Formulation problems
Download 326.65 Kb.
|
- Navigate this page:
- Year 1 Year 2 Year 3
- Alternative Total annual profitability Capital requirements
- Build factory in San Fransisco
- Build warehouse in San Fransisco
- Warehouse Monthy Capacity Monthly Fixed Cost
- Chicago (3) 280 units $1,200 Denver (4)
- Marketing area Warehouse North (N) South (S) West (W)
- (Fixed Charge and Facility Location)
- Farms Fixed Annual Costs ($1,000s) Projected Annual Harvest (thousands of tons)
- Plant Available Capacity (thousands of tons)
- Plant (shipping costs, $/ton) Farm A B
- There are 3 types of machines among which tha manager can cohhose: the first one costs $200, the second one has a fixed cost of $150 per week had the third one costs $100.
- Resource Requirements for Gandhi
- Shorts 2 3 Pants
- Sales Price Variable Cost Shirt
- Transportation costs ($1,000s) To Warehouse
- From Plant A B C
- Annual Demand
|
An A in a course earns 4 quality credits per credit-hour, a B earns 3 quality credits, a C earns 2 credits, a D earns 1 quality credits, an F earns no quality credits per hour. Melissa wants to select a schedule that will provide the highest possible grade point avarage. In order to remain a full-time student, which she must do to continue receiving financial aid, she must take at least 18 credit-hours. Principles of Accounting, Corporate Finance, Quantitative Methods, and C-Programming all require a lot of computing and mathematics, and Melissa would like to take no more than two of these courses. Melissa wants to develop a course which is within her capability of working 58 hours per week. Formulate a 0-1 integer programming model for this problem. (Binary Programming) 5. A corporation is planning its R&D budget over the next three years the table below shows the costs of each of the three possible projects and the quantity of funds available (both in hundreds of thousands of dollars) in each of the three years. Project Project Costs
The present values of expected future profits from the three projects are $800,000, $700000 and $ 850,000 respectively. Formulate the problem. (8) (Binary Programming) A manufacturing company has decided to expand by building a new factory in either Los Angeles or San Francisco. It is also considering building a new warehouse in whichever city is selected for the new factory. (It may or not may not build a warehouse, but if it decides to build it, it should be built at the city in which the factory is built). The total profitability of each of these alternatives is shown in the Table below. The last column gives the capital required for the respective investments, where the total capital available is $40,000,000. The objective is to find the feasible combination of alternatives that maximizes the total profitability.
Define the decision variables and formulate the problem by taking into account that Note that: The company wants to build only one new factory The company may or may not build a warehouse in a city selected for new factory. But in order to build a warehouse in a city, the decision to build a factory should have to be made, ie. İt cannot build a warehouse in a city in which a factory is not built. (Fixed Charge) GAP Inc. needs to decide on the locations for two new warehouses. The candidate sites are Philadelphia, Tampa, Denver and Chicago. The following table provides the monthly cpacities and the mothly fixed costs for operating warehouses at each potential site.
The warehouses will need to ship to three marketing areas: North, South, and West. Monthly requirements are 200 units for North, 180 units for South, and 120 units for West. The following Table provides the cost to ship one unit between each location and destination:
In addition the following conditions must be met by the final decision: A warehouse must be opened in either Philadelphia or Denver If a warehouse is opened in Tampa, then one must also be opened in Chicago Define the decision variables and formulate the model in order to determine which two sites should be selected for the new warehouses to minimize total fixed and shipping costs (Fixed Charge and Facility Location) Frijo-Lane Products own farms in Southwest and Midwest where it grows and harvests potatoes. It then ships these potatoes to three processing plants in Atlanta, Baton Rouge and Chicago where different varieties of potato products, including chips, are produced. Recently, the company has experienced a growth in its product demand so it wants to buy one or more new farms to produce more potato products. The company is considering six new farms with the following annual fixed costs and projected harvest.
The company currently has the following additional available production capacity (tons) at its three plants that it wants to utilize:
The shipping costs ($) per ton from the farms being considered for purchase to the plants are as follows:
The company wants to know which of the six farms it should purchase that will meet available production capacity at the minimum total cost, including annual fixed costs and shipping costs. (Fixed Charge). Gandhi Cloth Company is capable of manufacturing three types of clothing: shirts, shorts and pants. The manufacture of each type of clothing requires Gandhi to have the appropriate type of machinery available. There are 3 types of machines among which tha manager can cohhose: the first one costs $200, the second one has a fixed cost of $150 per week had the third one costs $100. The machinery needed to manufacture each type of clothing must be rented at the following rates: shirt machinery, $200 per week; shorts machinery, $150 per week; pants machinery, $100 per week. The first has a capacity of 400 machine hours per week, the second 350 hours qer week and thethird has a production capacity of 350 hours. The manufacture of each type of clothing also requires the amounts of cloth and labor shown below. Each week 150 hours of labor and 160 sq. yd. of cloth are available. The variable unit cost and selling price for each type of clothing are also shown below. (do not forget that Gandhi Cloth need the appropriate machinery if it is going to produce the item that require that machinery) Define the decision variables and formulate the problem in order to maximize Gandhi’s weekly profits. Resource Requirements for Gandhi
Revenue and Cost Information for Gandhi
(Fixed Charge) During the war in Iraq, Terraco Motor Company produced a vehicle for the military. The company is now planning to sell the vehicle to the public. It has four plants that manufacture the vehicle and four regional distributon centers. The company is unsure of public demand for the vehicle, so it is considering reducing its fixed operating costs by closing one or more plants, even though it would incur an increase in transportation costs. The relevant costs for the problem are provided in the following table. The transportation costs are per thousand vehicles shipped. For example, the cost of shipping 1,000 vehicles from plant 1 to warehouse C is $32,000. Transportation costs ($1,000s) To Warehouse
Formulate an integer programming model for this problem that will assist the company in determining which plants should remain open and which should be closed and the number of vehicles that should be shipped from each plant to each warehouse to minimize total cost. Download 326.65 Kb. Share with your friends:
| |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||