Applications and Implementation A SEPARABLE PROGRAMMING APPROACH TO EXPECTED COVERAGE: AN APPLICATION TO AMBULANCE LOCATION

The maximum expected covering location problem (MEXCLP) is reformulated using a separable programming approach. The resulting formulation—nonlinear maximum expected covering location problem (NMEXCLP)—guarantees optimality and also solves more quickly than previous heuristic approaches. NMEXCLP allows two important extensions. First, minor formulation changes allow the specification of the minimum number of times each node is to be covered in order to satisfy expected coverage criteria. Second, coverage matrices can be constructed that consider two different types of coverage simultaneously. Both extensions are useful for ambulance location problems and are demonstrated in that setting.     

STRATEGIC FACILITY PLANNING: THE ANALYSIS OF OPTIONS

This paper addresses the issue of uncertainty in planning the long-term development of facility systems. In certain instances, the high variance of a single future forecast can be reduced by using a set of alternative future scenarios. By carefully selecting facility configurations, the planner can delay the selection of a future set of facility sites at little or no sacrifice while additional information is gathered and uncertainty reduced. This allows the planner to maintain flexibility in adapting to a complex and dynamic environment. Several models are presented for different planning contexts. Examples for each, as well as a robust bicriterion solution heuristic, are also provided.     

DYNAMIC LOCATION MODELING FOR PUBLIC-SECTOR FACILITIES: A MULTICRITERIA APPROACH*

A major complication in the planning of facility systems and in the analysis of their locational configurations is the fluctuating nature of the systems they serve. Locations identified now, based on current conditions, may be undesirable in the future, and those based on future conditions may be undesirable now. This paper proposes a general methodology using multiobjective analysis to plan public-sector facility systems operating in a dynamic environment. A model is developed for the specific case of locating emergency services and an illustrative example is presented.     

A Bicriterion Maximal Covering Location Formulation Which Considers the Satisfaction of Uncovered Demand

There have been many applications of the maximal covering location problem (MCLP). An underlying assumption of the MCLP is that demand not covered (i.e., not within a prespecified maximal distance of a facility) is not served. This may be an unrealistic assumption in many location planning scenarios, especially in the public sector. For example, in cases such as fire protection or ambulance service, calls not technically covered will still be serviced. The MCLP, however, does not consider the distances or travel times necessary to service such demand. This paper presents a bicriterion locational covering model which explicitly considers the travel distance or time necessary to service demand not within the maximal covering distance of a facility. The model may be used to generate noninferior (Pareto optimal) siting configurations which demonstrate the inherent trade-offs between a siting scheme designed to maximize total coverage and one designed to minimize total travel time for uncovered demand to reach its nearest facility. In addition, it is shown that for any particular weighting scheme on the two objectives, the problem can be solved as a p-median problem; a problem for which several efficient solution methods exist.     

APPLICATION OF AN EXPECTED COVERING MODEL TO EMERGENCY MEDICAL SERVICE SYSTEM DESIGN*

The Emergency Medical Service (EMS) Act specifies the fraction of all demands for service that must be reached in a given amount of time for urban and rural areas. The conditions have traditionally been interpreted to apply to the case in which all EMS vehicles are available to respond to demands. A model that considers the probability of a vehicle being busy is formulated and model properties are briefly discussed. The model is then applied to two problems: a 55-node test case and a 33-node census tract representation of Austin, Texas. The implications of the new model for EMS system design are discussed as are the limitations of the modeling approach.     

STOCHASTIC COST-VOLUME-PROFIT ANALYSIS WITH A LINEAR DEMAND FUNCTION

In this paper we incorporate a linear demand function to model the price-volume causal relationship into stochastic cost-volume-profit (CVP) analysis. We assume that the objective function is to maximize expected profit; other objective functions are also discussed and compared. A linear stochastic model follows from which probabilistic statements can be easily obtained if the random variables are assumed to be multivariate normal. The basic framework is shown to be a special case of project value maximization where project value is the cash flow of the project discounted for time and risk according to the capital asset pricing model. Moreover, an intertemporal extension that considers inventory is developed. In summary, a new approach to stochastic CVP analysis that incorporates the management decision process in an uncertain environment is developed.     

A Principle for Corner Store Positioning under Intrinsic Modeling for Traffic Orientation*

This paper presents the following normative positioning principle in convenience store competition at an intersection. In countries where traffic advances on the right (left) side of the street, other things being equal, a convenience corner store should locate clockwise (counterclockwise) adjacent to the already established stores. This principle is established within a spatial framework emphasizing the relationship among the following: consumer-driver preferences, relative volume of traffic movements, and store potential at different corners. The analysis demonstrates the dependence of competitor strategy on available locations, sequence of positioning, and utility considerations.     

