum of 51 percent when equilibrium is reached. The model also predicts that 95 percent of the equilibrium level will be reached 5.5 years after the program's start. Although below expectations, the 51 percent equilibrium participation rate is not low compared with other government transfer programs; it is about the same as New York City's welfare and food stamp programs, for example. The model provides valuable insights into the dynamics of government transfer programs. In particular, it shows that the equilibrium participation rate equals the ratio of the rate at which eligible nonparticipants enroll in the program (enrollment rate) to the sum of the enrollment rate and the rate at which participants leave the program (termination rate). If the enrollment and termination rates are equal to each other, as they tend to be in the transfer programs studied, then in equilibrium at a given time only 50 percent of the eligible households will be program participants. The analysis suggests that the most practical way to increase participation is to increase the enrollment rate.

This paper addresses the time management problem confronted by sales representatives. The sales representative planning his itinerary must decide the best way to ration time among the accounts comprising his territory. The time management problem is formulated as an integer program whereby each admissible call frequency for each account is represented by a zero-one decision variable. A branch-and-bound integer programming algorithm for this problem is presented. The algorithm is unique in that two integer programming formulations of the problem are used simultaneously in the search procedure and an approximation-cum-relaxation is evaluated at each branch in the search. Computational testing of the algorithm shows that it can solve many realistic time management problems optimally in fractions of a second.

This paper is principally concerned with the development of a competitive pricing model aimed at predicting the impact of a vector of price increases on sales of a given brand of a low priced, frequently purchased product. The model has its base in a set of assumptions describing the purchasing behavior of the individual consumer. A method for testing the model against empirical data is described and illustrated. The competitive pricing model is found to perform somewhat better than a simple regression model in the application reported.

This paper considers the problem of locating capacitated facilities to meet customer demands. The objective of the problem considers both a bottleneck transportation cost and a total cost of opening facilities. The structure of the problem is similar to that of the total cost capacitated facility location problem. Problems with a bottleneck objective function are solved via a Lagrangean relaxation. An implicit enumeration algorithm is developed to solve the relaxed problem. After a feasible facility configuration is selected, the resulting allocation problem is a bottleneck transportation problem. Special attention is given to the dual of the bottleneck transportation problem to aid the branching and fathoming steps of the solution procedure. Computation results are presented for several test problems.