Simulations - Industrial Engineering - Lecture Slides, Slides of Industrial Engineering

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Simulations

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Hot Dog Sales

• Revenue to carry out club activities
• Basketball game – 10 games a year – all

are similar with respect to hot dog sales

(as all the tickets are sold out)

• Facts:

Selling price of a hot dog: $ Buns ( “sandviç ekmeği”): $1. 44 /dozen Hot dogs can be bought: $6. 56 /dozen All unsold hot dogs are donated.

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Hot Dog Sales (Analysis cont.)

Scenario 1:

• Ordered (bought) 16 dozen of buns and

hot dogs. Sold 9 dozen. Profit?

• Compute profit if 9 dozen were ordered.
• What is the profit loss of over-ordering?

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Hot Dog Sales (Analysis cont.)

Scenario 2:

• Ordered (bought) 9 dozen of buns and hot

dogs. Extreme demand of 14 dozen

(estimate, keep records) Profit?

• Compute profit if 14 dozen were ordered.
• What is the profit loss of under-ordering?

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Hot Dog Sales - Simulation

• One possibility: Create a demand randomly – if

hot dog is available sell it, otherwise do not. Record sales. Continue creating demands until game is over. Compute profit.

• Other possibilities? Learn with simulation

modeling

• What is the advantage? You can mimic the real

world in milliseconds, once the simulation is ready – computer lives faster!

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Key in simulation:

• Generating randomness to represent sales

(or other things in general)

• We do it several times for each set of

decisions, and select the one that gives

greater profits (hot dog case: how much to

order initially – just one decision variable)

• Compute performance measures
• This problem: Typical inventory decision

problem (how much to stock?)

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Modeling uncertainty in demand

• For this case, I am telling you how to do it.

Learn next year

• Roll three unbiased dice each with six

faces, numbered from 1 to 6 and add the

numbers. This represents the demand (in

dozens) for hot dogs (Computer can do be

very efficient and effective in this game).

• Unbiased: For each die, the outcome is

equally likely.

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More on the demand for hot dogs

• How many possible triplets?
• Each triplet is equally likely
•  demand vs. number of triplets

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More on the demand for hot dogs

• Comparison with data:
• Minimum demand: 5 – 3 , 4 (4/216)
• Maximum demand: 16– 17, 18 (4/216)
• Average Demand: around 10 or 11– 10.
• Most demand: between 9 and 12 (104/216)
• Demand being less than 9 dozen or more

than 12 dozen was rare (56/216 each)

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Generalize randomness

representation

• Demand value vs. proportion
• Proportions add up to 1
• Same computation can be made with an

arbitrary set of proportions

• Called probability mass function - pmf (discrete),

or probability density function - pdf (continuous)

• Randomness representation is identical to

selecting a pmf (or pdf)

• Column G : Computation of Expected Value

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