Optimizing Shift Scheduling for Retail Cashiers Using Binary Integer Programming

Abstract

Workforce scheduling in small-scale retail environments presents operational challenges due to limited staffing flexibility and fairness considerations in shift allocation. Existing scheduling approaches often emphasize large-scale systems and may not adequately address fairness-oriented constraints in compact retail settings. This study develops a Binary Integer Programming (BIP) model to generate a seven-day shift schedule for seven cashiers at a retail outlet (Eco-Shop Balok branch). The model satisfies operational staffing requirements while minimizing violations of soft constraints, including consecutive workdays, excessive full-day assignments, and imbalance in morning shift distribution. Hard constraints ensure daily coverage and regulatory compliance, whereas soft constraints are incorporated through weighted penalty variables in the objective function. The model is implemented using LINGO, and results indicate that the optimized schedule increased morning shift staffing from one staff member working twice the morning shift to three staff to match preferences for lighter workloads and earlier finishes, while decreasing full-day shifts from five to three staff, improving work-life balance. Noon shift efficiency was maintained with a cashier working it three times a week, reduced from two to one. A seven-week cyclical schedule was also proposed to ensure long-term fairness and sustainability. The findings confirm that BIP provides a transparent and computationally efficient framework for small-scale retail workforce optimization, offering practical applicability for similar operational environments.