An optimization algorithm for the workforce management in a retail chain

Keywords: Workforce management Hybrid heuristic Personnel scheduling Matheuristic Retail a b s t r a c t This work proposes a scheduling problem for the workforce management in a chain of supermarkets operating in Italy. We focus on determining the ideal mix of full-time and part-time workers which are needed every week to guarantee a satisfactory service level during the check-out operations. The generation of working shifts, to be assigned to retail workers, is subject to several constraints imposed by both labour laws and enterprise bargaining agreements. We present a mathematical formulation of the problem followed by an exact solution approach which relies on the definition of feasible daily working shifts. The number of feasible daily shifts, that are combined to determine feasible weekly shifts, could drastically increase, depending on the selected planning interval. In addition, there may exist additional constraints, that are difficult to incorporate into the mathematical model. For these reasons, a hybrid heuristic, which does not require the generation of all feasible weekly shifts, is proposed in this paper. Using appropriate statistical techniques, a sensitivity analysis is performed to test the design of the hybrid heuristic. Computational tests are carried out by solving several real instances provided by the retail firm. The results obtained by the heuristic are compared both with an exact approach and with the solutions adopted by the retail company, which have been determined by using a naïf approach. Our hybrid heuristic exhibits excellent performance finding optimal or near optimal solutions in a very limited CPU time. In retail stores, that belong to the large-scale distribution sector, personnel costs usually range from 8% to 20% of the sales volume, with around 30% of the overall store personnel working on direct service to customers at the cash points (Levy, Weitz, & Grewal, 2013; Schmidt, 2013). Therefore, there is a potential of significant cost savings through a proper personnel management. The first step to achieve these savings is a good staff planning strategy. The goal of the staff planning is represented by an objective function which minimizes the staffing costs, while the operative constraints are of two types, essentially related to: (i) achieve a predefined service level and (ii) comply with the national labour legislation. Sometimes, instead of considering the personnel cost, the staff planning addresses the minimization of the number of full-time equivalent (FTE) employees that a store needs to achieve a certain corporate service …