(a) Formulate a mixed-integer programming model that could be used to help Martin-Beck determine which new plant or plants to open in orderto satisfy anticipated demand and minimize total cost (in thousands of dollars). (Let x = units shipped in thousands from plant i todistribution center with the existing plant in St. Louis being plant number 5. Let Y, 1 fa plant is constructed in Detroit and o if not,Y, = 1 if a plant is constructed in Toledo and o if not, y, =1 if a plant is constructed in Denver and o if not, and y, = 1 if a plant isconstructed in Kansas City and O if not.)Mins.t.Detroit CapadityToledo CapacityDenver CapacityKansas City CapacitySt. Louis CapacityBoston DemandAtlanta DemandHouston Demand20 for all i and j and y, y, Y Y, binary(b) Solve the model you formulated in part (a). What is the optimal cost (in s)?What is the optimal set of plants to open? (Select all that apply.)O DetroitO ToledoO DenverD Kansas CityAttanta DemandHouston Demand2o for all i and j and y Y binary(b) Solve the model you formulated in part (a). what is the optimal cost (in s)?What is the optimal set of plants to open? (Select all that apply.)ODetroitO ToledoDenverKansas City(9 Uing equation (13.1),(Sum of varables in the set O) - (sum of varlables in the set 2) (number of variables in the set o) -1where O is the set of binary variatles in our original optimal solution set to one and 2is the set of those set to zero, find a second bestsolution What is the increase in cost (in $) versus the best solution from part (b) The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution centerslocated in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin-Beck plans to increase capacity by constructing anew plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas City. The estimated annual fixed cost and the annual capacityfor the four proposed plants are as follows:Plant NumberProposed PlantAnnual Fixed CostAnnual CapacityDetroit$200,00010,0002.Toledo$325,00020,0003.Denver$350,00030,0004Kansas City$525,00040,000The company's long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows.DistributionDistributionAnnual DemandCenter NumberCenterBoston20,0002.Atlanta30,000Houston30,000The shipping cost per unit from each plant to each distribution center is an follows.Distribution CentersPlant SiteBostonAtlantaHoustonDetroit3Toledo434DenverKansas City104St. Louis3.4.new nlantor nlants to nnen in orderin1,

Answered: The Martin-Beck Company operates a…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section6.5: Set-covering And Location-assignment Models

