Abstract: This paper presents an approximate procedure for computing selected performance characteristics of an urban emergency service system. Based on a recently developed hypercube queuing model, the procedure requires for N servers solution of only N simultaneous equations, rather than 2N as in the exact model. The procedure relies on the theory of M/M/N queues in which servers are selected randomly and without replacement until the first available free server is found. The underlying model is intended for analyzing problems of vehicle location and response district design in urban emergency services, includes interdistrict as well as intradistrict responses, and allows computation of several point-specific as well as area-specific performance measures.

Abstract: This paper deals with the problem of computing optimal ordering policies for a single product with a lifetime of exactly m periods. Costs are charged against ordering, holding, shortages, and out-dating. To take explicit account of the perishability, we substitute a cost to be incurred at the time of outdating. The functional equation approach of dynamic programming is used to extend this model to the multiperiod case, and the structure of optimal ordering policies is analyzed.

Abstract: Marketing managers make decisions about price, advertising, promotion, and other marketing variables on the basis of factual data, judgments, and assumptions about how the market works. BRANDAID is a flexible, on-line model for assembling these elements to describe the market and evaluate strategies. This paper motivates the model and presents its mathematics. The structure is modular so that individual decision areas can be added or deleted at will. The model is of the aggregate response type, in which decision variables relate closely to specific sales performance measures. The major submodels are advertising, promotion, price, salesmen, and retail distribution. The advertising submodel employs a long-run sales response to advertising function and a linear lag process. Promotional effects are built up from a characteristic time pattern for the type of promotion and a response curve. Salesman affect sales through a response process structurally similar to that for advertising. Retail distribution variables are intermediaries that the company affects and that in turn affect customer response. Submodel outputs combine multiplicatively. Competition enters in a modular, symmetric way through a matrix of competitive coefficients that determine the source of sales for each brand as it seeks to increase its market position.

Abstract: Suppose we have n jobs that arrive simultaneously to be processed on a continuously available machine that can handle only one job at a time. Each job has a fixed processing time and a cost function that is nondecreasing in its finishing time. We want to find a schedule that minimizes total costs. After reviewing the relevant work on this problem, we present a new algorithm for a general cost function. The algorithm is tested for the well known case of a weighted tardiness criterion.

Abstract: This paper develops a formulation of the one-dimensional trim problem when there is a fixed charge associated with using a cutting pattern. The purpose of the fixed charge is to limit the number of...

Abstract: A simple physical model of the way fire engines travel leads to the hypothesis that T, the average fire engine travel time, depends on D, the distance travelled according to TD = 2D/a1/2 if D ≦ d and TD = vc/a + D/vc if D >d. The parameter a can be interpreted as an acceleration and vc as a cruising velocity. A field experiment was run, and the above model validated and the parameters estimated, for New York City. It was also found that regional traffic conditions and hour of day appear to have only minor effects on average response velocities.

Abstract: Standard works on queuing theory are in error in the calculation of the equilibrium delay distribution-and even of the average delay-in a single-server system with batch input, when the batches are not of constant size. This paper corrects the error, which occurs in connection with that portion of the delay of a customer due to the service times of other members of the same batch.

Abstract: This paper establishes a fundamental decomposition theorem in multiattribute utility theory. The methodology uses fractional hypercubes to generate a variety of attribute independence conditions that are necessary and sufficient for various decompositions: the additive, Keeney's quasi-additive, Fishburrt's diagonal, and others. These other nonaddirive utility decompositions contain some nonseparable interaction terms and are therefore applicable to decision problems not covered by earlier models. The paper defines a fractional hypercube and introduces the corresponding multiple element conditional preference order. The main theorem is produced from the solution of equations that are derived from transformations of linear functions that preserve these conditional preference orders. The computations and scaling required in implementing the main result are demonstrated by obtaining four utility decompositions on three attributes: apex, diagonal, quasi-pyramid, and semicube. We illustrate the methodology with geometric structures that correspond to the fractional hypercubes.

Abstract: This paper analyzes a heuristic for the knapsack problem that recursively determines a solution by making a variable with smallest marginal unit cost as large as possible. Recursive necessary and sufficient conditions for the optimality of such “greedy” solutions and a “good” algorithm for verifying these conditions are given. Maximum absolute error for nonoptimal “greedy” solutions is also examined.

