Question

A manager in a manufacturing company is trying to decide whether to expand the present production facility, or subcontract to increase production capacity, or to build a new production facility. Depending on future demand levels, the payoffs (or losses in $thousands) associated with the alternatives have been estimated and placed in the following table:

                                                                       

                                                High Demand    Moderate Demand   Low Demand

                        Expand                  200                          100                       -25

Alternatives    Subcontract          225                          50                       25

                        Build                    200                         −100                        *

                        Probability             .4                              .3                         .3

* If the manager of the company decides to build a new facility and the demand turns out to be low, then he has three options. He can do nothing which would result in a loss of $200,000. He can rent out the facility which could create a profit of $450,000 with 50% probability or a profit of $100,000 with 50% probability. Or he can decide to sell the facility to earn a profit of $250,000.

Construct a decision tree which illustrates the decisions.

Answer 1

If company decided to Build a production facility, there is 3 different possibilities because if demand is low company have 3 options. do nothing, rent out the facility or sell the facility

• 3A

Company decided to build a facility. the profit if company have high demand is 200,000, loss if demand is moderate is 100,000

and company decided to do nothing so loss is 200,000

• 3B

Company decided to build a facility. the profit if company have high demand is 200,000, loss if demand is moderate is 100,000

and at low demand company decided to rent out the facility which could create a profit of $450,000 with 50% probability or a profit of $100,000 with 50% probability;  expected profit = 450,000 *0.5 + 100,000 *0.5= 275,000

• 3C

Company decided to build a facility. the profit if company have high demand is 200,000, loss if demand is moderate is 100,000

At low demand company will sell the facility for a profit 250,000

Decision no	Alternative	possibilities	probabilities	Profit or (loss)	probabliti * profit or (loss)	Expected profit or (loss)
1.	Expand	High demand	0.4	200,000	80,000	80,000+30,000-7500=102,500
moderate demand	0.3	100,000	30,000
Low demand	0.3	(25,000)	(7500)
2.	Subcontract	High demand	0.4	225,000	90,000	90,000 + 15,000-7500=97,500
moderate demand	0.3	50,000	15,000
Low demand	0.3	25,000	7,500
3A	Build	High demand	0.4	200,000	80,000	80,000-60,000-30,000= -(10,000)
moderate demand	0.3	(100,000)	(30,000)
Low demand	0.3	(200,000)	(60,000)
3B	Build	High demand	0.4	200,000	80,000	80,000- 30,000 +82,500=132,500
		moderate demand	0.3	(100,000)	(30,000)
		Low demand	0.3	275,000	82,500
3C	Build	High demand	0.4	200,000	80,000	80,000 -30,000 +75,000=125,000
moderate demand	0.3	(100,000)	(30,000)
Low demand	0.3	250,000	75,000