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.
solution |
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working note 1 |
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first of all we have to calculate range to identify demand and lead time |
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range for lead time |
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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 |
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range for unit sold |
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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 |
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random number set |
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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 |
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