Abstract: This paper presents a specialized method for solving transportation problems with several additional linear constraints. The method is basically the primal simplex method, specialized to exploit fully the topological structure embedded in the problem. It couples the poly-ω technique of Charnes and Cooper with the row-column sum method to yield an “inverse compactification” that minimizes the basis information to be stored between successive iterations, and in addition minimizes the arithmetic calculations required in pivoting. In particular, the solution procedure only requires the storage of a spanning tree and a (q + 1) × q matrix (where q is the number of additional constraints) for each basis. The steps of updating costs and finding representations reduce to a sequence of simpler operations that utilize fully the triangularity of the spanning tree. Procedures for obtaining basic primal “feasible” starts are also presented.

Abstract: This paper describes an experimental comparison of flow-shop algorithms, motivated by the need to consolidate recent research on this topic. Using a set of test problems, it investigated various branch-and-bound and elimination strategies in a comparative study and then combined them to produce a new and efficient solution algorithm.

Abstract: A bidder's strategy in one auction may affect his competitors' behavior in subsequent auctions. When this occurs, bidding in a sequence of auctions can be modeled fruitfully as a multistage control process. This paper presents such a model. In it the control is the bidder's strategy, the state characterizes the competitors' behavior and the state transition represents the competitors' reaction to the bidder's strategy. Dynamic programming is used to derive the infinite horizon optimal bidding strategy. We show that in steady state this optimal strategy generalizes a previous result for equilibrium bidding strategy in “one-shot” auctions.

Abstract: Model implementation starts with introductory steps that include orienting management, forming a team, selecting and formulating a problem, calibrating the model, and initial use. Then on-going steps take over with firefighting, tracking and diagnosis, updating and evolution, and re-use. Calibration of the model is approached eclectically in stages that include judgment, analysis of historical data, tracking, field measurement, and adaptive control. A three-year case study shows that unexpected events intersperse a planned implementation. The model emerges with multiple roles in the marketing management process. The model serves not only as a means of evaluating strategies in annual planning and day-to-day operations but also as part of a monitoring system that compares model predictions with actual sales to uncover marketing problems and focus managerial attention upon them.

Abstract: This paper develops a model for describing some aspects of competitive bidding. The motivating purpose of the model was that of formally examining the hypothesis put forward by Capen, Clapp and Campbell: In a competitive oil and gas lease sale, or indeed in any bidding situation in which the ultimate value of the object to be won is subject to uncertainty, the highest bidder tends to be one who has overvalued the prize. As a result, any company tends to win tracts (or prizes) which it has overvalued and tends to lose those which it has undervalued. Therefore, even if the pre-sale value estimates, on the average, turn out to be correct for each of the tracts bid on, the estimates for those that are actually won will tend to prove to have been too high. The model developed not only supports the hypothesis as set forth, but also establishes its validity much more generally.

Abstract: This paper introduces the concept of generalized utility independence. Subject to various generalized utility independence assumptions, we derive three functional forms for a multiattribute von Neumann-Morgenstern utility function u. These are the additive, the multiplicative, and the quasi-additive forms, each of which expresses u as a combination of utility functions defined on the separate attributes. It is demonstrated that if u is unbounded from above and below, then given the three forms, either reversal of preferences over some attributes occurs or else the additive form must hold.

Abstract: This paper discusses efficient methods for determining optimal lower bounds (and concomitant dual variables) for lot-size problems of both fixed and variable capacity. The approach unifies lower bounding procedures for several common forms of the problem on the basis of generalized duality theory. Through the optimal (lower bounding) dual solution, a production plan can be generated that when “rounded” to feasibility may be optimal or near optimal for problems of appropriate configuration.

Abstract: This paper considers the following model, described in terms of an investment problem. We have D units available for investment. During each of N time periods an opportunity to invest will occur with probability p. As soon as an opportunity presents itself, we must decide how much of our available resources to invest. If we invest y, then we obtain an expected profit P(y), where P is a nondecreasing continuous function. The amount y then becomes unavailable for future investment. The problem is to decide how much to invest at each opportunity so as to maximize total expected profit. When P(y) is a concave function, the structure of the optimal policy is obtained (§1). Bounds on the optimal value function and asymptotic results are presented in §2. A closed-form expression for the optimal value to invest is found in §3 for the special cases of P(y) = log y and P(y) = yα, for 0 < α < 1. §4 presents a continuous-time version of the model, i.e., we assume that opportunities occur in accordance with a Poisson ...

Abstract: Branch-and-bound algorithms are adequate for the solution of a wide range of 0-1 knapsack problems. It is shown that the simplest method of branching is as good as any. However, problems with highly correlated large weights and values quickly become unsolvable in a reasonable time. This paper develops algorithms that are aimed specifically at the hardest possible examples. The new methods use merging and sorting ideas and require a moderate amount of additional memory space. They are, however, faster by factors far in excess of 1,000 in many cases, thereby extending considerably the range of practically solvable 0-1 knapsack problems.