FIRM EXPANSION THROUGH FRANCHISING: A MODEL AND SOLUTION PROCEDURES

This paper presents a practical model for firm expansion through franchising. The model allows the possibility of opening both company-owned and franchised stores. The objective is to maximize the expected returns to the franchisor from both types of stores, subject to the total capital outlay budget and the excess capacity available at each warehouse. A relaxation for this problem is studied and a heuristic solution procedure that makes use of this relaxation is developed. Experimental results over a wide range of problem structures show this solution methodology to be very effective, with gaps between feasible solution values and upper bounds generally in the 0 to 1 percent range. An efficient branch-and-bound code also is developed. This code is tested on problems with up to 100 potential store locations and 20 regions. It is found to be at least two orders of magnitude faster than a state-of-the-art commercial integer programming package.     

AN ALTERNATE MODEL FOR LEAD-TIME DEMAND: CONTINUOUS-REVIEW INVENTORY SYSTEMS

The calculation of reorder points when the distribution of lead-time demand is normal is quite complex, primarily because of having to bound it away from negative demand values. A number of researchers have sought feasible alternative forms of lead-time demand which can be calculated without undue difficulty. It is proposed here to assume a Poisson (daily) demand and an exponential lead time (days). If they are assumed independent their convolution is geometric, which is itself asymptotically exponential. This has a number of advantages: (1) The exponential lead time is appropriate where the lead time is often short (i.e., local source), occasionally longer (when the local sources stock out), and, infrequently, quite long. (2) The geometric lead-time demand is independent of changes of time scale. (3) Reorder points and lot sizes appear in simple closed form. (4) The exponential asymptote is sufficiently close that this further simplification is usually warranted.     

FOUR APPROACHES TO THE CLASSIFICATION PROBLEM IN DISCRIMINANT ANALYSIS: AN EXPERIMENTAL STUDY*

Four discriminant models were compared in a simulation study: Fisher's linear discriminant function [14], Smith's quadratic discriminant function [34], the logistic discriminant model, and a model based on linear programming [17]. The study was conducted to estimate expected rates of misclassification for these four procedures when observations were sampled from a variety of normal and nonnormal distributions. In contrast to previous research, data were taken from four types of Kurtotic population distributions. The results indicate the four discriminant procedures are robust toward data from many types of distributions. The misclassification rates for both the logistic discriminant model and the formulation based on linear programming consistently decreased as the kurtosis in the data increased. The decreases, however, were of small magnitude. None of these procedures yielded statistically significant lower rates of misclassification under nonnormality. The quadratic discriminant function produced significantly lower error rates when the variances across groups were heterogeneous.     

ESTIMATION OF MISCLASSIFICATION PROBABILITIES IN THE LINEAR PROGRAMMING APPROACHES TO THE TWO-GROUP DISCRIMINANT PROBLEM

Expressions for misclassification probabilities are derived under a contaminated multivariate normal model for the linear-programming approaches to the two-group discriminant problem.     

Heuristic Procedures for Practical-Sized Uncapacitated Location-Capacitated Routing Problems*

Facility location and vehicle routing are two important logistical problems closely interrelated in many real-world applications where locating facilities and determining the associated multi-stop vehicle routes are required simultaneously. Previous research has found that using the classical facility location models on these location-routing problems (LRPs) may lead to suboptimal solutions. We propose an approximate approach for the LRPs, which first generates and improves feasible location/allocation schemes with the associated multi-stop routing costs approximated using some route length estimators. We then design the minimum-cost routes based on the location/allocation results. We review two estimators that can provide accurate approximations to the multi-stop route distances; define the uncapacitated location-capacitated routing problem; and evaluate several heuristic procedures for approximately solving the problem. Computational results show that when vehicle capacities are not too restrictive, the sequential procedures that incorporate the two robust route length estimators can produce good solutions to practical-sized problems with a reasonable amount of computational efforts.     

MARKET PENETRATION AND LOCATIONAL CONFLICT IN FRANCHISE SYSTEMS*

This paper addresses the questions of market penetration and locational conflict in a franchise system of distribution. The models developed provide a means to evaluate alternative scenarios and the effects of various franchise policies. It is shown that the market penetration and location goals of the members of a franchise system coincide only under a very limited set of circumstances.     

