Question

Average daily sales of a product are 10 units. The actual number of units each day is 9, 10, or 11
with frequencies of 75, 90 and 85 respectively during the last 250 days. The lead time for delivery of
this product averages 4 days, although the time may be 3, 4, or 5 days with frequencies of 25, 60
and 20 respectively as observed in 105 recent orders. The company plans to place an order when the
inventory level drops to 25 units (based on average demand and lead-time). The beginning inventory
is 35. The following random numbers have been generated:
Set 1: 52, 78, 13, 06, 99, 98, 80, 09, 67, 89
Set 2: 60, 87, 46, 63, 50, 76, 11, 04, 97, 96
Use Set 1 to generate lead-times and use Set 2 to simulate daily demand for a 10 days period.
Determine how often the company runs out of stock before the shipment arrives.
Assume an order quantity of 40 (Q = 40).
Reorder point is 25 units (ROP = 25).
Beginning Inventory = 35 units.

Answer 1

solution
working note 1
first of all we have to calculate range to identify demand and lead time
range for lead time
days	working	%	approx	cumulative	range
3	25/105*100	23.80952381	24	24	0-23
4	60/105*100	57.14285714	57	81	24-80
5	20/105*100	19.04761905	19	100	81-99
			100
range for unit sold
unites	working	%		cumulative	range
9	75/250*100	30		30	0-29
10	90/250*100	36		66	30-65
11	85/250*100	34		100	66-99
Answer
random number set
set 1	set 2	lead time set 1	sale unit	opening stock	purchase	sold	closing stock	order
52	60	4	10	35	0	10	25	40 units
78	87	4	11	25		11	14
13	46	3	10	14		10	4
6	63	3	10	4		4	0
99	50	5	10	0	40	10	30
98	76	5	11	30		11	19	40units
80	11	4	9	19		9	10
9	4	3	9	10		9	1
67	97	4	11	1		1	0
89	96	5	11	0		0	0
Company shall out of stock before arrival 2 times which is highlighted