An exact algorithm for the type-constrained and variable sized bin packing problem

In this paper, we introduce an additional constraint to the one-dimensional variable sized bin packing problem. Practically, some of items have to be packed separately in different bins due to their specific requirement. Therefore, these items are labelled as different types. The bins can be used to pack either any type of items if they are empty originally or the same type of items as what they already have. We model the problem as a type-constrained and variable sized bin packing problem (TVSBPP), and solve it via a branch and bound method. An efficient backtracking procedure is proposed to improve the efficiency of the algorithm.