Metaheuristics for the Pick-up and Delivery Problem with contracted orders

Abstract

Contracted orders represent a novel extension to the Pick-up and Delivery Problem (PDP) with soft time windows. This extension to the multiple depot problem has depots managed by separate, competing haulage companies “carriers”. Orders may be assigned to a specific carrier “contracted”, “allocated” to a specific carrier but allowed to swap if this improves the solution or free to use any carrier “spot hired”. Soft time windows lead to a multi-objective problem of minimising distance travelled and delay incurred. In this paper we use real order data supplied by 3 large distributors and 220 carriers. Additional, randomised, orders are generated to match the distributions observed in this data, representing backhaul orders for which no data is available. We compare a manual scheduling technique based on discussions with industry partners to popular metaheuristics for similar problems namely Tabu Search (TS), Variable Neighbourhood Search (VNS) and Hybrid Variable Neighbourhood Tabu Search (HVNTS), using our modified local search operators. Results show that VNS and HVNTS produce results which are 50% shorter than greedy approaches across test instances of 300 orders in a one week period.