Transportation asset acquisition under a newsvendor model with cutting stock restrictions: approximation and decomposition algorithms

Logistics service providers use transportation assets to offer services to their customers. To cope with demand variability, they may acquire additional assets on a one-off (spot) basis. The planner’s problem is to determine the optimal level of assets acquired upfront, such that their cost is minimized, for a given planning horizon. Our formulation captures a nontrivial complication: Although ordering quantities are pertinent to asset acquisition, customer demand is in the form of service requests. Not only does each request have a stochastic duration, but also the total number of requests per customer is uncertain. We introduce a two-stage newsvendor model where demand for spot assets is derived through optimal cutting-stock patterns. Leveraging results from bin-packing, we propose polynomial algorithms that have worst-case guarantees for upper and lower bounds. Our method finds optimal solutions to instances intractable by commercial solvers. We investigate demand variability by means of a factorial experiment. We find that, whereas variability in the number of requests leads to higher costs, variability in each request’s duration can reduce costs. Finally, we demonstrate the modularity of our approach with two extensions: asset routing and outsourcing. Our results provide a practical approach to transportation asset acquisition and offer insights on the differing impact of demand uncertainty on the total acquisition cost.