Mathematical Optimization Techniques for Scheduling and Planning in Small Business Operations

Efficient scheduling and resource planning remain critical success factors for small businesses operating under resource constraints and limited operational budgets. Unlike large corporations with dedicated planning teams and advanced ERP systems, small enterprises frequently rely on manual or heuristic-based approaches that may lead to suboptimal resource utilization, delays, and increased costs. Mathematical optimization offers systematic, data-driven solutions for addressing these challenges, leveraging methods such as linear programming (LP), integer programming (IP), and heuristic algorithms to improve scheduling and planning decisions. This paper explores various mathematical optimization techniques applicable to small business operations, focusing on workforce scheduling, production planning, and service appointment management. The study presents model formulations, case examples, and practical considerations for implementation, providing actionable insights into how small businesses can enhance their operational efficiency through optimization.