Simulation Examples Continued. Modeling and Simulation CS 313. SIMULATION OF INVENTORY SYSTEMS. EXAMPLE 2.3 THE NEWSPAPER SELLER'S PROBLEM: The paper seller buys the papers for 33 cents each and sells them for 50 cents each.
Modeling and Simulation
Tables 2.16 and 2.17 provide the random-digit assignments for the types of newsdaysand the demands for those newsdays.
Solving this problem by simulation requires setting a policy of buying a certain number of papers each day, then simulating the demands for papers over the 20-day time period to determine the total profit. The policy (number of newspapers purchased) is changed to other values and the simulation is repeated until the best value is found.
Profit = $30.00 − $23.10 − 0 + $50 = $7.40
Profit = $35,00 − $23,10 − $3,40 + 0 = $8,50
Total profit = $645,00 − $462,00 − $13,60 + $5,50 = $174,90
To make an estimate of the mean units in ending inventory, many cycles would have to be simulated.
The random-digit assignments for daily demand and lead time are shown in the rightmost columns of Tables 2.19 and 2.20. The resulting simulation table is shown in Table 2.21.
The simulation has been started with the inventory level at 3 units and an order of 8 units scheduled to arrive in 2 days' time.
The order for 8 units is available on the morning of the third day of the first cycle, raising the inventory level from 1 unit to 9 units.
Demands during the remainder of the first cycle reduced the ending inventory level to 2 units on the fifth day. Thus, an order for 9 units was placed.
The lead time for this order was 1 day. The order of 9 units was added to inventory on the morning of day 2 of cycle 2.
Notice that the beginning inventory on the second day of the third cycle was zero. An order for 2 units on that day led to a shortage condition. The units were backordered on that day and the next day also. On the morning of day 4 of cycle 3 there was a beginning inventory of 9 units.
The 4 units that were backordered and the 1 unit demanded that day reduced the ending inventory to 4 units.
Based on five cycles of simulation, the average ending inventory is approximately 3.5 (88% 25) units. On 2 of 25 days a shortage condition existed.
A baker is trying to determine how many dozens of bagels to bake each day. The probability distribution of the number of bagel customers is as follows:
Customers order 1, 2, 3, or 4 dozen bagels according to the following probability distribution:
Bagels sell for $5.40 per dozen. They cost $3.80 per dozen to make.
All bagels not sold at the end of the day are sold at half-price to a local grocery store.
Based on 5 days of simulation, how many dozen bagels should be baked each day? Simulate for initial quantity of 30.