23 research outputs found
Integer programming models for the semi-obnoxious p-median problem
The p-median problem concerns the location of facilities so that the sum of
distances between the demand points and their nearest facility is minimized. We
study a variant of this classic location problem where minimum distance
constraints exist both between the facilities and between the facilities and
the demand points. This specific type of problem can be used to model
situations where the facilities to be located are semi-obnoxious. But despite
its relevance to real life scenarios, it has received little attention within
the vast literature on location problems. We present twelve ILP models for this
problem, coupling three formulations of the p-median problem with four
formulations of the distance constraints. We utilize Gurobi Optimizer v9.0.3 in
order to compare these ILP models on a large dataset of problems. Experimental
results demonstrate that the classic p-median model proposed by ReVelle \&
Swain and the model proposed by Rosing et al. are the best performers
Pivoting rules for the revised simplex algorithm
Pricing is a significant step in the simplex algorithm where an improving
nonbasic variable is selected in order to enter the basis. This step is
crucial and can dictate the total execution time. In this paper, we perform a
computational study in which the pricing operation is computed with eight
different pivoting rules: (i) Bland’s Rule, (ii) Dantzig’s Rule, (iii)
Greatest Increment Method, (iv) Least Recently Considered Method, (v) Partial
Pricing Rule, (vi) Queue Rule, (vii) Stack Rule, and (viii) Steepest Edge
Rule; and incorporate them with the revised simplex algorithm. All pivoting
rules have been implemented in MATLAB. The test sets used in the
computational study are a set of randomly generated optimal sparse and dense
LPs and a set of benchmark LPs (Netliboptimal, Kennington,
Netlib-infeasible)