From cloud computing to Covid quarantines, requests for service can arrive in batches. How should this impact the service's staffing? Here, we find that there is no economy of scale as batches grow large, a stark contrast with classical square root rules. By consequence, the queue length is not asymptotically normal; in fact, the fluid and diffusion-type limits coincide. When arrivals are both quick and in batches, an economy of scale can exist, but we show that it is weaker than expected.

Motivated by hotel housekeeping, we study shift construction decisions for room attendants amid uncertainty about customer arrival and departure times. We provide analytical results using the framework of M-convexity. A numerical case study for one hotel suggests that reallocating a small number of workers to later shifts can effectively eliminate guest waiting after the posted check-in time. We also identify alternate optimal solutions that can be useful for recruiting and retaining workers.

We consider the multi-period problem of jointly allocating resources to J supply nodes and assigning jobs of I different demand origins to the nodes. The goal is to maximize rewards for matching or minimize costs of waiting and assignment. We introduce a distributive decision rule, which represents the proportion of jobs served by each of the supply nodes. We test against benchmark models developed specifically for allocation or assignment decisions only and record 1-15% reductions in costs.