BUS 660 Week 5 Linear Programming Distribution and Network Models – Homework

(BUS 660 Week 5 Linear Programming Distribution)

Problem 10-05: Premier Consulting’s two consultants, Avery and Baker, can … to work for clients up to a maximum of 160 hours each over the next four weeks. A third consultant, Campbell, has some administrative assignments already … and is available for clients up to a maximum of 140 hours over the next four weeks. The company has four clients with projects in process. The … hourly requirements for each of the clients over the four-week period are as follows:

Hourly rates vary for the consultant–client combination and are … on several factors, including project type and the consultant’s experience. The rates (dollars per hour) for each consultant–client combination are as follows:

1. Choose the correct network representation of the problem.
2. Formulate the problem as a linear program, with the optimal solution providing the hours each consultant should … for each client to maximize the consulting firm’s billings. What is the schedule and what is the total billing? Let xij = number of hours from consultant i … to client j.
3. New information shows that Avery doesn’t have the experience to … for client B. If this consulting assignment is not permitted, what impact does it have on total billings? What is the revised schedule?

Problem 10-25: Cleveland Area Rapid Delivery (CARD) operates a delivery service in the Cleveland metropolitan area. Most of CARD’s business involves rapid delivery of documents and parcels between offices during the business day. CARD promotes its ability to make fast and on-time deliveries anywhere in the metropolitan area. When a customer calls with a delivery request, CARD quotes a … delivery time. The following network shows the street routes available. The numbers above each arc indicate the travel time in minutes between the two locations.

6. Develop a linear programming model that can … to find the minimum time … to make a delivery from location 1 to location 6. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank.
7. How long does it take to make a delivery from location 1 to location 6?
8. Assume that it is now 1:00 P.M. and that CARD just … a request for a pickup at location 1. The closest CARD courier is 8 minutes away from location 1. If CARD provides a 20% safety margin in guaranteeing a delivery time, what is the … delivery time if the package … up at location 1 is to … to location 6?

Problem 10-21 (Algorithmic): United Express Service (UES) uses large quantities of packaging materials at its four distribution hubs. After screening potential suppliers, UES … six vendors that can provide packaging materials that will satisfy its quality standards. UES … each of the six vendors to submit bids to satisfy annual demand at each of its four distribution hubs over the next year. The following table lists the bids received (in thousands of dollars). UES wants to ensure that each of the distribution hubs is … by a different vendor.

Which bids should UES accept, and which vendors should UES select to supply each distribution hub?

Problem 10-13: Sports of All Sorts produces, distributes, and sells high-quality skateboards. Its supply chain consists of three factories (… in Detroit, Los Angeles, and Austin) that produce skateboards. The Detroit and Los Angeles facilities can produce 350 skateboards per week, but the Austin plant is larger and can produce up to 700 skateboards per week. Skateboards must … from the factories to one of four distribution centers, or DCs (located in Iowa, Maryland, Idaho, and Arkansas). Each distribution center can process (repackage, mark for sale, and ship) at most 500 skateboards per week.

Skateboards are then … from the distribution centers to retailers. Sports of All Sorts supplies three major U.S. retailers: Just Sports, Sports ’N Stuff, and The Sports Dude. The weekly demands are 200 skateboards at Just Sports, 500 skateboards at Sports ’N Stuff, and 650 skateboards at The Sports Dude. The following tables display the per-unit costs for shipping skateboards between the factories and DCs and for shipping between the DCs and the retailers.

1. Choose the correct network representation of this problem.
2. Build a model to minimize the transportation cost of a logistics system that will deliver skateboards from the factories to the distribution centers and from the distribution centers to the retailers. What is the optimal production strategy and shipping pattern for Sports of All Sorts? What is the minimum attainable transportation cost? If required, round your answers to two decimal places.
3. Sports of All Sorts is considering expansion of the Iowa DC capacity to 800 units per week. The annual … cost of expansion is $40,000. Should the company expand the Iowa DC capacity so that it can process 800 skateboards per week? (Assume 50 operating weeks per year.)

Problem 10-07 (Algorithmic): Aggie Power Generation supplies electrical power to residential customers for many U.S. cities. Its main power generation plants are … in Los Angeles, Tulsa, and Seattle. The following table shows Aggie Power Generation’s major residential markets, the annual demand in each market (in megawatts or MWs), and the cost to supply electricity to each market from each power generation plant (prices are in $/MW).

1. If there are no restrictions on the amount of power that can … by any of the power plants, what is the optimal solution to this problem? Which cities should … by which power plants? What is the total annual power distribution cost for this solution? If required, round your answers to two decimal places.
2. If at most 4000 MWs of power can … by any one of the power plants, what is the optimal solution? What is the annual increase in power distribution cost that results from adding these constraints to the original formulation? If required, round your answers to two decimal places.

Problem 10-11: The distribution system for the Herman Company consists of three plants, two warehouses, and four customers. Plant capacities and shipping costs per unit (in $) from each plant to each warehouse are as follows: Customer demand and shipping costs per unit (in $) from each warehouse to each customer are as follows:

1. Choose the correct network representation of this problem.
2. Formulate a linear programming model of the problem. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank.
3. Solve the linear program to determine the optimal shipping plan.

Problem 10-31: A long-distance telephone company uses a fiber-optic network to transmit phone calls and other information between locations. Calls are … through cable lines and switching nodes. A portion of the company’s transmission network is shown here. The numbers above each arc show the capacity in thousands of messages that can … over that branch of the network.

To keep up with the volume of information … between origin and destination points, use the network to determine the maximum number of messages that may be sent from a city … at node 1 to a city … at node 7.

Problem 10-03: Tri-County Utilities, Inc., supplies natural gas to customers in a three-county area. The company purchases natural gas from two companies: Southern Gas and Northwest Gas. Demand forecasts for the coming winter season are as follows: Hamilton County, 400 units; Butler County, 200 units; and Clermont County, 300 units. Contracts to provide the following quantities have been written: Southern Gas, 500 units; and Northwest Gas, 400 units. Distribution costs for the counties vary, depending upon the location of the suppliers. The distribution costs per unit (in thousands of dollars) are as follows:

1. Choose the correct network representation of this problem.
2. Develop a linear programming model that can … to determine the plan that will minimize total distribution costs.
3. Describe the distribution plan and show the total distribution cost.
4. Recent residential and industrial growth in Butler County has the potential for increasing demand by as much as 100 units. Which supplier should Tri-County contract with to supply the additional capacity?

(BUS 660 Week 5 Linear Programming Distribution, BUS 660 Week 5 Linear Programming Distribution)