during the months of October, November and December; 10,000 kg during the months of
January, February, March and April; and 30,000 kg during the remaining months. The demand
of product 2 is 50,000 kg during the months of October through February and 15,000 kg during
the remaining months. Suppose that cost of producing a kg of product 1 and 2 is $5 and $8,
respectively, provided that these were produced prior to June. After June, the costs are reduced
to $4.5/kg and $7/kg because of the installation of an improved production system. The total
amount of products 1 and 2 that can be produced during any particular month cannot exceed
120,000 kg for Jan-Sept and 150,000 kg for Oct-Dec. Furthermore, at the end of each month
products left at the hand are carried to the inventory space in order to be used in the coming
months. Each kg of product 1 occupies 2 cubic-feet and each kg of product 2 4 cubic-feet of
inventory. Suppose that the maximum inventory space allocated to these products is 150,000
cubic-feet and that the holding cost per cubic foot during any month is $0.10. Formulate the
production scheduling problem so that total production and inventory costs are minimized.
Q3)
A paper manufacturer produces rolls of standard fixed width
w
and of standard length
l
.
Customers order rolls of width
w
but varying lengths. In particular,
d
k
rolls with length
l
k
and
width
w
are ordered for customer
k
=1…n (assume
l
k
≤ l forall k=1.
..n
). What is the minimum
number of rolls that should be cut to meet the demand?
Hint:
Let M be a large number such that M number of rolls are enough to satisfy all demand
(e.g. M=
∑
?
𝑘
𝑛
𝑘=1
). Assume the manufacturer has M number of unmanufactured rolls in the
stock. Use the following decision variables:
?
𝑖
= {
1 𝑖? ???? 𝑖 𝑖? ????
0 ?. ?.
𝑖 = 1 … 𝑀
?
𝑖𝑘
= ?????? ?? ????? ?? ???? ? (?? ?????ℎ ?
𝑘
)??? ???? ???? 𝑖, 𝑖 = 1 … 𝑀, ? = 1 … ?
Q4)
A power plant has three boilers. If a given boiler is operated, it can be used to produce a
quantity of steam (in tons) between the minimum and maximum given in the first table below.
The cost of producing a ton of steam on each boiler is also given. Steam from the boilers is used
to produce power on three turbines. If operated, each turbine can process an amount of steam
(in tons) between the minimum and maximum given in the second table. The cost of processing

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- Spring '16
- BAHAR YETİŞ
- Willy Wonka & the Chocolate Factory, sugar type