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Practice Problems
Module F—Simulation
Problem 1:
The time between arrivals at a drive-through window of a fast-food restaurant follows the
distribution given below. The service time distribution is also given in the table. Use the random
numbers provided to simulate the activities of the first five arrivals. Assume that the window
opens at 11:00 A.M. and that the first arrival is after this, based on the first interarrival time.
Time Between Arrivals
Probability
Service Time
Probability
1
0.2
1
0.3
2
0.3
2
0.5
3
0.3
3
0.2
4
0.2
Random numbers for arrivals: 14, 74, 27, 03
Random numbers for service times: 88, 32, 36, 24
What time does the fourth customer leave the system?
Problem 2:
Average daily sales of a product are 8 units. The actual number of units each day is 7, 8, or 9
with probabilities 0.3, 0.4, and 0.3 respectively. The lead time for delivery of this product
averages 4 days, although the time may be 3, 4, or 5 days with probabilities 0.2, 0.6, and 0.2. The
company plans to place an order when the inventory level drops to 32 units (based on average
demand and lead-time). The following random numbers have been generated:
Set 1: 60, 87, 46, 63, 50, 76, 11, 04, 97, 96, 65
Set 2: 52, 78, 13, 06, 99, 98, 80, 09, 67, 89, 45
Use set 1 to generate lead-times and use set 2 to simulate daily demand. Simulate two ordering
periods and determine how often the company runs out of stock before the shipment arrives.
Use an order quantity of 32 and assume orders arrive early in the day prior to demand.
ANSWERS
Problem 1:
Time
Between
Arrivals
Probability
Random
Number
Service
Time
Probability
Random
Number
1
0.2
01 - 20
1
0.3
01 - 30
2
0.3
21 - 50
2
0.5
31 - 80
3
0.3
51 - 80
3
0.2
81 - 00
4
0.2
81 - 00
Arrival
Arrival
Time
Start of
Service
Service
time
End of
Service
Server
Idle
Wait
Time
1
11:01
11:01
3
11:04
1
0
2
11:04
11:04
2
11:06
0
0
3
11:06
11:06
2
11:08
0
0
4
11:07
11:08
1
11:09
0
1
Therefore, the fourth arrival leaves at 11:09.
Problem 2:
Day
Demand
0
Ending
Inventory
Order Placed?
Lead-time
32
Order placed
4 days
1
8
24
2
9
15
3
7
8
4
7
33
Stock arrives
5
9
24
Order placed
6
9
15
7
9
6
8
7
0
Stockout - sales of one unit lost.
9
8
0
Stockout - sales of eight units lost
10
9
23
Stock arrives
Order placed
5 days