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Example simulation execution. The Able Bakers Carhops Problem There are situation where there are more than one service channel. Consider a drive-in restaurant where carhops takes orders and bring food to the cars. Cars arrive in the manner

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Example simulation execution

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Example simulation execution

The Able Bakers Carhops Problem

There are situation where there are more than one service

channel. Consider a drive-in restaurant where carhops takes

orders and bring food to the cars. Cars arrive in the manner

shown in Table 3.0. There are 2 carhops- Abu and Bakar. Abu

works faster and works better than Bakar. The distribution of

their service is as shown in Table 3.1 and Table 3.2.


Example simulation execution

The Abu Bakar Carhops Problem

Because this system has two service servers, the simulation

is more complex. Because Abu is a senior, in this case a simple

rule is applied. When both of them (carhops) idle then Abu will

get the customer. Please take note that this condition is

specifically for this drive-in restaurant and can change

according to situation or other applied rules







Service node

Figure 3.0 Abu and Bakar Carhops node diagram


Arrival Event



Server1 Busy




Server2 Busy


Unit enters


Figure 3.1 Arrival Event

Unit enters

Queue for service






Another Unit



Remove the waiting

unit from the queue

Begin server

idle time

Begin servicing

the unit

Figure 3.1 Departure Event for each service station


1. Average waiting time ( minutes )


total time customer wait in queue (minutes)

total numbers of customers



2. Probability (wait)


Number of customers who wait

total numbers of customers




3. Probability of idle server


total idle time of server (minutes)

total run time of simulation



4. Average service time (minutes) for each Abu And Bakar


Total service time (minutes)

total numbers of customers




5. Expected Service time ( minutes )

E(s) =

Σ sp(s)



6. Average time between arrivals (minutes)


Sum of all times between arrival


Number of arrivals - 1



7. Average waiting time of those who wait ( minutes )


total time customer wait in queue (minutes)

total numbers of customers who wait



8. Average time customer spends in the system


total time customer spend in

system (minutes)

total numbers of customers




Example simulation execution

The newspaper Seller’s Problem:

Concern on the purchase and sale of newspaper. The paper

seller buys the newspaper for 33 cents each and sells them for

50 cents each. The newspaper not sold for the day will be sold

as scrap for 5 cents each. Newspaper can be purchase in

bundle of 10 and usually bought in bundle of 50,60 so on. Three

type of newdays good, fair and poor with probabilities 0.35,0.45

and 0.20. The distribution on demand is in Table 3.4. Try to

simulate demands for 20 days and recording profits for each



The newspaper Seller’s Problem

Profit’s formula =

(Revenue from sales) – (cost of newspapers) –

(Lost of profit from excess demand) + (salvage from sale of scrap



A simple model

Let me go through a simple example that clarifies some

concepts. Suppose we wish to procure some items for a

special store promotion (call them pans). We can buy these

pans for RM22 and sell them for RM35. If we have any pans left

after the promotion we can sell them to a discounter for RM15.

If we run out of special pans, we will sell normal pans, of which

we have an unlimited supply, and which cost us RM32. We must

buy the special pans in advance. How many pans should we



Clearly, the answer depends on the demand. We do not

know the demand that the promotion will generate. We do

have enough experience in this business to have some feel for

the probabilities involved. Suppose the probabilities are:


We will attack this problem through simulation. In this model,

we have captured uncertainty (demand) in a single random

variable. To simulate a possible demand, we will determine a

random value. This returns a value between 0 and 1 with a

number of nice properties: no value is more likely to occur than

another, and two successive values are not correlated.


Suppose I generate the random number .78. How can

I generate a demand. Simply assign each demand to a

range of values proportional to its probability and determine

where the .78 occurs. One possibility is:

Looking at the ranges, we see the demand is 11. The demand

for .35 is 10 while that for .98 is 13.


How can we use this random demand? Suppose we have

decided to procure 10 pans. We could determine the total profit

for each of our random demands: the profit for the first is 133,

for the second is 130, and 139 for the third. Our estimate for the

profit if we order 10 is $134.

We could then go on to check the profit if we order a different

amount. For instance, if we order 13, our profit is estimated

at $162.33.


At the end, we would have a guess at the best order quantity,

and an estimate of the expected profit. We would not know for

certain that we made the right move, but statistical analysis can

estimate how far off we might be (by the way, to get statistical

significance for this problem, you need roughly 20 runs at each

demand level). Note also, for this problem there is an analytic