Linear optimization of fish processing: A Case study of Lake Harvest Company, Kariba, Zimbabwe

Abstract

The aim of this study was to develop a Net Profit Contribution maximisation model that can be used as a decision tool to aid production managers in determining how best to allocate materials for fish processing, allocate labour hours, meeting customer demand while also preventing inventory build-up. The data was obtained from the operations data obtained from the company’s internal reports availed by management. Analysis was done using the linear programming (LP) model. LP is a renowned tool for the purposes of optimisation when faced with resource constraints, yet profits are to be maximised. Two LP models were developed, to determine the processing allocation that maximises Net profit contribution and examine if it was profitable to use overtime with the available production capacity. Several assumptions were made, which are common when formulating LP models. First is that of linearity of variables. The expression to be optimized and the inequalities are assumed to be linear functions of the variables. Second, it was assumed that prices are fixed, for the period under consideration, and possible returns were fixed. The result show that the company stands to realise a high objective value when there is no overtime (Model 2). This indicates that the costs associated with overtime are not offset with the associated benefit. As such, in financial terms, it is advisable that the company do away with overtime. However, management also should consider other factors such as the need to continue providing products which could be forgone by discontinuing overtime. When overtime is avoided, model 2, more of product type B is produced and less of product type A. As such, the need to keep the customers loyal to product type A may compel management to continue with overtime, however at the expense of a declining objective value.