On the Concept of Opportunity Cost in Integrated Demand Management and Vehicle Routing

Integrated demand management and vehicle routing problems are characterized by a stream of customers arriving dynamically over a booking horizon and requesting logistical services, fulfilled by a given fleet of vehicles during a service horizon. Prominent examples are attended home delivery and same-day delivery problems, where customers commonly have heterogeneous preferences regarding service fulfillment and requests differ in profitability. Thus, demand management methods are applied to steer the booking process to maximize total profit considering the cost of the routing decisions for the resulting orders. To measure the requests’ profitability for any demand management method, it is common to estimate their opportunity cost. In the context of integrated demand management and vehicle routing problems, this estimation differs substantially from the estimation in the well-examined demand management problems of traditional revenue management applications as, for example, found in the airline or car rental industry. This is because of the unique interrelation of demand control decisions and vehicle routing decisions as it inhibits a clear quantification and attribution of cost, and of displaced revenue, to certain customer requests. In this paper, we extend the theoretical foundation of opportunity cost in integrated demand management and vehicle routing problems. By defining and analyzing a generic Markov decision process model, we formally derive a definition of opportunity cost and prove opportunity cost properties on a general level. Hence, our findings are valid for a wide range of specific problems. Further, based on these theoretical findings, we propose approximation approaches that have not yet been applied in the existing literature, and evaluate their potential in a computational study. Thereby, we provide evidence that the theoretical results can be practically exploited in the development of solution algorithms.