Determining optimal workforce size and schedule at the retail store considering overstaffing and understaffing costs

Abstract

A three-stage iterative sequential methodology is proposed for the staffing and tour scheduling problem of a retail store. The proposed work differs from the existing works in the following ways (i) Existing studies usually considered the tour scheduling problems for a given workforce size. However, this work attempts to solve both staffing and tour scheduling problems. (ii) The proposed work incorporates a large number of shift flexibilities such as the requirement of break window, meal break assignment, day-off scheduling, multiple shift start time, and other business and regulatory constraints. Previous studies have usually focused on limited flexibility as it makes the problem formulation complex and difficult to solve. The first stage of our methodology uses deterministic finite automata (DFA) that handle the above-mentioned flexibilities well and generates all the feasible shifts. The use of DFA reduces the problem complexity, search space, and the number of constraints. The second stage formulates a mixed-integer linear programming (MILP) model considering all the feasible shifts generated in the first stage. The MILP finds the optimal workforce schedule for the given workforce demand. The third stage presents a heuristic that iteratively solves MILP by varying the workforce size and determines the near-optimal staffing level that minimizes the total overstaffing and understating cost. The proposed methodology is applied in a specialty store on 550 randomly generated problem instances of realistic sizes. It obtains the solution within a 2.35 percent average optimality gap in a reasonable computational time. The result shows that the proposed heuristic outperforms in terms of solution quality and runtime on the workforce demand instances generated using Poisson distribution over those generated using Uniform distribution. The percentages of overstaffing and understaffing decrease with the increase in the mean and standard deviation of hourly workforce demand.