- مبلغ: ۸۶,۰۰۰ تومان
- مبلغ: ۹۱,۰۰۰ تومان
In this paper we study the effect of a decision maker's risk attitude on the median and center problems, two well-known location problems, with uncertain demand in the mean–variance framework. We provide a mathematical programming formulation for both problems in the form of quadratic programming and develop solution procedures. In particular, we consider the vertex and absolute median problems separately, and identify a dominant set for the center problem. Glover's linearization method is applied to solve the vertex median problem. We also develop a branch and bound algorithm and a heuristic as the linearization technique takes too long for the vertex median problem on large networks. A computational experiment is conducted to compare the performance of the algorithms. We demonstrate the importance of taking into account the volatility and correlation structure when a location decision is made. The closest assignment property is also discussed for these location problems under the mean–variance objective.
experiment A computational experiment was carried out to test the performance of the linearization method as well as the other algorithms in terms of CPU time and solution quality. All the solution procedures were coded in Microsoft Visual Cþ þ and run on a PC with Intel Core i5-1.70G Hz CPU and 8 GB RAM. We used the following parameter values to construct test instances for each problem studied: Networks were randomly generated for the number of nodes n¼10, 25, 50, 75, 100, 150 and 200; n nodes were randomly positioned inside a square with a side length of 100 units; the distance matrix fdijg was evaluated using the Euclidean distances; the mean and standard deviation of each demand weight and the correlation coefficient between a pair of demand weights were randomly chosen; the number of facilities p ¼ 0:2n, 0:4n and 0:6n; the risk attitude coefficient λ ¼ 5; 1; 1 and 5. In total, 84 test instances were generated for p MPUD and p CPUD. In the experiment, we assumed that the nodes of a network were potential location sites.