OM470 Supply Chain Network and Additional Linear Programming Practice This is a more professional assignment, I need an excellent student of OM major to complete. This section shows only some of the r

OM470 Supply Chain Management Fall 2018

Homework 2

Computation Problems

1. A grain cooperative with warehouses in Lincoln, Des Moines and Pierre must meet market demands in Denver, Kansas City, Minneapolis and St. Louis. The following table summarizes data relevant to this week’s distribution problem. The number in the first three rows and the first four columns are the transportation costs/unit from each warehouse to each market.

1. Draw a network diagram representing the problem of minimizing total transportation cost associated with shipping product from the warehouses to meet market demand.

2. Formulate an LP model to solve this problem. Please list all the decision variables, objective function and constraints.

3. Suppose the cooperative also has a warehouse in Omaha with a supply of 500 units and transportation cost to Denver, Kansas City, Minneapolis and St. Louis of, respectively, 6, 5, 7, and 9. Extend the LP formulation of part (b) to include this option.

4. Explain why the cost of meeting the demand in part (C) cannot exceed the cost of meeting demand in part (b).

5. Solve the model given in part (b) and (c) using Excel Solver.

1. SC consulting, a supply chain consulting firm must decide on the location of its home office. Its clients are located primarily in the 16 states listed in Table provided. These 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 $165,428, Tulsa is $131,230, Denver is $140,000 and Seattle is $145,000. The expected numbers of trips to each state and the travel costs from each potential site are shown in Table. Each consultant is expected to take at most 25 trips each year.

a. If there are no restrictions on the number of consultants at a site and the goal is to minimize costs, where should the home offices be located and how many consultants should be assigned to each office? What is the annual cost in terms of the facility and travel?

b. If, at most, 10 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?

c. What do you think of a rule by which all consulting projects out of a given state are assigned to one home office? How much is this policy likely to add to cost compared to allowing multiple offices to handle a single state?

Additional Linear Programing Problems:

1. The management of the Best Laptop Manufacturing (BLM) has decided to expand its product mix. Market research studies have focused on diversifying the product line. BLM has decided to produce two lines of laptop computer cases: X-gens & Y-gens. Production is simple - cutting & sewing only. Assume this is a one day plan and they can sell all that are produced during the day. Contribution to profit is $30 per case for X-gens and $80 for Y-gens.

Production Constraints: Cutting Sewing

X-gens 3 hrs/case 2 hrs/case

Y-gens 2 hrs/case 4 hrs/case

The cutting line can run 1 1/2 shifts per day and the sewing line 2 shifts per day (assume 8 hr per shift).

Management Constraint: Despite the current production situation, the managerial team requires the production of at least two Y-gens cases per day to keep the production line busy. BLM wants to know the number of X-gens and Y-gens to produce in order to maximize its total profit.

FORMULATE an appropriate Linear Programming model of this problem and solve it using MS Excel Solver.

1. The U-Save Loan Company is planning its operations for the next year. The company makes four types of loans, listed below, together with the annual return (in percent) to the company. Legal requirements and company policies place the following limits on the various types of loans.

Signature loans may not exceed 10 percent of the total amount of loans. The amount of signature and furniture loans together may not exceed 20 percent of the total amount of loans. First mortgages must be at least 40 percent of the total mortgages and at least 20 percent of the total amount of loans. The company can lend a maximum of 1.5 million dollars next operating period.

Type Annual Return (percent)

Signature loan 15

Furniture loan 12

Second Home Mortgage 10

First Home Mortgage 7

U-Save wants to know the amounts it should invest in each type of loan to maximize its total annual return. Formulate this problem as a linear programming problem and solve it using MS Excel Solver.

1. A young couple, Eve and Steven, want to divide their main household chores (budgeting, cooking, dishwashing, and laundering) between them so that each has two tasks but the total time they spend on household duties is kept to a minimum. Their efficiencies on these tasks differ, where the time each would need to perform the task is given by the following table:

Formulate this problem as a linear programming problem and solve it using MS Excel Solver