Introduction
In an optimization problem, the nature of mathematical relationship between the objective and constraints as well as the interconnection between the decision variables determines the optimum level of any operation (Solver.com, 2009). If the objective and all of the constraints involved are convex in nature – that is adjustable according to the needs – then it becomes possible to find a feasible solution. “To optimize a manufacturing system means that the effort to find best solutions focuses on finding the most effective use of resources over time.” (Yu-Lee, n.d.)
Main Body
In the case of the Ribble Kitchen Company the product mix that will generate optimum profits using the resources subject to the constraints has been worked out using excel solver function and the results are shown as appendix to this report. This report analyzes the results shown by the solver.
It can be observed from the results that the final values of the objective function (profit as shown by the target cell) and the decision variables (products as shown in the adjustable cells) are clearly indicated. The report also shows the status of the usage and slack in respect of each of the constraint. The final product mix and the resulting profit are shown in the following table.
The answer sheet showing the calculation of optimum profit and slacks is shown in appendix 1.
It may be noticed that the constraint of the minimum production quantities in respect of chairs and cabinets and the maximum production quantities in respect of tables and cupboards have been met. The optimum profit has been arrived at 13,590.
The status of usage and the slacks in the resources is represented by the following table adopted from the results of the solver exercise.
From the results it can be observed that the resources of machine and labor have been completely utilized and there is a slack of 140 in respect of wood and 40 in respect of corian which can be effectively used in other production.
Suggestions for Improving Profitability
Although the optimum profit from the operations of the company subject to the production constraints has been calculated, if there is no constraints on arranging for more labor and machines the company can profitably use the remaining wood and corian.
The other option available is to reduce the margin on the tables and try to get a contract for some of the tables which may increase the profits for the company. The company can work on increasing the quantities on contract in respect of chairs and cabinets especially cabinets where the profitability is more. Based on the revised product mix the resources can be rearranged so that the company would be able to maximize its profits. However on these variables the management has no control. Therefore the sensitivity is worked out on different levels of increase in the resources to use the slack in the wood and corian.
Sensitivity Analysis
The sensitivity analysis is worked out in three scenarios assuming that the management has no constraint in arranging for additional resources.
Scenario 1
- Increase in Machines 10%
- Increase in Labor 10%
- The answer report of excel solver with the increase of 10% in machine and labor is shown as appendix 2. In this case with the original constraints on the production, the profit has increased to 14,960.
Scenario 2
- Increase in Machines 20%
- Increase in Labor 20%
- The answer report of excel solver with the increase of 20% in machine and labor is shown as appendix 3. In this case with the original constraints on the production, the profit has increased to 15,930.
Scenario 3
- Increase in Machines 30%
- Increase in Labor 30%
- The answer report of excel solver with the increase of 30% in machine and labor is shown as appendix 4. In this case with the original constraints on the production, the profit has increased to 16,700.
Conclusion
Subject to the feasibility the management may decide to increase the labor and machines by 20% as at this level there is the optimum utilization of all resources and a profit of 15,930. If the labor and machines are increased by 30% even though the profit increases to 16,700, there is a slack of 26 wood and 20 labor remaining unutilized. With the increase of 10% in both the resources, still there is a slack of 102 wood. When the machines and labor is increased by 20% the only slack is 64 in wood which scenario appears to be the best possible, of course subject to the feasibility of increasing the labor and machines to the required extent.
Reference
Solver.com, 2009. Problem Types – Overview. [Online] Web.
Yu-Lee, R.T., n.d. Manufacutring Optimization: It’s about Time. [Online] Web.
Appendix 1
Answer Report showing the Optimum Profit with the available Resources and Constraints on Production
Appendix 2
Sensitivity Report – Scenario 1 – Increase in Machine and Labor by 10%
Appendix 3
Sensitivity Report – Scenario 2 – Increase in Machine and Labor by 10%