Term Project 1

IPPM ONLINE EXAM July 26^th 2023
SECTION 1 -MULTIPLE CHOICE QUESTIONS
Tick the only one right answer out of four listed. Each question is worth 1 point if correct, 0 points if not given and -0.25 for wrong answers.

1. Scheduling – 2 points (Solution must be written directly into the text box of exam platform)

Given the following precedence matrix, calculate the total project duration in days.

Task	Duration (days)	Successor
A	2	C
B	5	D
C	7	E
D	6	E
E	8	F; G
F	4	H; I
G	5	J
H	6
I	3
J	4

Project duration = 29 days

1. Scheduling – 2 points (Solution must be written directly into the text box of exam platform)

Automated storage and retrieval system (AS/RS) can handle 540 unit loads per hour. Assuming that stacker crane can do a single command cycle (either storage or retrieval operation) with 30 cycles per hour and 90% efficiency. Please, define the number of cranes. 

Number of cranes = TH rate / (number of cycles per hour * efficiency) = 20 cranes

2. Inventory Management – 6 points (Solution must be written into front page of the single paper then it should be scanned by Italian Professors)

The weekly demand for a class C product is normally distributed with average value equal to 3,000 units and standard deviation equal to 600 units. The order lead time is also normally distributed with average value equal to 3 weeks and standard deviation equal to 1.5 week. The unit selling price is 5 €/unit, the ordering cost is equal to 15 €/order, and the unit cost of holding inventory is equal to 20% of the selling price on a yearly basis. Assume 1 year equal to 50 weeks. 

What is the best inventory management model? Motivate your answer. In case you choose a fixed-time period model assume the time between inventory reviews equal to 4 weeks.
Calculate the objective inventory level and the safety stock so that the probability of not having stock outs is equal to 96.5%.
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Solution:

This is a class C product, so a product that has a low economic value (in fact SP = 5 €/unit). It is a less important product whose inventory level does not need to be checked on a continuous basis.
For such a reason the best inventory management policy is the Fixed‐Time Period model where the inventory level is reviewed at fixed time intervals.

Numerical solution:

Given:
Class C product
Weekly demand (normally distributed) – d = 3 000 units
Standard deviation of weekly demand – _d = 600 units

Order lead time is also normally distributed and L = 3 weeks
Standard deviation of order lead time - _L = 1.5 weeks
Unit selling price – SP = 5 €/unit
Order cost – S = 15 €/order
Annual unit holding cost = 20% * SP = 0.2*5 = 1 €/unit
Number of weeks in a year = 50 weeks
inventory reviews equal to T= 4 weeks.

For Fixed‐Time Period model we have to calculate the safety stock and objective level. Safety stock for probabilistic demand and lead time can be computed by the following equation:

In order to calculate k we use the provided table. Since the probability of no stockout equal to 96.5% is not available from the table
we calculate k by interpolating the k values corresponding to the two closest probability values:

p1(no stockout) = 0,9599 k1 = 1.75

p2(no stockout) = 0,9772 k2 = 2 k = (k1+k2)/2 = 1.875

SS = 8947.11 = 8948 units

Objective level can be calculated through the following formula:

OL = (4+3)*3000 +8948 = 29 948 units