Model Formulations for Pickup and Delivery Problems in Designated Driver Services

Designated driver services use company vehicles to deliver drivers to customers. The drivers then drive the customers from their origins to their destinations in the customers’ own cars; at the destinations the drivers are picked up by a company vehicle. We typically see teams of drivers assigned to company vehicles serving customers. When, however, the drivers may be dropped off by one vehicle and picked up by another, a challenging, novel pick-up and delivery problem arises. In this paper, we introduce two formulations to solve this problem to optimality using a general purpose solver. In particular, we present a three-index and a two- index mixed integer program formulation to generate optimal, least-cost routes for the company vehicles and drivers. Using these MIPs, we find that the two-index formulation outperforms the three-index formulations by solving more instances to optimality within a given run time limit. Our computational experiments also show that up to 60% cost savings are possible from using a flexible operating strategy as compared to a strategy in which drivers and company vehicles stay together throughout a shift.

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