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In this article, we address a version of the capacitated vehicle routing problem where there is a constraint on the total time that can be spent on computing delivery routes and loading the vehicles. This problem, which we call the vehicle loading and routing problem (VLRP), can arise, for example, in the delivery of small, quick-turnaround orders from a warehouse. We propose a computation-implementation parallelization (CIP) approach to solving large VLRP instances, and present computational results showing that CIP improves upon the conventional compute-first-implement-later method. Our approach allows us to find lower-cost solutions in the same amount of time, or alternatively to find equally good solutions that allow improvements in order cutoff time or truck dispatching time to increase customer satisfaction.

Retailers use different mechanisms to enable sales and delivery. A relatively new offering by companies is curbside pickup where customers purchase goods online, schedule a pickup time, and come to a pickup facility to collect their orders. To model this service structure, we consider a service system where each arriving job has a preferred service completion time. Unlike most service systems that operate on a first‐come‐first‐serve basis, the service provider makes a strategic decision for when to serve each job considering their requested times and the associated costs. For most of our results, we assume that all jobs must be served before or on their requested time period, and the jobs are handled in overtime when capacity is insufficient. Costs are incurred both for overtime and early service. We model this problem as a Markov decision process. For small systems, we show that optimal capacity allocation policies are of threshold type and provide additional structural results for special cases. Building on these results, we devise two capacity allocation heuristics that use a threshold structure for general systems. The computational results show that our heuristics find near‐optimal solutions, and dependably outperform the benchmark heuristics even in larger systems. We conclude that there is a considerable benefit in using our heuristics as opposed to a very greedy or a very prudent benchmark heuristic, especially when the early service costs are not prohibitively high and the service capacity is scarce or there are high volumes of customer arrivals. Our results also demonstrate that as the length of the customer order horizon increases, performance of all heuristics deteriorate but the benefits of using our threshold heuristic remain considerable. Finally, we provide guidelines to select an appropriate solution method considering the trade‐off between solution quality and computation time.

Motivated by the operational problems in click and collect systems, such as curbside pickup programs, we study a joint admission control and capacity allocation problem. We consider a system where arriving customers have preferred service delivery times and gauge the service quality based on the service provider's ability to complete the service as close as possible to the preferred time. Customers can be of different priority classes, and their priority may increase as they wait longer in the queue. The service provider can reject customers upon their arrival if the system is overloaded or outsource the service (alternatively work overtime) when the capacity is not enough. The service provider's goal is to find the minimum-cost admission and capacity allocation policy to dynamically decide when to serve and whom to serve. We model this problem as a Markov Decision Process. Our structural results partially characterize a set of suboptimal solutions, and we develop solution methods using these results. We also develop a problem-specific approximation method that is based on state aggregation to overcome the computational challenges. We present extensive computational results and discuss the impact of problem parameters on the optimal policy.