Problem 34P

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The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution centers located in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin-Beck plans to increase capacity by constructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas City. The estimated annual fixed cost and the annual capacity for the four proposed plants are as follows: Proposed Plant Annual Fixed Cost Annual Capacity Detroit $175,000 20,000 Toledo $300,000 30,000 Denver $375,000 40,000 Kansas City $500,000 10,000 The company’s long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows: Distribution Center Annual Demand Boston 20,000 Atlanta 30,000 Houston 20,000 The shipping cost per unit from each plant to each distribution center is as follows: Distribution Centers Plant…
The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution centers located in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin-Beck plans to increase capacity by constructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas City. The estimated annual fixed cost and the annual capacity for the four proposed plants are as follows: Proposed Plant Annual Fixed Cost Annual Capacity Detroit $175,000 20,000 Toledo $300,000 30,000 Denver $375,000 40,000 Kansas City $500,000 10,000 The company’s long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows: Distribution Center Annual Demand Boston 20,000 Atlanta 30,000 Houston 20,000 The shipping cost per unit from each plant to each distribution center is as follows: Distribution Centers Plant…
The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution centers located in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin-Beck plans to increase capacity by constructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas City. The estimated annual fixed cost and the annual capacity for the four proposed plants are as follows: Plant Number Proposed Plant Annual Fixed Cost Annual Capacity 1 Detroit $150,000 10,000 2 Toledo $275,000 20,000 3 Denver $400,000 30,000 4 Kansas City $475,000 40,000 The company's long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows. DistributionCenter Number DistributionCenter Annual Demand 1 Boston 20,000 2 Atlanta 30,000 3 Houston 30,000 The shipping cost per unit from each plant to each distribution center is as…
A rapidly expanding company is looking to lease a small plant in Memphis, Tennessee, Biloxi, Mississippi, or Birmingham, Alabama. Prepare a cost benefit study for each of the three locations using the following data: The annual construction, facilities, and administration expenses for Memphis, Biloxi, and Birmingham will be $40,000, $60,000, and $100,000, respectively. In Memphis, labour and materials are estimated to cost $8 per month, $4 in Biloxi, and $5 in Birmingham. The Memphis site would add $50,000 a year to device transportation expenses, the Biloxi location would add $60,000 per year, and the Birmingham location would add $25,000 per year. The annual production is expected to be 10,000 units.
The Executive Furniture Corporation, which manufactures office desks at three locations: Des Moines, Evansville and Fort Lauderdale. The firm distributes the desks through regional warehouses located in Albuquerque, Boston and Cleveland. The production costs per desk are the same at each factory and hence the only relevant costs are those of shipping from each source to each destination. They are assumed to be constant regardless of their volume shipped. An estimate of the monthly production capacity at each factory and estimate of the number of desks required per month at each destination and the shipping cost ($) per desk from each source to each destination is given in the following table: Transportation table for Executive Furniture Corporation To From Albuquerque Boston Cleveland Factory capacity Des Moines 6 5 8 300 Evansville 5 9 8 400 Fort Lauderdale 4 5 6 350 Requirements 350 250 450…
SC Consulting, a supply chain consulting firm, must decide on the location of its home offices. Its clients are located primarily in the 5 states listed below. There are four potential sites for home offices: Los Angeles, Tulsa, Denver, and Seattle. The annual fixed cost of locating an office in Los Angeles is $165,000, Tulsa is $131,000, Denver is $140,000, and Seattle is $145,000. The expected number of trips to each state and the travel costs from each potential site are shown below. Each consultant is expected to take at most 40 trips each year.If at most 3 consultants are to be assigned to a home office, where should the offices be set up? How many consultants should be assigned to each office? What is the annual cost of this network? Please generate the conceptual model and excel model to answer these questions.Travel cost ($)Los Angeles Tulsa Denver Seattle Number of trips requiredWashington 150 250 200 25 40Oregon 150 250 200 75 35California 75 200 150 125 100Idaho 150 200 125…
SC Consulting, a supply chain consulting firm, must decide on the location of its home offices. Its clients are located primarily in the 5 states listed below. There are four potential sites for home offices: Los Angeles, Tulsa, Denver, and Seattle. The annual fixed cost of locating an office in Los Angeles is $165,000, Tulsa is $131,000, Denver is $140,000, and Seattle is $145,000. The expected number of trips to each state and the travel costs from each potential site are shown below. Each consultant is expected to take at most 40 trips each year. If at most 3 consultants are to be assigned to a home office, where should the offices be set up? How many consultants should be assigned to each office? What is the annual cost of this network? Travel cost ($) Los Angeles Tulsa Denver Seattle Number of trips required Washington 150 250 200 25 40 Oregon 150 250 200 75 35 California 75 200 150 125 100 Idaho 150 200 125 125 25 Nevada 100 200 125 150 40 Tips: The limit number of consultants…
Anderson Watch Company is considering opening four possible distribution centers located in Atlanta, Lexington, Milwaukee, and Salt Lake City with a fixed cost to open of $17,000, $22,000, $35,000, and $25,000, respectively. They currently have ten retail stores located in Seattle, San Francisco, Las Vegas, Tucson, Denver, Dallas, Birmingham, Orlando, Cleveland, and Philadelphia. Lisa, the supply chain VP, wants to minimize the transportation costs of shipping their French down pillows. The per-unit shipping cost from each distribution center to each retail location and the amounts currently in inventory and ordered at each retail location are shown in the following tables. What is the minimum cost solution? What is the minimum cost solution if Lisa wants to use single sourcing?
A concrete company transports concrete from their three plants in Nyanyano.- town, Feteh. -town and Tuba.- town to their three construction sites in Ofaakor.- site, Papaase.- site and Krodua. -site. The supply capacities of the three plants, the demand requirements at the three sites, and the transportation costs per ton are as follows: Construction Site Plant O.- site P.- site K. -site Supply(tons) N. town GHs 8 GHs 5 GHs 6 GHs 120 F. town 15 10 12 80 T. town 3 9 10 80 Demand(tons) 150 70 100 280 XXXa) Establish the decision variables for this transportation problem. XXXb) Develop a network graph showing all costs and decision variables. c) i. Formulate the mathematical model that will be used to solve the problem on a computer ii. Fine the initial feasible solution using the Northwest Corner Rule and the total cost. PLEASE ANSWER ONLY C i and C ii PART OF THE QUESTION.
A semiconductor manufacturer produces a particular solid-state module that it supplies to four different television manufacturers. The module can be produced at each of the corporation's three plants, although the costs vary because of differing production efficiencies at the plants. Specifically, it costs 110 units to produce a module at plant A, 95 units at plant B and 103 units at plant C. Monthly production capacities of the plants are 7500, 10000, and 8100 modules, respectively. Sales forecasts project monthly demand at 4200, 8300,6300 and 2700 modules for television manufacturers I, II, III and IV respectively. If the cost for shipping a module from a factory to a manufacturer is as shown below, find a production schedule that will meet all needs at minimum total cost. II II IV 1 13 9. 19 В 1 16 1 14 2 13 1 15 4
A salesman for Healthproof Pharmaceutical Company travels each week from his office in Atlanta to one of five cities in the Southeast where he has clients. The travel time (in hours) between cities along interstate highways is shown along each branch in the following network: A. Determine the shortest route from Atlanta to each of the other five cities in the network. B. Assume that the network now represents six different communities in a city and that the local transportation authority wants to design a rail system that will connect all six communities with the minimum amount of track. The miles between each community are shown on each branch. Develop a minimal spanning tree for this problem.
Tommy Hilfiger is currently considering to source certain textile goods, Tommy Jeans, from Mexico. The estimated shipping time from Mexico to the U.S. for each shipment of Tommy Jeans is 4 days and the estimated freight cost of each shipment is $800. On the other hand, the current average shipping time from Vietnam to the U.S. for each shipment of Tommy Jeans is 23 days and the average freight cost is $2300. Even though the shipping time and freight cost seem to be much lower in case of Mexico, Tommy Hilfiger management is concerned about the production cost of each Jeans shipment. The management anticipates that the production cost of each Jeans shipment will be higher in Mexico compared to Vietnam. However, Tommy Hilfiger management has decided that even if the total cost (sum of production cost, freight cost, and holding cost) remain similar to Vietnam, Tommy Hilfiger will still source Jeans from Mexico because of the reduced shipping time, which, in turn, will result in better…

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