Question

Question 1

We have options for changing capacity:

- Do nothing, add small facility, or add large facility

- More capacity = higher fixed costs

- Lower capacity = higher variable costs

- Compare production potential against possible demand

Capacity	Low Demand	Medium Demand	High Demand
Don’t add	$3m	$4m	$5m
Add small	$1m	$5m	$8m
Add large	($3m)	$3m	$13m

Question 2

A manufacturer is considering switching vendors to get higher quality inputs. After substantial research, we have gathered the following information:

Cost of breaking contract with existing vendor is $1m

Distribution of potential payoffs after switching:

- 70%: $2.5m

- 30%: $0.5m

Alternately, we can ask the current vendor to improve quality, with distribution of potential payoffs:

- 50%: $0

- 50%: $1.6m

Based on expected payoffs, should the manufacturer switch?

Question 2

Suppose you have aggregated customer demand as:

Zone	Demand Location	Weight
A	(4, 1)	20
B	(-1, -5)	15
C	(-3, 1)	25
D	(-1, 5)	30

You are considering two potential new facilities:

One at (1, 0)

One at (0, 1)

Which facility has the shortest sum of distances?

Find the Euclidean distance for each zone

Multiply that distance by its weight

Add all four weighted distances

Question 3

Using the previous aggregated customer demand:

Zone	Demand Location	Weight
A	(4, 1)	20
B	(-1, -5)	15
C	(-3, 1)	25
D	(-1, 5)	30

Again, we compare two potential new facilities:

One at (1, 0)

One at (0, 1)

Which facility has the shortest sum of distances?

Find the metropolitan distance for each zone

Multiply that distance by its weight

Add all four weighted distances

Answer 1

Please refer to the matrix/table above and read the explanations below for the answers. First image is for question 1 and 2. Second image is for question 3 and 4.

Question 1

There are several ways to approach this.

Optimistic approach (Maximax)

Pessimistic approach (Maximin)

Opportunistic approach (Minimax regret)

Let’s take a look at the payoff table. And determine both of them

Optimistic: For this, you need to choose the best possible outcome of the each of the decisions. For each of the decisions (don’t add, add small and add large), the best outcomes are 5, 8 and 13. Among these three, the best payoff is 13. Hence, using the optimistic approach is to decide to add large capacity.

Pessimistic: For this, you need to choose the minimum of the each alternative. For each of the decisions, the worst payoff is 3, 1, and -3. Among these three the best option is not to add a facility as the best payoff from the worst outcome is 3 for this decision.

Opportunistic: The objective here is to reduce the opportunity loss. For this we need to look at the regret table. Regret table notes down the regret or opportunity loss. Opportunity loss is the best possible value of any decision – the current decision. Using this approach first we calculate the maximum regret for each decision. They are 8, 5 and 6. Now among these three we need to minimize our regret. Hence we shall choose 5, or decide to add small capacity.

Hence depending on the type of approach you want to make, you could choose either of the three decisions for each of the approach.

Question 2

For this problem we know that if we switch vendor our current contract will be terminated. That means there will be a penalty of $1m. This means the payoff from switching vendors must be reduced by 1. That is why we have written (2.5 – 1) and (0.5 – 1) in the payoff table. Using the decision tree, we can see that

Switching vendor our Expected value is

0.7*1.5 + 0.3*(-0.5) = 0.9

Similarly keeping the current vendor, our EV is

0.5*0 + 0.5*1.6 = 0.8

Since the best value is 0.9, we should decide to switch vendor.

Question 3

For this, draw the tables as shown. Then calculated the Euclidean distance using the formula

D = sqrt [ (x₁-x₂)² + (y₁-y₂)² ], where D is the distance between (x₁,y₁) and (x₂,y₂)

Using the formula above and the information provided we can decide to use the second facility (0,1)

Question 4

Similarly draw a table for Manhattan(metropolitan distance) using the formula

D = | (x₁-x₂) + (y₁-y₂) |

The distance for both the facility are the same in this case. So you could choose either of them.