An optimization algorithm for the workforce management in a retail chain

• A model to generate optimized work shifts in a chain of supermarkets in Italy is proposed.
• A mathematical formulation of the workforce management problem is defined.
• An exact approach to solve the problem is described.
• An efficient hybrid heuristic is presented and statistically tested.
• 27 real problem instances faced by the firm within its supermarkets are solved.

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.