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 300 - 600,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 )