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Problem 1
Consider the following demand scenario:
Quantity Probability
2000 3%
2100 8%
2200 15%
2300 30%
2400 17%
2500 12%
2600 10%
2700 5% Suppo the manufacturer produces at a cost of $20/unit. The distributor
lls to end customers for $50/unit during ason and unsold units are
sold for $10/unit after ason.
a)What is the system optimal production quantity and expected profit
under global optimization?
Production Quantity = 2500
where the Cumulative Probability > Critical Ratio
Expected Profit = $68,240
b)Suppo the manufacturer lls is make-to-order (i.e., the distributor
must order before it receives demand from end customers).
(i).Suppo the manufacturer lls to the distributor at $40/unit,
how much will the distributor order? What is the expected profit
for the manufacturer and distributor?
Ordered Quantity = 2200
Expected Profit for the Manufacturer = $44,000
Expected Profit for the Distributor = $21,440
Total Expected Profit = $65,440
(ii).Find an option contract such that both the manufacturer and distributor enjoy a higher expected profit than (b)(i). What is the expected profit for the manufacturer and the distributor? Solution:
U a buyback contract with w = 40, b = 37.
Critical Raito for Distributor = CU / (CU+CO) = 0.77
Ordered Quantity = 2500
Expected Profit for the Manufacturer = $45,437
Expected Profit for the Distributor = $22,803
Total Expected Profit = $68,240
cathartic
c)Suppo the manufacturer is make-to-stock. (i.e., the manufacturer
must decide how much to stock before the distributor es the demand and places an order.)
(i).Using the same wholesale price contract as part (b)(i), calculate
the production/inventory level of the manufacturer. What is the
expected profit for the manufacturer and distributor? Compare
your results with part (b)(i).
Solution:queena
Critical Raito for Manufacture = CU / (CU+CO) = 0.667
Ordered Quantity = 2400
Expected Profit for the Manufacturer = $45,120
Expected Profit for the Distributor = $23,040
Total Expected Profit = $68,160
公使
distributor enjoy a higher expected profit that that in (c)(i), and calculate their expected profits.
Solution:
深圳会计继续教育U Pay-back contract with w = 39.9, b = 12.7
Critical Raito for Manufacture = CU / (CU+CO) = 0.7316
Ordered Quantity = 2500
vscExpected Profit for the Manufacturer = $45,153.2
Expected Profit for the Distributor = $23,086.8
Total Expected Profit = $68,240
Problem 2
Using the data as problem 1, suppo the manufacturer has an inflated
demand forecast given below (we assume here that the distributor knows
the true forecast, given in problem 1 – but the manufacturer has a
ppgoudistorted forecast, as given below):
Quantity Probability
dlist2200 5%
2300 6%
2400 10%fencer
catia培训
2500 17%
2600 30%
2700 17%
2800 12%
2900 3% a)Suppo the manufacturer is make-to-order. Using your propod
contract in Problem 1(b)(ii), find order quantity, expected profit of the
distributor and the expected profit of the manufacturer. Compare your
answers with 1(b)(ii).
Solution:
Since the manufacturer is make-to-order, the supply chain is
