A comparison of piecewise linear programming formulations for stochastic disassembly line balancing

Recently, several mathematical programming formulations and solution approaches have been developed for the stochastic disassembly line balancing problem (DLBP). This paper aims at finding optimal solutions for the stochastic DLBP. Two second-order cone programming (SOCP1 and SOCP2) models and five piecewise linear mixed integer programming (PwLP) models are presented. The PwLP formulations involve two specially ordered sets of type 2 (S1 and S2) models and three convex combination (CC1, CC2 and CC3) models. In each modelling category, the latter models strengthen the initial S1 and CC1 models. Our computational analysis of a total 240 instances of ten problems demonstrates that all the seven models can be used to solve practical-sized DLBP problems to optimality using GUROBI. The SOCP2 model and the strengthened S2 and CC2 models lead to lower computation times, compared to SOCP1, S1, CC1 and CC3, respectively. Using the strengthened S2 and CC2 formulations, the CPU times of the CC3 model available in the literature can be reduced by 50 and 40%, respectively. Besides analysing the optimal solutions and the differences of the computation times, we present insights gained from our results