Solution of Goal Programming Product Mix Problem with Cohort Intelligence Algorithm

The product mix problem in supply chain management refers to the problem of selecting the optimal combination of products for manufacturing. It is the problem of deciding which products to manufacture and in how many quantities to fulfil the customer demand while minimizing the costs and maximizing the profits. It is considered as an important enabler for the sustainable supply chain. It is often a complex, multi-variate and multi-objective problem with various parameters such as customer demand, production costs, inventory costs, marketing costs, profitability levels, etc. Goal Programming (GP) is proved to be an effective technique for modelling such complex multi-objective problems. In this work, a GP-based product mix problem with four products (variables) and five objectives (related to the supply of products) is solved with Cohort Intelligence (CI) algorithm. Three constraint handling approaches viz. Penalty Function-based (PF), Probability-based (Prob) and Hybridization of PF and Prob are applied along with four variations of CI algorithm. CI algorithm yields 28.4% improved results as compared to Simulated Annealing, Tabu Search and LINGO algorithms. In the near future, a large-size product mix problem can be solved with the proposed techniques.