Optimising Production Portfolios for Profitability in a Libyan Bottled-Water SME: A Linear Programming Case Study of Shimaa Food Industries Company

Abstract

In the highly-competitive Libyan bottled-water market, Shimaa Food Industries Company faces the recurrent dilemma of allocating limited resources among four product sizes (200 mL, 330 mL, 500 mL and 1.5 L) while maximizing monthly profit. This study develops and validates a deterministic Linear Programming (LP) model that integrates real production costs, market demand limits, and technological capacity constraints. Using verified 2023 operational data, the model was solved with the Simplex algorithm via Python-SciPy and verified with Excel-Solver. The optimal production plan recommends 14,250, 25,000, 20,000, and 15,000 cartons per month for the four sizes respectively, yielding a maximum attainable profit of 150,975 LYD, an increase of 18.7% over the current heuristic plan. Sensitivity analyses were expanded to confirm solution stability within ±10 % price fluctuations and ±5 % sales capacity deviations, and to specifically examine the impact of raw material cost volatility. The paper contributes an evidence-based decision-support tool that can be embedded in Shimaa’s Sales & Operations Planning (S&OP) cycle and offers a replicable framework for similar Small and Medium Enterprises (SMEs) in the MENA region.