Five thousand new smart camera systems are needed annually to expand the security surveillance of roads, buildings, airports, parks, etc. in a large met­ropolitan area. The system components can be ob­tained in one of three ways: (1) Make them in one of three plants partially owned by the government; (2) Buy them off the shelf from the one and only manufacturer; or (3) Contract to have them made to specifications by a vendor. The estimated annual cost for each alternative is dependent upon specifics of the plant, the producer, or the vendor. The information below details the alternative, a proba­bility of occurrence, and the estimated annual cost. (a) Construct and solve a decision tree to determine the least-cost alternative to provide the components. (b) Once you have chosen the

Question

alternative on the tree, use a spreadsheet to determine the change in prob­ability that the Buy alternative requires to make it equally attractive with the chosen alternative. Assume that the probability change will be equally distributed to the other probability estimates. Write the new probability values.

Answer 1

(a) Select the minimum E(cost) alternative. Monetary values are in $1000 units





Make: E(plant cost) = 0.3(-250) + 0.5(-400) + 0.2(-350)

= $-345 ($-345,000)



Buy: E(quantity cost) = 0.2(-550) + 0.7(-250) + 0.1(-290)

= $-314 ($-314,000)



Contract: E(delivery cost) = 0.5(-175 - 450)

= $-312.5 ($-312,500)



Select the contract alternative since the E(delivery cost) is the lowest at $-312,500

(b) Let ?P = change in probability is placed in cell A2 of a spreadsheet.



Function: = ((0.2 - 0.5*$A$2)*-550) + ( (0.7+$A$2)*-250) + ((0.1 - 0.5*$A$2)*-290)



Use Goal Seek to set the function = $-312.5 and change cell A2. Display is 0.0088.

New probabilities are:

P(< 5000, pay premium) = 0.2 - 0.5(0.0088) = 0.1956

P(5000 available) = 0.7 + 0.0088 = 0.7088

P(> 5000, forced to buy) = 0.1 - 0.5(0.0088) = 0.0956