Evaluating strong, weak and hybrid formulations of the single stage capacitated warehouse location problem

Abstract

Lower bound (LB) of weak formulation of single stage capacitated warehouse location problem (SSCWLP) has low strength when compared to that of the strong formulation. Hence, the overall computational time to solve the weak formulation of SSCWLP is very high. Strong formulation take lesser branch-and-bound (B&B) nodes to solve SSCWLP but at the cost of higher computational time for linear programming (LP) relaxation at each node. Thus a trade-off is required, leading to the hybrid formulation, containing better characteristics of strong and weak formulations. Most promising constraints are utilised to reduce computational effort. Extensive computational experiments show that significantly superior LB are obtained by hybrid formulation compared to those obtained from weak formulation while significantly less computational time is taken for solving the LP relaxation compared to that taken by strong formulation. The gain in reduction of computational time using reformulation outweighs the cost of expanding the earlier formulation.