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Motivated by operational problems in click-and-collect systems, such as curbside pickup programs, we study a joint admission control and capacity allocation problem. We consider systems where customers have preferred service delivery times and can be of different priority classes. The service provider can reject customers upon arrival or serve jobs via overtime when service capacity is insufficient. 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 and present structural results to partially characterize suboptimal solutions. We then develop a linear programming-based exact solution method using these results. We also present a problem-specific approximation method using a new state aggregation rule to address computational challenges faced due to large state and action spaces. Finally, we develop heuristic policies for large instances based on the behavior of optimal policies in small problems. We evaluate our methods through extensive computational experiments where we vary the service capacity, arrivals, associated service costs, customer segmentation, and order patterns. Our solution methods perform significantly better than several benchmarks in managing the tradeoff between the computation time and solution quality. [ABSTRACT FROM AUTHOR]

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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. [ABSTRACT FROM AUTHOR]

Cross‐training is an important tool to improve the performance of manufacturing and service systems through dynamic worker allocation. This study investigates how cross‐training can be leveraged when worker collaboration is not possible and frequent worker reassignment is undesirable. We consider a tandem queueing system with finite buffers between tasks. We show that if each worker is the fastest at a different task, then the optimal policy is always dedicated, regardless of the magnitude of the reassignment costs. Otherwise, if the system is Markovian with two homogeneous tasks and a faster and a slower worker, we completely characterize how the profit‐optimal policy depends on the (constant) reassignment cost. We also prove that for any given reassignment cost, dedicated worker allocation policies are strictly suboptimal for large enough buffer sizes. Instead, the faster worker should move to the downstream task only if there are enough jobs in the intermediate buffer and return to the upstream task when the buffer is sufficiently empty. Furthermore, the benefit of task switching increases as the buffer size becomes larger. We use our theoretical results to develop worker allocation heuristics both for more general systems with two tasks and for systems with more tasks. Numerical experimentation provides insights on how the profit depends on the buffer sizes and reassignment costs, shows that policies that are optimal when workers are collaborative result in excessive switching for non‐collaborative workers, and indicates that our pick‐the‐best heuristics perform well in all settings. [ABSTRACT FROM AUTHOR]