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Application of Linear Programming to the Product Mix Problem of a Joinery Factory
Thesis Abstract:
This study primarily determined the profitable product mix of a joinery factory producing a variety of designs and sizes of different types of products. It presupposed that among these various prodcuts, there was an optimum combination that was most appropriate for the processing system which could give the highest possible economic returns. It then focused on the allocation of the input wood resource among the different alternative products and on the processing requirements of each product in the entire manufacturing system.
Three versions of a linear programming model were used in this study. The first described the present conditions in the processing system. Its function was to determine the products and quantities to be produced and how much profit would be realized if the company stuck to its sales commitments. The second version disregarded minimum sales requirements to see how the system's profitability was affected by ignoring sales restrictions. The third version depicted complete freedom from outpost restrictions to see what further profit improvement could be possible by concentrating only on the high-revenue producing products, provided that the total output of any type was within the system's capability to produce.
The results showed that there was an optimal product mix for each of the three coniditions assumed to exist in the mill. Further, the present production policy of the company, whereby it produced a minimum quantity of most of the caskets, gave the least amount of profit. Profit increased if no lower output limits on these produts wre imposed. Maximum profit was attained when no production limits were defined for all the products with only the processing capability of the mill as the limiting factor.