Question

The materials manager of a firm wishes to determine the expected value of demand for a particular SKU (stock-keeping unit) during the lead-time for replenishment. This information is important to decide how far in advance to re-order supplies to avoid stock-outs.

However, both lead-time and demand rate for the SKU seem to vary at random, as recorded in the following table.

LEAD-TIME	PROBABILITY	DEMAND/DAY	PROBABILITY
(days)		(units)
1	50%	1	10%
2	30%	2	30%
3	20%	3	40%
		4	20%

Required of you:

Simulate five trials in an experiment to compute the expected value of demand for this SKU during the lead-time. Use the following random numbers that have been generated for the experiment.

For lead-time: 83, 11, 48, 02, 17
For demand/day: 08, 91,79, 18, 61

Answer 1

Lead time	Probability	Cumulative Probability	Random number ranges
1	0.50	0.50	00 - 49
2	0.30	0.80	50 - 79
3	0.20	1.00	80 - 99

Demand	Probability	Cumulative Probability	Random number ranges
1	0.10	0.10	00 - 09
2	0.30	0.40	10 - 39
3	0.40	0.80	40 - 79
4	0.20	1.00	80 - 99

Using the above ranges, find the demand per day and lead time for the 5 cycles as follows:

Trial	RN	Demand (d)	RN	Lead time (L)	Lead time demand (d.L)
1	8	1	83	3	3
2	91	4	11	1	4
3	79	3	48	1	3
4	18	2	2	1	2
5	61	3	17	1	3
				Average	3.0

So, the expected (average) lead time demand in 3 units.