MULTI-PERIOD STAFFING SCHEDULING OPTIMIZATION BASED ON COLUMN GENERATION AND NETWORK FLOW ALGORITHMS

Abstract

This study develops an algorithmic staffing-scheduling framework for multi-day, multi-group, and multi-period service systems. The model minimizes temporary workforce size while satisfying hourly demand, eight-hour work-pattern rules, and individual assignment restrictions. A fixed-group mode is first modeled through column generation, where a restricted master problem is iteratively expanded by work patterns with negative reduced cost. A flexible mode is then formulated for single-group-per-day service with cross-day reassignment. It introduces employment variables, group assignment variables, pattern variables, and a pricing subproblem represented as a minimum-cost maximum-flow network with node-capacity constraints. MATLAB implementation and branch-and-price obtain a 406-worker solution for the flexible mode, reducing the benchmark workforce by 18 workers and improving allocation efficiency by 4.25%. Visual results verify demand coverage, feasible work calendars, mode-frequency alignment with demand peaks, and balanced workforce distribution across groups and days.