Arthur P. Hurter

Spatial duopoly with discriminatory pricing

Abstract The concept and existence of an equilibrium is established for profit maximizing competitors whose decisions involve choices of both delivered price schedules and firm locations. Each firm faces a production function; each is allowed to locate in the plane and to set discriminatory prices. Any transport cost function that is continuous in the firm location variable may be used. It is shown that the locations of the two firms are in equilibrium if each firm is minimizing social cost (i.e., the total cost to the firms of supplying the market with the good it demands is minimized) with respect to the opponents fixed location.

Minimization of a Non-Separable Objective Function Subject to Disjoint Constraints

We consider an important class of mathematical programs, in which the vector variable can be partitioned into two subvectors corresponding to independent constraint sets. Necessary and sufficient conditions for optimal solutions are developed, and two approaches for obtaining solutions are reviewed. We present an enumeration approach, reducing the problem to a finite number of subproblems, and show that duality makes the solution of many of the subproblems unnecessary. Next, we develop an alternating approach, wherein the problem is solved for one of the subvectors while the other is held constant, and then the subvector roles are reversed. This procedure is observed to converge to partial optimum solutions. A widely applicable subclass of problems includes a linear program in one of the subvectors. For this subclass a sufficient condition for local optimality is determined. The condition is easily testable and fails to hold, in many cases, only if a better solution is obtained. Also, this condition shows that partial optimum solutions are almost always local optima.

Economic Impacts of Subsidized Housing Location

Abstract. In recent years increased emphasis has been placed on use of “tenant-based” housing subsidies for acquisition of market-rate housing that is more economically and racially integrated than traditional “project-based” public housing. In this article, we model the short-term economic effects upon various groups of a hypothetical program in which low-income families move from inner-city public housing to spatially dispersed Section 8 rental housing. Using cross-section data from the Chicago region, impacts are computed for two of these groups. Preliminary results indicate that the short-term net economic impact of this hypothetical housing relocation is negative, that these impacts have a spatial character, and that there is a potential tradeoff between tenant benefits, housing subsidies from society and housing integration.

On the Explicit Solution of a Special Class of Linear Economic Models

This paper derives explicit solutions for a class of linear (inequality) economic models heretofore treated by linear programming. These solutions are quite elementary and the decision criteria given are easily interpreted. The explicit solutions may involve the inversion of a single matrix, but even this is not necessary for the three applications in capital budgeting, production planning, and input-output analysis given in the paper.

Dependence of bilevel mathematical programs on irrelevant constraints

A major topic in aggregation of linear programming problems is the estimation of the aggregation error, i.e., the computation of bounds for the loss of optimality which results from the coarsening of information caused by aggregation. A widely used method to compute bounds for variable-aggregated linear programs was developed by Zipkin [2, p. 41, 3]. Several extensions and modifications have been proposed. We present an overview of these bound computation methods and extend the methods in case that: (1) several dual solutions are available and (2) optimal disaggregation is performed. By means of a small numerical study, indications for the quality of the bounds are derived. The discussion is restricted to column (i.e. variable) aggregation.

Generalized comparative statics for the production-location problem

Abstract This paper presents a general parametric analysis of deterministic production-location and design-location problems. The analysis characterizes the effects of changes in output level, input and output prices, and transport rates on the firms optimal production and location solutions. The approach, which uses arguments similar to those used in revealed preference analysis, does not rely on differential methods, so that it is applicable to more general situations, such as non-differentiable production and transport cost functions, and does not assume interior optimal locations. Several numerical examples are provided to explain major results and to illustrate apparent anomalies which can occur in spatial economic models.

An Approach to Zero-One Integer Programming

By starting with an all-integer zero-one linear programming problem, it is possible to develop a modified, possibly linear, programming problem that provides a characterization of the basis corresponding to a feasible zero-one solution to the integer problem. This characterization is based on the number of variables equal to one in the feasible solution. This paper develops an approach to zero-one programming based on this characterization. The method uses the criterion function of the original problem as a constraint, and then generates a sequence of feasible zero-one solutions, each with a greater value of the objective function. The solution technique is terminated when no more feasible solutions can be found, indicating that the last feasible solution determined is the optimum.

An Optimization Model for Location of Subsidized Housing in Metropolitan Areas

This paper presents an optimization model for evaluation of alternative spatial configurations of rent-subsidized housing in a large metropolitan area as well as associated monetary and nonmonetary impacts. Groups affected by these configurations include residents of subsidized housing, owners of nearby single-family housing, employers and society at large. Since impacts of subsidized housing are very localized, the first stage of the model creates potential location patterns for many small geographic areas. The second stage of the model uses local benefits to derive a location scheme for the metropolitan area which balances net social benefit with equity considerations of the geographical impact of subsidized housing. We apply this methodology to a small region in metropolitan Chicago and demonstrate alternative location schemes. *mpjr@merle.acns.nwu.edu **hurter@iems.nwu.edu

Input price uncertainty and the production-location decision: A Critique and Synthesis

Abstract This paper compares the recent work of Hsu and Mai with other recently published and soon to be published work incorporating input price uncertainty in production-location problems. It also clarifies, strengthens, and corrects some results contained in recently published papers.

Network production-location problems under price uncertainty☆

Abstract The scope of the network plant location problem is extended in three significant ways: (i) The ‘design’ of the facility, including consideration of input substitution and the level of output, is combined with the location decision; (ii) input and output prices are treated as random variables, and (iii) the risk preferences of the decision maker are considered explicitly in the decision making process. Node optimality properties are developed for several model variations. An elimination-by-bound solution algorithm is presented along with suggested upper and lower bounds and methods of simplification. Under certain conditions, the optimal input ratios and plant locations are shown to be invariant with some parametric changes. The potential for influencing the location decisions of firms, depending upon the characteristics of their risk preferences, production functions, and the demand functions for their input, through manipulation of the risk they face, is illustrated.