Computational comparison on the partitioning strategies in multiple choice integer programming

In this paper we review the theoretical background of two partitioning strategies, the Weighted-Mean-Method (WMM) and the Reformulation-and-Transformation-Technique (RTT), incorporated in the special ordered set branch-and-bound procedures leading to the global optimum in Multiple Choice Integer Programming (MCIP). Procedure flow is developed with a numerical example presented to illustrate the effect of these two partitioning strategies in the algorithm. This procedure flow is then coded using IBM APL2. A total of 24 test problems are solved by this APL2 code for MCIP to analyze the performance of WMM and RTT in MCIP. The preliminary computational results indicate that, on the average, RTT produces smaller branching trees than does WMM. Its performance tends to be better for those MCIP problems having more multiple choice sets and a smaller average number of variables in each set. However, the average CPU time consumed by using RTT does not differ much from that consumed by using WMM.