The Cost of Scheduling Customers in Routing Problems

Both for less-than-truckload (LTL) and full-truckload (FTL) routing and scheduling, customers tend to differ a lot with respect to the flexibility they give to the dispatcher to design routes. The more flexibility they give, the more cost efficient the routes the dispatcher can design. In practice, the cost-driving effect of scheduling inflexibility has been recognized for a longer time. E.g., express delivery companies charge higher rates for customers requiring a faster delivery. In most cases, reliable cost estimates of the various sources of scheduling inflexibility are unavailable. Correct estimates of the incremental cost of customers or customer types are nevertheless essential for pricing routing services and accepting new customers. The additional cost of routing a customer acts as a price-floor: the freight rate should at least cover the additional cost of servicing that customer. This information remains valuable, even if prices in the industry are not cost-based. If prices are aimed at capturing customers’ willingness to pay (e.g., perceived value pricing) or if prices are based on competitors’ price levels (e.g., going-rate pricing), the incremental cost of servicing a customer is vital for determining the contribution or profitability of servicing each customer. In this paper, several methods for determining the incremental cost of a customer in a vehicle routing problem with heterogeneous vehicles in which service at customers is restricted to prespecified hard time windows. The Fleet Size and Mix Vehicle Routing Problem (FSMVRP) is a Vehicle Routing Problem (VRP, see Toth and Vigo [17]) where the homogeneous fleet assumption of the traditional VRP has been lifted. A number of vehicle types with different capacities and acquisition costs are given. The objective is to find a fleet composition and a corresponding routing plan that minimizes the sum of routing and vehicle costs. For reviews on the FSMVRP, we refer the reader to Salhi and Rand [14], Osman and Salhi [13], and Lee et al. [10]. Section 2 presents 8 different approximation methods for estimating the incremental cost of a customer. They are extensively tested on problem instances for heterogeneous routing problems in Section 3. This section also looks at factors influencing the incremental costs of customers. Section 4 concludes the paper.