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Giant Motor Company I 1 This problem deals with strategic-(Answered)

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I need a solution (decision variables, objective function and constraints) for the attached case study. Please use excel solver to solve the solution.?


Giant Motor Company I

 


 

1

 


 

This problem deals with strategic planning issues for a large company. The main issue is

 

planning the company's production capacity for the coming year. At issue is the overall

 

level of capacity and the type of capacity ? for example, the degree of flexibility in the

 

manufacturing system. The main tool used to aid the company's planning process in GMC

 

I is a mixed integer programming (MIP) model. A mixed integer program has both

 

integer and continuous variables.2

 


 

Problem Statement

 

The Giant Motor Company (GMC) produces three lines of cars for the domestic (U.S.)

 

market: Lyras, Libras, and Hydras. The Lyra is a relatively inexpensive subcompact car

 

that appeals mainly to first?time car owners and to households using it as a second car for

 

commuting. The Libra is a sporty compact car that is sleeker, faster, and roomier than the

 

Lyra. Without any options, the Libra costs slightly more than the Lyra; additional options

 

increase the price further. The Hydra is the luxury car of the GMC line. It is significantly

 

more expensive than the Lyra and Libra, and it has the highest profit margin of the three

 

cars.

 


 

Retooling Options for Capacity Expansion

 

Currently GMC has three manufacturing plants in the United States. Each plant is

 

dedicated to producing a single line of cars. In its planning for the coming year, GMC is

 

considering the retooling of its Lyra and/or Libra plants. Retooling either plant would

 

represent a major expense for the company. The retooled plants would have significantly

 

increased production capacities. Although having greater fixed costs, the retooled plants

 

would be more efficient and have lower marginal production costs ? that is, higher

 

marginal profit contributions.

 

1 From Practical Management Science (2nd ed., Winston and Albright, 2001 Duxbury

 

Press, pp. 334?335).

 

2 A continuation of this problem, GMC II (at the end of Chapter 10 in Winston and

 

Albright), deals with capacity planning in a multi?period, multi?scenario framework. In

 

GMC II the MIP model is extended to handle the multi?period stochastic nature of the

 

problem.

 


 

In addition, the retooled plants would be flexible ? they would have the capability of

 

producing more than one line of cars.

 

The characteristics of the current plants and the retooled plants are given in Table 1. The

 

retooled Lyra and Libra plants are prefaced by the word new. The fixed costs and

 

capacities in Table 1 are given on an annual basis. A dash in the profit margin section

 

indicates that the plant cannot manufacture that line of car. For example, the new Lyra

 

plant would be capable of producing both Lyras and Libras but not Hydras. The new

 

Libra plant would be capable of producing any of the three lines of cars. Note, however,

 

that the new Libra plant has a slightly lower profit margin for producing Hydras than the

 

Hydra plant. The flexible new Libra plant is capable of producing the luxury Hydra

 

model, but is not quite as efficient as the current Hydra plant that is dedicated to Hydra

 

production.

 

The fixed costs are annual costs that are incurred by GMC independent of the number of

 

cars that are produced by the plant. For the current plant configurations, the fixed costs

 

include property taxes, insurance, payments on the loan that was taken out to construct

 

the plant, and so on. If a plant is retooled, the fixed costs will include the previous fixed

 

costs plus the additional cost of the renovation. The additional renovation cost will be an

 

annual cost representing the cost of the renovation amortized over a long period.

 


 

Demand for GMC Cars

 

Short?term demand forecasts have been very reliable in the past and are expected to be

 

reliable in the future. The demand for GMC cars for the coming year is given in Table 2.

 

A quick comparison of plant capacities and demands in Tables 1 and 2 indicates that

 

GMC is faced with insufficient capacity. Partially offsetting the lack of capacity is the

 

phenomenon of demand diversion. If a potential car buyer walks into a GMC dealer

 

showroom wanting to buy a Lyra but the dealer is out of stock, frequently the salesperson

 

can convince the customer to purchase the better Libra car, which is in stock. Unsatisfied

 

demand for the Lyra is said to be diverted to the Libra. Only rarely in this situation can

 

the salesperson convince the customer to switch to the luxury Hydra model.

 

From past experience, GMC estimates that 30% of unsatisfied demand for Lyras is

 

diverted to demand for Libras and 5% to demand for Hydras. Similarly, 10% of

 

unsatisfied demand for Libras is diverted to demand for Hydras. For example, if the

 

demand for Lyras is 1,400,000 cars, then the unsatisfied demand will be 400,000 if no

 

capacity is added. Out of this unsatisfied demand, 120,000 (=400,000 x 0.3) will

 

materialize as demand for Libras, and 20,000 (=400,000 x 0.05) will materialize as

 

demand for Hydras. Similarly, if the demand for Libras is 1,220,000 cars (1,100,000

 

original demand plus 120,000 demand diverted from Lyras), then the unsatisfied demand

 

for Libras would be 420,000 if no capacity is added. Out of this unsatisfied demand,

 

B60.2350

 


 

2

 


 

Prof. Juran

 


 

42,000 (=420,000 x 0.1) will materialize as demand for Hydras. All other unsatisfied

 

demand is lost to competitors. The pattern of demand diversion is summarized in Table 3.

 


 

Capacity (in 1000s)

 

Fixed cost (in

 

$millions)

 

Lyra

 

Libra

 

Hydra

 

Table 1: Plant Characteristics

 


 

New

 

Lyra

 

1600

 


 

New

 

Libra

 

1800

 


 

2000

 

2000

 

2600

 

3400

 

Profit Margin by Car Line (in $1000s)

 

2

 

?

 

?

 

2.5

 

?

 

3

 

?

 

3.0

 

?

 

?

 

5

 

?

 


 

3700

 


 

Lyra

 

1000

 


 

Lyra

 

Libra

 

Hydra

 

Table 2: Demand for GMC Cars

 


 

Lyra

 

Libra

 

Hydra

 

Table 3: Demand Diversion Matrix

 


 

Libra

 

800

 


 

Hydra

 

900

 


 

2.3

 

3.5

 

4.8

 


 

Demand (in

 

1000s)

 

1400

 

1100

 

800

 


 

Lyra

 

NA

 

0

 

0

 


 

Libra

 

0.3

 

NA

 

0

 


 

Hydra

 

0.05

 

0.10

 

NA

 


 

Question

 

GMC wants to decide whether to retool the Lyra and Libra plants. In addition, GMC

 

wants to determine its production plan at each plant in the coming year. Based on the

 

previous data, formulate a mixed integer programming model for solving GMC's

 

production planning?capacity expansion problem for the coming year.3

 


 

3 Acknowledgment: The idea for GMC I and II came from Eppen et al (1989).

 


 

B60.2350

 


 

3

 


 

Prof. Juran

 


 

 

Paper#9256075 | Written in 27-Jul-2016

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