A Multi-Objective Optimization of Probability and Capacity Utilization in a Feed Manufacturing Firm Using Goal Programming Techniques

Abstract

This study aimed to create a mathematical model for a feed manufacturing firm that maximizes profit, minimizes cost, and maximizes capacity utilization simultaneously. Data on materials, products, and targets were collected and analysed to form the necessary parameters for the model. Two models were developed: Weighted Lexicographic (WLGP) and Weighted Meta Goal Programming (WMGP). The models included various constraints such as goals, capacity, material proportion, material balance, and demand ratios. Lingo 20.0 optimization software was used to solve the models. The feed manufacturing firm dealt with 15 materials and produced 5 products. The target was to achieve a profit of ₦9,000,000 without exceeding a cost of ₦62,000,000, while utilizing 98% of the production capacity. In Case 1 (profit maximization), the firm achieved the profit target but slightly fell short of the capacity utilization goal by 0.14%. In Case 2 (cost minimization), the firm achieved the cost goal but had a profit shortfall and a slight underachievement in capacity utilization. In Case 3 (capacity utilization maximization), the firm attained the desired capacity utilization goal but had an excess profit and an overachievement in cost. Monthly feed type allocations varied based on the prioritized objective in each case. The WMGP method was also used, and all goals were achieved within acceptable limits. Material allocation aligned with the outcomes of Case 3 in the WLGP method. In conclusion, WLGP and WMGP approaches proved valuable for optimizing production in the poultry feed industry.