Multi-period distribution networks with stochastic demand and capacity commitment contracts

From the decision making perspective of a large-scale logistics company, our study focus on reducing transportation costs by activating mid-term contracts with carriers over a long-term planning horizon for parcel transportation. This company is interested in ensuring truck capacity at low rates. On the other hand, carriers are concerned about maximizing truck utilization and maintaining profitable return on their assets. Considering the dynamic and uncertain nature of future demand, the planning horizon is divided in several periods during which transportation orders must be duly delivered. The stochastic demand is represented by a discrete probabilistic distributions simulating those potential demand realizations over time. The purpose is to evaluate the benefit of a tactical approach for transportation procurement based on capacity-commitment contracts : e.g. the shipper commits to pay for a minimum truck fleet per period at low rates and to confirm effective orders which might imply to under-utilize this reserved capacity. Yet,
in case of a larger demand, as a last-minute sourcing option (recourse) extra-capacity can be requested at higher off-contract rates. Our analysis considers the economical advantages of approaching capacity planning from this tactical point of view. The mathematical problem is formulated as a mixed-integer linear stochastic program. Several algorithmic methods are compared to assess the efficiency in finding optimal or applicable solutions to the problem. Results are presented with performance profiles evaluating algorithms in terms of computational time and solution quality and show that for large instances, the heuristic based on a double relaxation of the contract length and the variable integrality followed by a contract repairing phase performs faster while reaching small gaps.