Abstract: This paper presents an algorithm for determining an optimum solution to a two-stage production sequencing problem with these characteristics: There are n jobs to be sequenced in a two-stage production environment; each production stage is equipped with a single facility; jobs to be sequenced are subject to due-date constraints; facilities in both stages require setup prior to processing each job; setup times in both stages are sequence dependent, and setup cost is assumed to be directly proportional to setup time; and the optimal solution is one that minimizes the total setup cost (of stages I and II) without violating job-due dates. The algorithm employs controlled enumeration through branch-and-bound procedures, together with feasibility tests.

Abstract: Recursive formulas for computing the Laplace-Stieltjes transform and the mean of the distribution of the lengths of busy periods for the M/G/1 finite queue are derived by a simple method that avoids simultaneous equations.

Abstract: We formulate a diffusion approximation to a stochastic advertising model of the Vidale-Wolfe type. This formulation allows solution of problems of optimum and on-line sales forecasting, parameter identification, and advertising control under uncertainty. For practical solutions, we suggest approximations and use simulation to forecast the probabilistic response of sales to an advertising program. Examples contrasting the stochastic process and the diffusion approximations approaches are included.

Abstract: In this paper we investigate the output process of the M/D/1 queuing system. We derive expressions for the distributions and first two moments, in both steady-state and transient conditions, of the following random variables: 1 the time until the nth departure measured from a departure epoch, T0, 2 the time between the n-1st and nth departures after T0, and 3 the number of departures in T0, T0 + t]. Further we study the autocorrelation functions of random variables 1 and 2 in the steady state.

Abstract: This paper presents computationally efficient techniques for approximating several behavioral aspects of the Mxt/EY/1 queue. The nonstationary arrival stream allows demands for service to follow different distributions over different time intervals. Specific performance characteristics evaluated are the first two moments of queue length, virtual waiting time, and system utilization. These are based on approximating the distribution of Qt at the time points E[Tn] by the distribution of Qn, where Tn is the epoch of the nth departure and Qn = QTn + 0. The results are in agreement with those obtained by simulation but require much less computing time. Sample results are presented for both stationary and nonstationary examples.

Abstract: This paper describes the development and validation of a set of mathematical programming models directed at optimal manpower utilization in Health Maintenance Organization HMO's. An application of the models in a planning context for an emerging HMO is presented and the results compared to those of actual staffing patterns. Two basic models are discussed in detail: an overall planning model and a subscriber maximization model. Each model treats the interaction between effective manpower utilization, facility requirements, and available capital. The objectives used in the models pertain to either minimum cost or minimum feasible use of physicians through the substitution of physician extenders. Field trials indicate that the models accurately represent the actual system and can be used effectively as planning aids.

Abstract: A previous research report of the authors presented a formal model of the one-machine job-shop scheduling problem with variable labor capacity. This report presents some computational experience with the algorithm proposed previously and a discussion of the structural aspects of the problem. Extensions and refinements of the algorithm are introduced to deal with nonsimultaneous job arrivals and the production smoothing problem. These results provide insight into the structure of the aggregate-detailed cost trade-off problem and suggest a good heuristic decision rule for problems of realistic size and complexity.

Abstract: This paper describes a finite procedure for locating a global minimum of a problem with linear objective constraints except for one nonlinear constraint, which is of the “reverse convex” variety; that is, the direction of the inequality is the opposite of that requited for a convex constraint. Budget constraints in which the cost functions are subject to economies of scale are typically of this form. An illustrative example of the procedure is provided.

Abstract: This paper comments on the limiting distribution of the inventory position in a continuous-review (s, S) inventory system with arbitrary customer interarrival-time distribution. The limiting distribution is derived for the general case in which the demand quantity is random. We show that the limiting distribution is uniform on (s + 1, …, S) if and only if units are demanded one at a time. However, with a slight modification of the procurement policy, the uniform distribution is recaptured even with random demand quantities.

Abstract: Steady-state distribution functions are derived for waiting time in an S-1, S inventory system in which arrivals are governed by members of the geometric Poisson family, resupply times are independently and identically distributed negative exponential variates, and service is on a first-come-first-served basis. For small values of S, probabilities can be computed readily from the final forms of the distribution functions using gamma and exponential function tables.

Abstract: An enumerative algorithm is presented for the solution of 0-1 many-knapsack or loading problems. It is based on the principle that before a search is attempted as many decisions as possible should be made about inclusion or exclusion of objects from the knapsacks. This is accomplished by the introduction of a new ordering relation among the objects. This ordering relation, coupled with other relations we define, allows a drastic reduction in the extent of the search required to determine a solution.