ENGG6140: Optimization Techniques - Engineering Assignment Help

Assignment Task

Many of the following problems are adopted from chapter 2 of the Operations Research textbook by Hamdy Taha.

1. A manufacturer firm has discontinued the production of a certain unprofitable product line. This act created considerable excess production capacity. Management is considering devoting this excess capacity to one or more of three products; call them product 1,2 and 3. The available capacity on the machines that might limit output is summarized in the first table below

The number of machine hours required for each unit of the respective products is as shown in the second table below.

The sales department indicates that the sales potential for products 1 and 2 exceeds the maximum production rate and that the sales potential for product 3 is 20 units per week. The unit profit would be 50$, 20$ and 25$, respectively, on product 1,2, and 3. The objective is to determine how much of each product the firm should produce to maximize profit. Formulate the linear programming model for this case and use Excel Solver to find the optimal product mix and the maximum profit.

2. The Windor glass Company produces high quality glass products, including windows and glass doors. It has three plants. Aluminum frames and hardware are made in plant 1, wood frames are made in plant 2, and plant 3 produces the glass and assembles the products. Because of declining earnings, top management has decided to revamp the company’s product line. Unprofitable products are being discontinued, releasing production capacity to launch two new products having large sales potential? Product 1: an 8-foot glass door with aluminum framing Product 2: a 4 x 6 foot double hung wood framed window Product 1 requires some of the production capacity in plants 1 and 3, but none in plant 2. Product 2 needs only plants 2 and 3. The marketing division has concluded that the company could sell as much of either product as could be produced by these plants. However because both products would be competing for the same production capacity in plant 3, it is not clear which mix of the two products would be most profitable. You have been assigned the mission of determining the production rates for the two products to maximize the company’s total profit subject to the restriction imposed by the limited production capacities available in the three plants. Each product will be produced in batches of 20, so the production rate is defines as the number of batches produced per week. Any combination of production rate that satisfies these restrictions is permitted. Including producing none of one product and as much as possible of the other. You asked for some data gathering regarding the number of hours production time available per week as well as time in each plants and profits of the two products which is summarized in the table below

Formulate this product mix problem and solve it using Excel Solver

3. A restaurant is open 24 hours a day. Waiters and busboys report for duty at 3 A.M., 7 A.M., 11 A.M., 3 P.M., or 11 P.M., and each works an 8-hours shift. The following table shows the minimum number of workers needed during the six periods into which the day is divided

How should the restaurant manager schedule the workers so that the total staff required for one day’s operation is minimized? Formulate the mathematical programming model of this problem and use Excel solver to find the optimal solution.

4. The Hudson group has opened a new city center mall in West of Mississauga , the mall general manager want to make sure that enough support staff are available to clean the mall before it opens each day. The mall operates seven days a week, and the cleaning staff work between 12:30 A.M. 2 and 8:30 A.M. each night. Based on projected mall traffic data for the upcoming week, the manager estimates that the number of cleaning staff required each day will be as shown in the table below.

The general manager can use the work schedules shown in the following table for the cleaning staff. With the wages for each schedule are also shown in the table.

In order to be perceived as being a fair employer, the manager wants to ensure that at least 75% of the workers have two consecutive days off and at least 50% of the workers have at least one weekend day off. Formulate the mathematical programming problem and use Excel solver to determine how should the manager schedule his cleaning staff in order to meet the mall’s requirement and minimize the total wages?

5. HSBC investment manager is considering investing $3 million USD in oil companies’ stocks intending to purchase a large blocks of shares and diversify the investment within the oil sector. The table below summarizes the Expected annual return and the cost for buying a block of shares (in thousands) for seven companies that are under consideration by the HSBC manager.

With the objective to maximize the annual return on investment and taking into consideration the following specifications made by the investment board

(a) Exactly one of the two Canadian companies must be included.

(b) At least two companies from USA must be in the portfolio.

(c) No more than one investment can be made in foreign (non North American companies).

(d) If British Petroleum is selected, then Texaco must also be included.

formulate the mathematical Binary Integer programming model and use Excel Solver to find the optimal stock choice and the expected maximum annual return.

6. (Problem category set coverage) Aloha trucking company is considering one or more location as a designated hub to serve the eight cities throughout the USA in which it has business. The hub location is such that it can serve other cities which are within 1400 mile radius from it. Aloha trucking wants to have the minimum number of hubs necessary to cover all the eight cities. The table below indicate the distances between the seven cities served by Aloha. Formulate the mathematical optimization problem and then find in which cities should Aloha trucking have their hubs? (Use Excel solver to find the optimal solution)

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