An integer programming model for the truck dock assignment problem with operational time constraint within cross docks has been proposed in (Miao, Z.,Lim, A.,Ma, H., 2009. Truck dock assignment problem with operational time constraint within crossdocks. European Journal of Operational Research 192 (1), 105–115). We address the following issues in this formulation: 1) from among those constraints in the model, there are n 4 constraints, which eliminate a subset of feasible solutions of the problem that has been described. Consequently, the model does not necessarily offer an optimal solution for the described problem, 2) another set of n 4 constraints, although do not cut off feasible solutions, but their upper bounds are incorrectly specified such that it leads to redundancy of a majority of them instead of contributing in numerical efficiency by tightening the polytope of LP relaxation, 3) there is a flaw in calculation of cost in the objective function such that the positive transportation costs are calculated even for not transporting anything. This article contributes in the following way: 1) describes the issue using an example and subsequently proposes a rectified model, 2) calculates the dimension of polytope in the revised model, 3) introduces several classes of valid inequalities resulting in an improved formulation with tighter LP-relaxation polytope facilitating resolution of larger instances and, 4) proves that some of the aforementioned valid inequalities are facets of polytope.

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LGI2A university of Artois

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