1. Fodak must schedule its production of digital camera memory card for the first four
months of the year. Memory card demand (in 1,000s of rolls) in January, February, March
and April is expected to be 300, 500, 650 and 400, respectively. Fodak’s production
capacity is 500 thousand memory cards per month. Business is highly competitive, so
Fodak cannot afford to lose sales or keep its customers waiting. Meeting month i ‘s
demand with month i +1’s production is unacceptable.
Memory cards produced in month i can be used to meet demand in month i or can be held
in inventory to meet demand in month i +1 or month i +2 (but not later due to various
reasons). There are no units in inventory at the start of January.
The production and delivery cost per thousand units will be $500 in January and
February. This cost will increase to $600 in March and April due to a new labor contract.
Any memory cards put in inventory requires additional transport costing $100 per
thousand units. It costs $50 per thousand units to hold memory cards in inventory from
one month to the next.
a. Draw the network representation of this production & inventory application. Hint:
Consider using a transshipment network (which you learned previously in this
class) where transshipment nodes are each month’s ending-inventory!
To save time: Draw manually. Insert image/picture of your work on next page.
b. Formulate and solve this problem to find the production and inventory quantities for
each of the 4 months so you can minimize total cost.
c. Show formulation:
d.
What is the optimal Z and optimal solution?
2. A large company may satisfy its fuel-oil requirements either by one annual contract or
a series of separate monthly contracts throughout the winter. The cost for the annual
contract is $0.80 per gallon. The cost for the monthly contract would depend on
availability of fuel during the year. With a monthly contract, if the year has “normal”
supply of fuel-oil, the cost per gallon will average$0.75 per gallon. But if the year has
“scarce” supply, the price will average $0.95 per gallon.
The company will use 100,000 gallons during the year, and the manager estimates a 1/10
chance (0.1 probability) of a scarce year.
The manager may spend $500 to obtain a professional economic forecast of whether the
year will be a normal or scarce one. Data on previous forecasts and actual occurrences for
the past 20 years is shown:
Actual Results
Actual Normal (AN)
Actual Scarce (AS)
Total
Forecast Results
Normal (FN)
Scarce (FS)
15
3
0
2
15
5
Total
18
2
20
Construct a decision tree for this problem. Populate all branches with labels and
probability values. Include dollar amounts where appropriate. Then solve.
To save time: Draw manually. Insert image/picture of your work on next page.
Should the manager purchase the forecast?
___ Yes
___ No
What is the expected cost of Annual Contract? $_________________
What is the expected cost of Monthly Contract? $________________
