The employee scheduling problem is crucial for increasing profits in the retail business as labor costs are among the largest costs to companies. We propose a general analytic approach to solve a real-life motivated employee scheduling problem and apply our approach for a large retail store in Turkey. There are multiple product categories in the retail store and sales of each product category are affected whether there is an employee(s) responsible for the product category at that period. Our approach provides a suggestion engine for a multi-period employee scheduling problem where the objective is to maximize the profit while generating a shift schedule for part-time and full-time employees.  

We start solving this problem by analyzing the past 12 months of sales data for a total of nine categories, taken from a large retail store company in Turkey. Then, we generate a contribution matrix for each category and each period via Arena capturing the stochasticity of both demand values and sales probabilities, conditional on the number and types of the employees working at that category and period. Following these, a deterministic integer linear programming model (ILP) is proposed to decide how many part-time and full-time employees should work at each category and each period to maximize the total profit. The ILP uses the contribution matrix generated by Arena, and also checks for legal working requirements, and it is solved by IBM ILOG CPLEX Optimization Studio version 20.1.0.