Practice For Group Work Week 2-3 [PDF]

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PRACTICE FOR GROUP WORK WEEK 2-3 Case 2.1 – ASSIGNING PLANTS TO PRODUCTS (BETTER PRODUCTS COMPANY) The Better Products Company has decided to initiate the production of four new products, using three plants that currently have excess production capacity. The products require a comparable production effort per unit, so the available production capacity of the plants is measured by the number of units of any product that can be produced per day, as given in the rightmost column of Table case 2.1. The bottom row gives the required production rate (number of units produced per day) to meet projected sales. Each plant can produce any of these products, except that Plant 2 cannot produce Product 3. However, the variable costs per unit of each product differ from plant to plant, as shown in the main body of the table. Management now needs to make a decision about which plants should produce which products. Product splitting, where the same product is produced in more than one plant, is permitted. Table case 2.1 – The Data for the Better Products Co. Problem Formulated as a Variant of a Transportation Problem Unit Cost Product

Capacity

1

2

3

4

1

$41

$27

$28

$24

75

2

$40

$29

-

$23

75

3

$37

$30

$27

$21

45

Required production

20

30

30

40

Plant

Available

Case 2.2 – ASSIGNING PLANTS TO PRODUCTS (BETTER PRODUCTS COMPANY) The Better Products Co. needs to assign three plants to produce four new products. The relevant data are given in Table case 2.2. Management had permitted product splitting (where the same product is produced in more than one plant). However, there are some hidden costs associated with product splitting that are not reflected in Table case 2.2, including extra setup, distribution, and administration costs. Therefore, management now has decided to have the problem analyzed again under the additional restriction that product splitting is prohibited. New Problem Statement: Given the data in Table case 2.2, minimize the total cost of assigning each plant to at least one new product where each product is to be produced in only one plant (no product splitting). Since there are three plants and four new products, two plants will produce one new product and a third plant will produce two. Only plants 1 and 2 have the capacity to produce two. Table case 2.2 – Data for the Better Products Co. Problem Cost ($/day) Product

Total

1

2

3

4

1

820

810

840

960

2

2

800

870

-

920

2

3

740

900

810

840

1

1

1

1

1

Plant

Total assigned

assignments

Case 3.1 – Production Scheduling of the Northern Airplane Company The Northern Airplane Company builds commercial airplanes for various airline companies around the world. The last stage in the production process is to produce the jet engines and then to install them (a very fast operation) in the completed airplane frame. The company has been working under some contracts to deliver a considerable number of airplanes in the near future, and the production of the jet engines for these planes must now be scheduled for the next four months. To meet the contracted dates for delivery, the company must supply engines for installation in the quantities indicated in the second column of Table case 1. Thus, the cumulative number of engines produced by the end of months 1, 2, 3, and 4 must be at least 10, 25, 50, and 70, respectively. Table case 1 – Production Scheduling Data for the Northern Airplane Company Problem

Maximum Production Scheduled Month Installations

Regular

Overtime

Time

Unit Cost of Production ($million) Regular

Overtime

Unit Cost of Storage ($thousand)

Time

1

10

20

10

1.08

1.10

15

2

15

30

15

1.11

1.12

15

3

25

25

10

1.10

1.11

15

4

20

5

10

1.13

1.15

The facilities that will be available for producing the engines vary according to other production, maintenance, and renovation work scheduled during this period. The resulting monthly differences in the maximum number of engines that can be produced during regular time hours (no overtime) are shown in the third column of Table case 1, and the additional numbers that can be produced during overtime hours are shown in the fourth column. The cost of producing each one on either regular time or overtime is given in the fifth and sixth columns.

Because of the variations in production costs, it may well be worthwhile to produce some of the engines a month or more before they are scheduled for installation, and this possibility is being considered. The drawback is that such engines must be stored until the scheduled installation (the airplane frames will not be ready early) at a storage cost of $15,000 per month (including interest on expended capital) for each engine, as shown in the rightmost column of Table case 1. Apply Excel Solver and QM for Windows to help the Northern Airlines Company’s production manager develop a schedule for the number of engines to be produced in each of the four months so that the total of the production and storage costs will be minimized.