Transportation Approach to Locating Plants in Relation to Potential Markets and Raw Material Sources

Proximity to the market place has been considered the most important locational factor in the literature so far. However, the growing need for frequent deliveries of materials in smaller lot sizes for just-in-time (JIT) manufacturing prefers plants closer to the raw materials sources. Locating plants for JIT manufacturing is, therefore, a problem of finding the right balance between the requirements of procurement and distribution. A comprehensive model is proposed in this paper to solve this problem. The model is solved by using the transportation algorithm and produces simultaneous decisions on procurement, production, and distribution. The model does not require plant sizes to be known a priori, but it allows upper limits to be placed on the size of each plant and raw material source. As such, optimal plant capacities along with the corresponding procurement and distribution quantities are all determined by the model solution.     

A ONE-PERIOD STOCHASTIC INVENTORY PROBLEM WITH A LUMP-SUM PENALTY COST

This paper presents an inventory problem related to the one-period stochastic inventory (or “newsboy”) problem. In this problem, the firm has to decide how much product to order to meet a random one-period demand. The version of the problem presented is novel in two respects. First, demand is explicitly permitted to be negative, and second, the penalty (or shortage) cost is assumed to be independent of the magnitude of the shortage. This situation is shown to change the form of the cost function and to complicate the determination of optimal policies. The form of the optimal policy is developed, and two example problems are presented in some detail.     

Locating Emergency Warning Sirens

In this paper, we report on the application of set covering and maximal covering location models to the problem of locating emergency warning sirens in a midwestern city. Two siren types are available, each having different costs and covering radii. Using a modified version of the set covering location model, we analyze the cost implications of several policy options being considered by the city's planners. Results of the study indicate that location covering models can be powerful and efficient tools in the design of such systems, and their use can lead to significant cost savings. In addition, such models provide decision makers the flexibility to examine the inherent costs associated with various policy options.     

Artificial Neural Network Models for Pricing Initial Public Offerings

In recent times, managerial applications of neural networks, especially in the area of financial services, has received considerable attention. In this paper, neural network models are developed for a new application: the pricing of Initial Public Offerings (IPOs). Previous empirical studies provide consistent evidence of considerable inefficiency in the pricing of new issues. Neural network models using publicly available financial data as inputs are developed to price IPOs. The pricing performance and the economic benefits of the neural network models are evaluated. Significant economic gains are documented with neural networks. Several tests to establish generalizability and robustness of the results are conducted.     

OPTIMAL ORDERING IN A DUAL‐SUPPLIER SYSTEM WITH DEMAND FORECAST UPDATES

We study how an updated demand forecast affects a manufacturer's choice in ordering raw materials. With demand forecast updates, we develop a model where raw materials are ordered from two suppliers—one fast but expensive and the other cheap but slow—and further provide an explicit solution to the resulting dynamic optimization problem. Under some mild conditions, we demonstrate that the cost function is convex and twice‐differentiable with respect to order quantity. With this model, we are able to evaluate the benefit of demand information updating which leads to the identification of directions for further improvement. We further demonstrate that the model applies to multiple‐period problems provided that some demand regularity conditions are satisfied. Data collected from a manufacturer support the structure and conclusion of the model. Although the model is described in the context of in‐bound logistics, it can be applied to production and out‐bound logistics decisions as well.     

MATERIAL PLANNING FOR A REMANUFACTURING FACILITY

This article describes the first fully integrated material planning system to facilitate the management of a remanufacturing facility. A number of firms are already engaged in this activity. They remanufacture automobile, truck, and other vehicle components, like starters, alternators, transmissions, and so forth. These firms take in used components, disassemble them, and assemble saleable products from the good parts they find. There is considerable uncertainty in the supply of used components, the good parts in those components, and the demand for remanufactured products. Our system is based on material requirements planning logic, something that many firms in the industry are already familiar with. Meetings with experts in the industry were used to set the parameters of the system and evaluate its approach.     

A Comment on Second-Order Polynomial Regression Models

In a recent article, Chatterjee and Greenwood [1] addressed the problem of multicollinearity in polynomial regression models. They noted that there is a high correlation between X and X²; therefore, a second-order polynomial model suffers the consequences of collinearity. Chatterjee and Greenwood [1] suggested a method they believe will overcome the problem. The contention of the present comment is that the suggested method accomplishes nothing and, indeed, has the potential to lead the unwary researcher to the wrong inference and misinterpretation of his results.