Integration of the cost allocation in the optimization of collaborative bundling

By bundling orders of different partners within the time windows suggested to their 3PLs, a large reduction in cost can be achieved. However, these benefits can be further enlarged by loosening the time window constraints. Using the real costs structure of delivering an order too early or too soon, a partner can give more delivery date options, given that he receives an adequate compensation for changing the delivery date of this order. To be able to create an operational plan and a compensatory cost allocation, we create a model that integrates the Shapley value when bundling and solve it with a heuristic. We show that such an integrated approach –in comparison to first plan, then divide– increases the satisfaction of the partners.