Summary: 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.
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