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Simple Simulation Example

Industrial EngineeringITENAS

2008

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1. Simple (S, p ) Inventory System

Single-item periodic review inventory system. Maximum inventory level S = 11 units.

Review period p = 5 days, inventory is evaluated every at the endof the review day.

Shortage is permitted, backorder condition applies.

(Order quantity) =(Maximum inventory level) – (Ending inventory) + (Shortage quantity)

Daily-demand probabilistic. Lead-time probabilistic, lead time of 1 day means that the order

from the supplier arrives at the second morning after.

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Simple (S, p ) Inventory System

Probabilistic lead time and daily demand data:

0.094

0.213

0.352

0.251

0.10

ProbabilityDaily Demand

0.13

0.32

0.61

ProbabilityLead Time

(days)

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Simple (S, p ) Inventory System

• Simulate the system to estimate average

ending units in inventory and percentage of

number of days when a shortage conditionoccurs!!!

Assume at the beginning of the simulation,

inventory is 11 units, and no-orderoutstanding.

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MS Excel screenshot for (S,p) Inventory Simulation

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2. Newspaper seller problem

The paper seller buys the papers for 33cents each and sells them for 50 cents each.

Papers not sold at the end of the day aresold as scrap for 5 cents each.

Papers can be purchased in bundles of 10.

There are three types of newsdays: “good”,“fair”, and “poor”, with probabilities of 0.35,0.45, and 0.20, respectively

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Newspaper seller problem

Profit for the newspaper seller is:

Profit = [(revenue from sales) – (cost of newspapers)

 – (lost profit from excess demand)

+ (salvage from sale of scrap papers)]

Evaluate some policies of the number of papers the

seller should purchase everyday, by using spreadsheetsimulation! (Test the purchase of 40, 50, 60, 70, and 80units of papers!)

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MS Excel screenshot for Newspaper Seller Simulation

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3. Project Activity Network Simulation

A project has an activity network as follow.

Time duration to perform each activity is probabilistic, assumed to bein Uniform distribution with parameters as stated by the picture.

0

1

32 4

A: U(2,4) C: U(2,6)

E: U(1,4)B: U(3,6) D: U(2,5)

F: U(5,13)

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Project Activity Network Simulation

Use spreadsheet simulation, with 100 trials

to estimate the time to finish the project.

Present the result statistic: mean (average),minimum, maximum, and sample standard

deviation.

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MS Excel screenshot for Project Activity Network Simulation

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4. Project With Probabilistic OccuringActivity

Suppose the project on Example 3 (Project ActivityNetwork), is extended to include an activity that may ormay not be required.

After Node 3, there is probabilistic situation, that withprobability 0.2 project should perform Activity G beforeAcitivity E, and with probability 0.8 project can directly

perform Acitivity E, as shown in the network as follow:

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Project With Probabilistic OccuringActivity

0

1

32 4

A: U(2,4)

C: U(2,6)

E: U(1,4)B: U(3,6) D: U(2,5)

F: U(5,13)

3x

(P=0.8)

(P=0.2)

G: U(2,7)

Direct

Modify the simulation of project activity network to

include this probabilistic occuring acitivity!

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5. Simple Queueing System Simulation

Please read Section 2.1 from book of Discrete-EventSystem Simulation (Banks, Carson II, Nelson, &Nicol), 4th ed., about Simulation of Queueing

System. Create spreadsheet simulation of Example 2.1

(Single-Channel Queue) and Example 2.2 (Able-

Baker Call Center Problem [two-channel queue])