Joint Capacity Allocation and Job Assignment Under Uncertainty

In this paper, we consider the multiperiod joint capacity allocation and job assignment problem. The goal of the planner is to simultaneously decide on allocating resources across the J different supply nodes and assigning jobs of I different demand origins to these J nodes, so as to maximize the reward for matching or minimize the cost of failure to match. We furthermore consider three features: (i) supply is replenishable after random time, (ii) demand is random, and (iii) demand can wait and need not be fully fulfilled immediately. Such problems emerge in many service management settings such as ride-sharing fleet repositioning and patient management in healthcare. We introduce a distributive decision rule, which decides on the proportion of jobs to be served by each of the supply nodes. We borrow ideas from the pipeline queue framework, which cannot be directly applied to our setting, and hence our model requires the development of new reformulation techniques. Our model has a convex reformulation and can be solved by a sequence of linear programs, in practice. We test our model against state-of-the-art models that focus solely on capacity allocation decisions and on job assignment decisions, in the settings of nurse scheduling and patient overflow, respectively. Our model performs strongly against the benchmarks, recording 1%–15% reductions in costs and shorter computation times. Our model opens the door to consider new problems in platform operations and online services where the planner is able to influence the supply of services or resources partially.

Funding: This work was supported by the Ministry of Education, Singapore [Grant MOE2016-SSRTG-059, Service Productivity and Innovation Research Programme].

Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2022.0255.