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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ERIM Report Series Research in Management
ERIM report series research in management Erasmus Research Institute of Management
Erasmus Research Institute of Management

Arslan, A.M, Agatz, N.A.H, & Srour, F.J. (2023). Model Formulations for Pickup and Delivery Problems in Designated Driver Services (No. ERS-2023-004-LIS). ERIM report series research in management Erasmus Research Institute of Management. Retrieved from