Question

1 Normal ABDUED AaBbcc AaBbcc AaBbcl AaBbcc No Spact. Heading 1 Heading 2 Subtitle Subtle in Paragraph Title A feed manufacturing company is faced with a capacity decision. Their present production facility is running at nearly maximum capacity. Management is considering the following three decision alternatives: Styles a) No expansion b) Add on the present facility c) Build a new facility They believe that if there is a large increase in demand for their product in the near future, they will need to have built a new facility in order to compete and capitalize on more efficient technology and design advances. However, if there is no increase in demand, it might be more profitable to maintain the present facility and add no capacity. A third alternative is to add on to the present facility that will suffice for a moderate increase in demand and will be cheaper than building an entirely new facility. A drawback of adding on to the old facility is that if there is a large increase in demand for their product, an addition to the old facility will preclude capitalizing on new efficiencies that cannot be built into the old plant. Shown in the table below are the payoffs (in $100,000's) for these three decision alternatives, for four different possible states of demand for the company's product. Suppose probabilities have been determined for the states of demand such that there is a 0.15 chance that demand will be less, a 0.20 chance that there will be no change in demand, a 0.40 probability that there will be a moderate increase in demand, and a 0.25 probability that there will be a large increase in demand. Less Large Option: No expansion Add on State of demand No change Moderate increase $15 ($10) ($20) SO increase $25 $45 (540) $20 D.-11.

Answer 1

A. In optimistic approach, we take the maximum of the maximum values of all options. In our case, the maximum values for each option are

No Expansion- $25 (Large Increase)
Add on- $45 (Large Increase)
Build a new facility- $120 (Large Increase)

So, in optimistic approach, we will hoose Build a new facility since it has highest value.

B. In conservative approach, we take maximum of minimum values. Minimum values for each option are

No Expansion- $-20 (Less)
Add on- $-40 (Less)
Build a new facility- $-150 (Less)

Maximum out of these is -20 for no expansion. Hence we will choose no expansion in conservative approach.

C. In minmax regret, we first calculate the maximum regret (that is, the difference between best and worst states of that particular case) and then taken the option with minimum of those maximum regrets. This is shown below for our cases

Option	Maximum Regret
No Expansion	45
Add on	85
Build a new facility	270

As an example, the maximum regret for No expansion is 25 (when there is a large increase)-(-20)(when demand is less)=45.

Now we choose the minimum of these, which is 45 in no expansion.

Hence, in minmax regret approach, we will choose No expansion option.

D. The expected values are probability*payoff for each option. So,

Option	Expected Value
No Expansion	9.25
Add on	11.25
Build a new facility	-2.5

Calculation-

Option	Expected Value
No Expansion	=0.15*-20+0.2*0+0.4*15+0.25*25
Add on	=0.15*-40+0.2*-10+0.4*20+0.25*45
Build a new facility	=0.15*-150+0.2*-40+0.4*-5+0.25*120

e. Using expected value, we will recommend Add on option as that gives highest expected value.