Previous work dealt with the problems of nervousness in Material Requirements Planning (MRP) Systems when production schedules were modified to include setups which previously had not been scheduled. In this work we further examine nervousness and its cost. By modifying the setup costs used in the Wagner-Whitin algorithm, we develop a generalized solution methodology for dealing with situations in which new setups are added to the production schedule and existing setups are cancelled.
In this paper, we analyze how a supplier can structure the terms of an optimal quantity discount schedule. The vendor's challenge is to adjust his present pricing schedule to entice his major customer to increase his present order size by a factor of “K.” Optimal levels for “K” and the corresponding price discount are determined in order to maximize the supplier's incremental net profit and cash flow. Implementation issues are discussed and future research needs identified.
This paper concerns marginal cost pricing in a capacity expansion problem for the electric utility industry. We develop a characterization of equipment selection and marginal capital cost allocation based on an optimal capacity plan, in the context of either a finite, discretely distributed stochastic demand forecast, or in the deterministic case of multiple users identified by temporal considerations. In either case, a two stage linear program with recourse is shown to result. The main purpose of this paper is to conduct an analysis in order to determine a marginal cost pricing strategy for sharing capital costs given an optimal capacity plan, and to provide insightful economic interpretations. Our results also generalize a special case previously studied to demonstrate how a marginal cost pricing strategy may result in some of the capacity costs being borne by off-peak users.
We develop an indirect method to estimate utility and willingness to pay (WTP) for reductions in the risk of death at various ages. Using a life-cycle model of consumption, we assume that an individual sets his consumption level each year so as to maximize his expected lifetime utility. Alternative assumptions about opportunities for borrowing and annuities characterize two polar types of societies. In our Robinson Crusoe case, an individual must be entirely self-sufficient, and annuities are not available. In our perfect markets case, an individual can borrow against future earnings and purchase actuarially fair annuities; we show that under these assumptions WTP is the sum of livelihood (discounted expected future earnings) and consumer surplus. To illustrate our methods, we derive WTP for an average financially independent American man under plausible assumptions. The model is calibrated to 1978 earnings (e.g., $18,000 per year for men aged 45–54 with at least some income). In the Robinson Crusoe case, WTP increases from $500,000 at age 20 to a peak of $1,250,000 at age 40, and declines to $630,000 at age 60. In the perfect markets case, age variations are less pronounced; WTP is $1,050,000 at age 20, peaks at $1,070,000 at age 25, and declines to $600,000 at age 60. These results suggest that individuals value risks to their lives at several times the pro-rata share of their future earnings.
In many cities, a substantial fraction of calls for police service require more than one patrol car. We compare Green's multiple dispatch queueing model to several M/M/c-based approximations for multiple car dispatching that are obtained by adjusting the parameters. We found that none of the approximate models yields consistently reliable results under a broad range of conditions. The best approximations are produced by reducing the actual number of servers. Increasing the call rate gives the worst results.
An interactive method employing pairwise comparisons of attainable solutions is developed for solving the discrete, deterministic multiple criteria problem assuming a single decision maker who has an implicit quasi-concave increasing utility (or value) function. The method chooses an arbitrary set of positive multipliers to generate a proxy composite linear objective function which is then maximized over the set of solutions. The maximizing solution is compared with several solutions using pairwise judgments asked of the decision maker. Responses are used to eliminate alternatives using convex cones based on expressed preferences, and then a new set of weights is found that satisfies the indicated preferences. The requisite theory and proofs as well as a detailed numerical example are included. In addition, the results of some computational experiments to test the effectiveness of the method are described.
A risk assessment was performed to assist in the evaluation of equipment improvements for a chemical storage facility. The risk assessment was accomplished through the use of several different methodologies e.g., fault tree analysis, event trees, and risk perspective techniques. The result of the study was a new alternative for a chemical storage facility. This new alternative eliminated the requirement for a large storage facility and reduced the capital project cost by over 10 million dollars.
This note provides a brief comparison between a three-dimensional layout planning system recently described in Management Science (Johnson [Johnson, Roger V. 1982. SPACECRAFT for multi-floor layout planning. Management Sci. 28 (4, April) 407–417.]) and a similar system developed earlier (Cinar [Cinar, Unver. 1975. Facilities planning: a systems analysis and space allocation approach. Charles M. Eastman, ed. Spatial Synthesis in Computer-Aided Building Design. Wiley, New York, 19–40.]).
Multiobjective mathematical programming has been one of the fastest growing areas of OR/MS during the last 15 years. This paper presents: some reasons for the rapidly growing increase in interest in multiobjective mathematical programming, a discussion of the advantages and disadvantages of the three general approaches (articulation of the decision maker's preference structure over the multiple objectives prior to, during, or after the optimization) towards multiobjective mathematical programming, a nontechnical overview of many of the specific solution techniques for multiobjective mathematical programming, and a discussion of important areas for further research. The overview concentrates on those techniques which require an articulation of the decision maker's preference structure either during or after the optimization, since these are the areas where most of the recent research has been conducted. It differs from previous overviews in that, in addition to the timing of the elicited preference information, the techniques are also classified according to the types of decision variables contained in the model (i.e., only continuous decision variables, or at least some discrete decision variables). In addition, the types of preference information (e.g., a ranking of outcomes) required of the various techniques are also discussed.
S. L. Albin has described extensive simulations of queue behavior for a system with a single server and an arrival process that is a superposition of n renewal processes. The simulations show, among other things, that as n increases for a fixed traffic intensity ρ, the queue behavior approaches that of the M/M/1 system. The rate of convergence, however, becomes much slower as the traffic intensity ρ comes closer to 1. Several qualitative effects shown in the simulations are explained here. In particular it is shown that the approach to the M/M/1 system requires that n(1 − ρ) 2 ≫ 1.