An Optimal Model and Production Planning in Upholstery by Linear Integer Programming

Abstract

This research effort used an upholstery factory as a case study to apply the idea of integer programming for an ideal model. In order to allocate limited and readily available material resources to competing products (Bed (6x6ft), Bed (6x4ft), Wardrobe (6x6ft), Wardrobe (6x4ft), Side Drawer, and Shoe Rack) in the furniture factory with a view to maximizing profit, the Revised Simplex method of solving linear programming and the branch and bound method of solving integer programming models were used in this study. The analysis was carried out with the help of the LINDO software version 6.1 using data containing the availability of materials, sales volume for each of the product types, machine and time it takes to complete the manufacturing process of each product type, as well as profit per unit of the product as collected from the factory. The outcome indicated that 38 units of the Bed (6x6ft), 10 units of the Wardrobe (6x4ft), and 0 units of the other products needed to be manufactured to make a monthly profit of no more than  ₦1711700. From the result, it was observed that the Wardrobe (6x4ft) and Bed (6x6ft) contributed majorly to the profit, hence the recommendation that more of the Wardrobe (6x4ft) should be produced and sold for optimum profit.