Question 1: Assignment LP Model The following matrix shows the costs in thousands of dollars for assigning Individuals P, Q, R, S and T to Jobs 1, 2, 3, 4 and 5. INDIVIDUALS JOBS 1 19 12 8 14 32 2 25 15 17 11 35

3 15 7 19 10 26 4 27 17 12 20 25

5 18 30 29 33 13

P Q R S T

a) Using the Hungarian (manual) method, determine the optimal assignment of individuals to Jobs in order to minimize the time for completion of Jobs. Indicate the overall costs. b) Write an LP formulation that could be used to solve this problem with the relevant LP

software packages like Microsoft Excel "solver".

Question 2: Materials Requirements Planning (MRP) An MRP exercise is being implemented over an 8-week period and the following relevant information is provided: One unit of A is made of two units of B, two unit of C, and two units of D. B is composed of

three units of E and one unit of D. C is made of one unit of B and two units of E. E is made of one unit of F. Items B, C, E and F have one week lead times; A and D have lead times of

two weeks. Assume that lot-for-lot (L4L) lot sizing is used for Items A, B and F; lots of size 50, 50 and 150 are used for Items C, D and E respectively. Items C, E and F have on-hand

(beginning) inventories of 10, 50 and 200, respectively; all other items have zero beginning inventory. We are scheduled to receive 10 units of A in Week 2, 50 units of E in Week 1, and also 50 units of F in Week 1. There are no other scheduled receipts.

a) Draw the product structure with low-level coding [5 marks] b) Draw the corresponding time-phased diagram showing lead times to scale. [5 marks]

c) If 40 units of A are required in Week 8, determine the necessary planned order releases for all components {6 schedules}see schedules table below

[15 marks] Question 3: Inventory Management

a) Describe ABC inventory analysis. What are some policies that may be based upon the results of an ABC analysis? [3 marks] b) Differentiate between perpetual inventory monitoring and periodic inventory monitoring. c) It is your responsibility as the new supervisor of the Sport's section of Ajaun Department Store to ensure that reorder quantities for the various items have been correctly established. You decide to test one item and choose the Size 5 Nike football. A perpetual inventory system has

been used, so you examine this as well as other records and come up with the following data: Cost per football $55 each

Holding cost 18% of football cost per year Demand 3,920 per year

Ordering cost $336.16 per order Standard deviation of daily demand 4 footballs

Delivery lead time 5 days Because customers generally do not wait for footballs but go elsewhere, you decide on a service probability of 98 percent. Current on-hand inventory is 96 footballs, with no open orders or

backorders. Assume the demand occurs 280 days per year. i.

ii.

iii. What would be the average time between orders? [2 marks]

iv. What is the Reorder Point (ROP)? [4 marks] v. An inventory withdrawal of 10 units was just made. - Is it time to reorder?

What is the Economic Order Quantity (EOQ)?

What is the number of order placed per year? vi. If the store currently uses a lot size of 600 units, determine the annual holding cost and

the annual ordering cost of this policy. [2 marks]

vii. What would be the annual cost saved, if any, by shifting from the 600-unit lot size to the EOQ? [3 marks]