Subhash C. Narula

Degree-constrained minimum spanning tree

Abstract In this paper the problem of a degree-constrained minimum spanning tree (DCMST) is defined. The problem is formulated as a linear 0–1 integer programming problem. A primal and a dual heuristic (construction) procedure and a branch-and-bound algorithm are proposed to construct a DCMST. These procedures are illustrated with a simple example. Some computational experience with these algorithms is also reported.

Hierarchical location-allocation problems: A classification scheme

Abstract In the literature, the p -median problem has been well studied. For the p -median problem our objective is to locate p facilities among n (⩾ p ) locations such that the total weighted travel distance is minimized. In the problem formulation, it is tacitly assumed that the facilities are of one type. In many practical situations, systems that provide products/services generally consist of k ( ⩾ 2) distinct types of facilities. In such problems, we would like to locate p i type i facilities, i = 1, 2, … k , among n ( ⩾ Σ i k = 1 p i ) available locations. Here also our objective may be to locate these facilities such that the ‘total weighted travel distance’ is minimized. What makes these problems difficult and interesting is that the extension of the p -median problem formulation and solution procedures to these problems is not always obvious, easy or straightforward. The problem formulation and solution procedures depend upon the hierarchical relationship among the facility types and the flow of goods and services allowed among them. In this paper we attemp to classify the hierarchical location-allocation problems.

Prediction, Linear Regression and the Minimum Sum of Relative Errors

When linear regression is used for prediction purposes, the minimization of the sum of relative errors (MSRE) is proposed as an alternative criterion to the minimization of the sum of squared errors (MSSE) and the minimization of the sum of absolute errors (MSAE). The problem is formulated as a linear programming problem and a solution procedure is given. The problem of subset selection with the MSRE criterion is also considered and results illustrated with an example.

An hierarchal location—allocation problem

We consider a 2-hierarchal location-allocation problem when p1 health centers and p2 hospitals are to be located among n potential locations so as to minimize the total weighted travel distance. We consider the possibility of the referral of [theta] (0

Selection of Variables in Linear Regression Using the Minimum Sum of Weighted Absolute Errors Criterion

An efficient implicit enumeration algorithm is proposed for the problem of selecting subsets of predictor variables in a multiple linear regression model using the minimum sum of weighted absolute errors (MSWAE) criterion. The proposed algorithm is illustrated with an example. Computational experience shows that the proposed algorithm is superior to the currently available algorithm in terms of computation time and the number of iterations required to solve a problem.

Do I have to go shopping again? A theory of choice with movement costs

Abstract In this model, the standard theory of the one-person household is extended into space and time. The theory is extended into space by imposition of a real trip cost on the act of purchase, separate from the money price of commodities. It is extended into time by imposition of a real cost of storage (represented by “deterioration”) on the stocks of goods held in the household between shopping trips. The necessity for storage permits the theory to include an endogenous choice of capacity to store as well as choices among consumption, leisure, and shopping trip frequency. By use of duality theory, the comparative static effects of price, wage, and trip costs are examined. Production and transformation within the household are integrated into the model and shown to be covered by the dual approach.

TWO-LEVEL HIERARCHICAL PROGRAMMING PROBLEM

In this paper we present an algorithm to solve a two-level hierarchical resource control problem with linear constraints and objective functions and one decision maker at each level. The algorithm explicitly takes into consideration the hierarchical structure of the problem and the sequential nature of the decision making process. An illustrative example is also included.

Testing Hypotheses Concerning Partial Correlations: Some Methods and Discussion

Summary A number of existing statistical procedures are reviewed which can be employed to test a variety of hypotheses involving partial correlations. Often in social science research investigators are interested in testing hypotheses concerning the values of specific simple population correlations, in testing that the differences between pairs of simple correlations are zero, and in testing that k simple population correlations are all equal. The procedures for making these tests are presented in numerous elementary and advanced social science statistics texts. Conceivably, investigators might also be interested in testing hypotheses concerning partial correlations that are similar to the types of hypotheses which are commonly tested involving simple correlations. The procedures for making such tests are not typically presented in elementary statistics texts. Although such procedures are alluded to in some advanced texts, specific results do not appear to be generally known by many social science researchers. The purpose of this paper is not to present new statistical methods for testing hypotheses concerning partial correlations; rather, this paper has been prepared for the purpose of reviewing a number of existing statistical procedures which can be employed to test hypotheses involving partial correlations. The procedures which are reviewed in the present paper involve applications of general statistical theory to data analyzing problems concerning partial correlations. The present authors feel that many of these procedures are not known to social

An algorithm for the minimum sum of weighted absolute errors regression

We propose an algorithm to estimate the unknown constants in a multiple linear regression model under the minimum sum of weighted absolute errors (MSWAE). The proposed algorithm, a generalization of an earlier algorithm, is compared to a bounded variable algorithm. Some somputational experience is reported.

Sample Size Calculations in Exponential Life Testing

Various transfomantions of chi-square to an approximate normal varialte are compared in the context of determining sample size in exponential life testing procedures for a given level of significance and probability of Type II error.