Please do not give image format The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distributioncenters located in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin-Beck plans to increase capacity byconstructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas City. The estimated annual fixed cost and theannual capacity for the four proposed plants are as follows:Proposed PlantDetroitToledoDenverKansas CityThe company's long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows:Distribution CenterBostonAtlantaAnnual Fixed Cost$175,000$300,000$375,000$500,000HoustonAnnual Capacity20,00030,00040,00010,000Annual Demand30,00020,00020,000 The shipping cost per unit from each plant to each distribution center is as follows:Plant SiteDetroitToledoDenverKansas CitySt. LouisBoston549108Distribution CentersAtlanta23744Houston34523(a) Develop a mixed-integer programming model that could be used to help Martin-Beck determine which new plant or plants to open in orderto satisfy anticipated demand. Solve the model and answer the following questions. What is the optimal cost?$ 104800What is the optimal set of plants to open?Detroit & Toledo(b) Using equation 13.1, find a second-best solution. What is the optimal set of plants to open?DenverWhat is the increase in cost versus the best solution from part (a)?$ 120000

Note: For Part B, the given equation is not provided, so we solved part A alone.Find the Given…

Answered: The shipping cost per unit from each…

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.
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…
A logistics company plans to provide coal logistics transportation services to HY coal sales enterprise. HY coal sales enterprise has coal storage and sales points in B and D, with available coal quantities of 1600t and 8000t, respectively; A and C represents the locations of two coal users, with a demand of 8000t and 1600t respectively. The distribution of relevant locations and travel distances are shown in Figure 1. Based on the above conditions, try to calculate and explain from the perspective of transportation capacity consumption: How should logistics company HY plan transportation routes in order to make them more reasonable? (a transportation route planning scheme needs to be illustrated) . Note:The solution should not be hand written.
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 $2300. Even though the shipping time and freight cost seem to be much lower in case of Mexico, Tommy Hilfiger management is concerned about the production cost of each Jeans shipment. The management anticipates that the production cost of each Jeans shipment will be higher in Mexico compared to Vietnam. However, Tommy Hilfiger management has decided that even if the total cost (sum of production cost, freight cost, and holding cost) remain similar to Vietnam, Tommy Hilfiger will still source Jeans from Mexico because of the reduced shipping time, which, in turn, will result in better…
The Executive Furniture Corporation, which manufactures office desks at three locations: Des Moines, Evansville and Fort Lauderdale. The firm distributes the desks through regional warehouses located in Albuquerque, Boston and Cleveland. The production costs per desk are the same at each factory and hence the only relevant costs are those of shipping from each source to each destination. They are assumed to be constant regardless of their volume shipped. An estimate of the monthly production capacity at each factory and estimate of the number of desks required per month at each destination and the shipping cost ($) 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…
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?
PharmaCo wants to determine how to deploy sales representatives across its Western U.S. region to support a new drug for obesity. Sales representatives will be located in a "home city", which they serve, in addition to cities with feasible commuting distance, with the objective that all cities must be served by at least one sales representative. The feasible connections between each city in the region are listed below (1 indicates a feasible connection, potential home cities are shown in columns, and cities served in rows): Potential Rep Home City Served? Albuquerque El Paso Denver Phoenix San Diego Los Angeles San Francisco Portland Seattle Las Vegas Salt Lake City Albuquerque 1 1 1 1 0 0 0 0 0 0 0 El Paso 1 1 0 1 0 0 0 0 0 0 0 Denver 1 0 1 1 0 0 0 0 0 0 1 Phoenix 1 1 1 1 1 1 0 0 0 1 1 San Diego 0 0 0 1 1 1 1 0 0 1 0…
PharmaCo wants to determine how to deploy sales representatives across its Western U.S. region to support a new drug for obesity. Sales representatives will be located in a "home city", which they serve, in addition to cities with feasible commuting distance, with the objective that all cities must be served by at least one sales representative. The feasible connections between each city in the region are listed below (1 indicates a feasible connection, potential home cities are shown in columns, and cities served in rows): Potential Rep Home City Served? Albuquerque El Paso Denver Phoenix San Diego Los Angeles San Francisco Portland Seattle Las Vegas Salt Lake City Albuquerque 1 1 1 1 0 0 0 0 0 0 0 El Paso 1 1 0 1 0 0 0 0 0 0 0 Denver 1 0 1 1 0 0 0 0 0 0 1 Phoenix 1 1 1 1 1 1 0 0 0 1 1 San Diego 0 0 0 1 1 1 1 0 0 1 0…

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