Data-driven integrated home service staffing and capacity planning: Stochastic optimization approaches

We address a home service staffing and capacity planning (HSCP) problem under uncertainty. Specifically, given sets of providers, service types, and days in the planning horizon, we aim to determine the number of providers to hire (staffing) and the allocation of hired providers to different types of services (capacity planning). Data from a collaborating home services provider in Beijing demonstrate significant variability in customer demand within and across service types. Service duration is also random. The objective is to minimize the total cost associated with staffing, capacity allocation, over-staffing, and under-staffing. We propose two-stage stochastic programming (SP) and data-driven distributionally robust optimization (DRO) approaches to address demand and service time uncertainty considering two types of decision-makers, namely an everything-in-advance decision-maker (EA) and a flexible adjustment decision-maker (FA). In the EA models, we determine the staffing and capacity allocation decisions in the first stage before observing the demand. In the FA models, we make staffing decisions in the first stage and then determine the allocations based on demand realizations in the second stage. We derive equivalent mixed-integer linear programming (MILP) reformulations of the proposed DRO models for the EA decision-maker that can be implemented and efficiently solved using off-the-shelf optimization software. We propose a computationally efficient column-and-constraint generation algorithm with valid inequalities to solve the proposed DRO models for the FA decision-maker. Numerical experiments based on data from a home services provider in Beijing are used to compare the proposed approaches and illustrate the potential for impact in practice.