Linear Optimization using Excel

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Presentation transcript:

Linear Optimization using Excel

3-Steps Optimization Process Model Development Optimization Evaluation Model development is the most difficult part of the optimization process. The evaluation involves sensitivity analysis of the optimized solution. It consists of the sensitivity analysis of the variables and the constraints.

Common Features Objective Input Variables Decision variables Constraints Objective to maximize or minimize Input variables may be resources and profits How many to make or allocate Constraints might be machine hours, labour hours or demand.

Case 1 Saleem & Co manufactures jugs and glasses using machines A and B. The following hours are required to make one jug and glass: Machine A: 2 hours (for jug) and 1.5 hours (for glass) Machine B: 1.4 hours (for jug) and 1.1 hours (for glass) Total 400 hours are available on Machine A and 350 hours on Machine B. Contribution margin from jug is Rs. 15 and from glass Rs. 10. Required: Determine the optimal mix of jugs and glasses in order to maximize the contribution

Case 2 Pak-Suzuki makes two types of air-filters: regular and premium. The unit profit of each of them is Rs. 500 and Rs. 700. Both uses the following inputs: Labour Hours: 3 (Reg.) and 4 (Prem.) ---- Max. Cap. 3000 hrs Plastic components: 2 (Reg.) and 3 (Prem.) --- Max. Cap. 2500 comp. Machine hours: 0.75 (Reg.) and 1.20 (Prem.) --- Max. Cap. 5000 hrs Required: Optimal product mix of the regular and the premium air filters

Case 3 Pak-Suzuki makes two types of air-filters: regular and premium. The unit profit of each of them is Rs. 500 and Rs. 700. Both uses the following inputs: Labour Hours: 3 (Reg.) and 4 (Prem.) ---- Max. Cap. 3000 hrs Plastic components: 2 (Reg.) and 3 (Prem.) --- Max. Cap. 2500 comp. Machine hours: 0.75 (Reg.) and 1.20 (Prem.) --- Max. Cap. 5000 hrs Demand: Max. (Reg.) 500 and Max. (Prem.) 400 Required: Optimal product mix of the regular and the premium air filters

Case 4 Required: Use the following information to find the optimal product mix of mice, keyboards and USB hubs.

Case 5 Investment Optimization Ali wants to invest Rs. 1,000,000/- in the financial assets in Pakistan. His analysis shows the following expected profits on the major asset classes: Derivatives 28% High Risk Equity 21% High Risk Bonds 16% Low Risk Money Market 13% Low Risk He does not want to invest more than 35% in anyone of the asset classes and more than 60% in the high risk assets. Required: Optimal portfolio mix that maximizes the annual return.