Minimization of total production cost using branch and bound integer programming

Abstract

With the acute depreciation of the naira, companies that rely on imported inputs are facing difficulties sourcing such. To survive this type of economic downturn there is need that these companies streamline costs. This state of affairs motivates the study of Harmony foam industry which imports most of its inputs. Harmony foam industry faces resource constraints occasioned by difficulty in sourcing foreign exchange to produce raw materials which makes cost minimization a necessary survival strategy. The objective of the study is to determine the quantity of each size of foam to produce using the available raw materials in order to minimize the production cost. The study employed interview and observation methods to determine the product mix that minimizes the cost of Harmony Foam industry in Ikwuano, Abia State, in a two hour production run using the branch and bound integer programming algorithm. Appling the branch and bound integer programming algorithm on eight (8) different sizes of Harmony foamled to a solution afterthirteenbranching from the initial linear programming optimal solution. This result showsthat for Harmony foam industry to achieve a minimum total production cost of N18, 624,202.74 from the production of the foams, it is required to produce 153 units of 54by75by10 inches foams and 430 units of 54by75by30 inches foams. Based on the result, we conclude that the unit production cost of 54X75X6, 54X75X8, 54X75X10, 54X75X14, 54X75X18, 54X75X20, 54X75X24 and54X75X30) inches are N8052.2; N10,507.0; N12,958; N21,850;N27,740; N32,600; N35,000 and N38,700 respectively. Apart from the recommendation that harmony foam industry adheres to the various cost of different foams to achieve a minimal production cost,we suggest that other companies should use integer programming approach to streamline their unit cost of production.