Question: Based on the following case study, imagine a similar problem and analyze it (a. Formulate a linear programming model and write down the mathematical model
Based on the following case study, imagine a similar problem and analyze it (a. Formulate a linear programming model and write down the mathematical model for this problem; b. Solve this problem using QM and SOLVER; c. Create a sensitivity report; d. Explain the shadow price, reduced cost and the allowable range (increase and decrease).
UDT is a consulting firm that develops e-commerce project, systems and websites for its clients. It has six available consultants and eight clients project is under contract. The consultants have different technical abilities and experience, and as a result, the company charges different hourly rates for its services. Also, the consultants skill are more suited for some projects than others, and clients sometimes prefer some consultants over others. The suitability of a consultant for a project is rated according to a 5-point scale, in which 1 is the worst and 5 is the best. The following table shows the rating for each consultant for each project, as well as the hours available for each consultant and the contracted hours and maximum budget for each project :
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| Project | ||||||||
| Consultant | Hourly wage | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | Available hours |
| A | $155 | 3 | 3 | 5 | 5 | 3 | 3 | 3 | 3 | 550 |
| B | $140 | 3 | 3 | 2 | 5 | 5 | 5 | 3 | 3 | 600 |
| C | $165 | 2 | 1 | 3 | 3 | 2 | 1 | 5 | 3 | 500 |
| D | $300 | 1 | 3 | 1 | 1 | 2 | 2 | 5 | 1 | 400 |
| E | $270 | 3 | 1 | 1 | 2 | 2 | 1 | 3 | 3 | 710 |
| F | $150 | 4 | 5 | 3 | 2 | 3 | 5 | 4 | 3 | 860 |
| Project Hours |
| 510 | 240 | 420 | 475 | 350 | 460 | 290 | 200 |
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| Contract budget (x1000 USD) |
| 90 | 80 | 110 | 90 | 65 | 85 | 50 | 55 |
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The company wants to know how many hours to assign each consultant to each project in order to best utilize their skill while meeting clients needs.
- Decision Making
Petrolimex Gas station are soon going to open a new dealership. They have 3 offers: from a local gas company, from a provider and from a big gas corporation. The success of each type of dealership will depend on how much gasoline is going to be available during the next few years.
Fill the profit of each type of dealership, giving the availability of gas data to the following payoff table (unit: million VND). Draw a decision tree to help Petrolimex choose whats best for the profit.
| Dealership | Gasoline Shortage | Gasoline Surplus |
| Local gas company |
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| Provider |
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| Corporation |
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| Prior probability % | 60% | 40% |
- Forecasting
Fill the monthly demand of a water bottle extracted from a supermarket data to the following table.
| Month | Demand |
| 1 |
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| 5 |
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| 6 |
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| 7 |
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| 8 |
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| 9 |
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| 11 |
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| 12 |
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- Using averaging forecasting method, calculate the forecast.
- Using 3-month moving average forecasting method (n=3), calculate the forecast.
- Using last-value forecasting method, calculate the forecast.
- Explain 3 methods of forecast. Which one is better and more accurate according to you? You can explain however you want.
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