Question 1 :LP Assignment model
The Akron Police Department
has five detective squads available for assignment to five open
crime cases. The chief of
detectives, Paul Kuzdrall, wishes to assign the squads so that the total
time to conclude the cases is
minimized. The average number of days, based on past
performance, for each squad
to complete each case is as follows:
|
CASE
|
|
SQUAD
|
A
|
B
|
C
|
D
|
E
|
|
1
|
14
|
7
|
3
|
7
|
27
|
|
2
|
20
|
7
|
12
|
6
|
30
|
|
3
|
10
|
3
|
4
|
5
|
21
|
|
4
|
8
|
12
|
7
|
12
|
21
|
|
5
|
13
|
25
|
24
|
26
|
8
|
a)
Using
the Hungarian (manual) method, determine the optimal assignment of squads to
cases in order to minimize the time for completion of cases. Indicate this
overall time.
( 15
marks )
b)
Write an
LP formulation for this problem with an objective function and constraints for
the squads and cases
( 15
marks )
Question
2MRP
The demand forsubassembly
Sis 100 units in week 7. Each
unit of S requires 1 unit of Tand 2units
ofU.Each unit of Trequires 1 unitof V, 2 units ofWand
1 unitofX.
Finally, each unit of U requires 2
unitsof Yand 3 units
ofZ.One firm manufactures all items.It takes 2 weeks to make S,1 week to make T,2 weeks to make U,2 weeks to
make V, 3 weeks to make W, 1 week to make X, 2 weeks to make Y, and1 week to
make Z.
The following
is the on-hand inventory for the various items.
|
ITEM
|
ON-HAND INVENTORY
|
ITEM
|
ON-HAND INVENTORY
|
|
S
|
20
|
W
|
30
|
|
T
|
20
|
X
|
25
|
|
U
|
40
|
Y
|
240
|
|
V
|
30
|
Z
|
40
|
a)
Construct a product structure.Identify all levels, parents, and components.
( 10 marks )
b)
Prepare
a time-phased product structure.
( 10 marks )
c)
Use the
pre-ruled schedules attached at back of the question sheet to determine
complete schedules for items S, T, W, U, Z and Y
( 15 marks )
Question3
a)Marilyn
Charles is the purchasing agent for Central Valve Company, which sells
industrial valves and fluid-control devices. One of Central’s most popular
valves is the Western, which has an annual demand of 4,000 units. The cost of
each valve is $90, and the inventory carrying cost is $9. Marilyn has made a
study of the costs involved in placing an order for any of the valves that
Central stocks, and she has concluded that the average ordering cost is $25 per
order. Furthermore it takes about 5 working days for an order to arrive from
the supplier. During this time the demand per week for valves is approximately
80.
Determine
:
i.
The economic order quantity ( 5 marks )
ii.
The average inventory if the EOQ is used ? ( 2 marks )
iii.
The optimal number of orders per year ? ( 3 marks )
iv.
The
optimal number of days between any two orders, assuming 250 working days per
year ? ( 4 marks )
v.
The
total annual inventory cost (carrying cost plus order cost) ( 3 marks )
vi.
The reorder point. ( 3 marks )
b)
Wang Distributors has an
annual demand for an airport metal detector of 1,400 units. The cost of a
typical detector to Wang is $400. Carrying cost is estimated to be 20% of the
unit cost and the ordering cost is $25 per order.
If Ping
Wang, the owner, orders in quantities of XXXXXXXXXX,he can get a 5% discount on the cost of the
detectors.
i.
Should Wang take the quantity
discount ?( 10 marks )
ii.
Would his decision change
ifthe discount was 10% for orders above
600 ?(
5 marks )