Simulation - Introduction
• Deterministic vs. Stochastic
Models
• Risk Analysis
• Random Variables
• Best Case/Worst Case Analysis
• What-If Analysis
• Simulation
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Simulation - Introduction
Deterministic
Inputs
Process
Output
Stochastic
Inputs
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Simulation - Random Variables
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Simulation - A Corporate Health
Insurance Example
Case Problem (R) p. 517
Lisa Pon has just been hired as an analyst in the corporate planning department of
Hungry Dawg Restaurants. Her first assignment is to determine how much money the
company needs to accrue in the coming year to pay for its employees' health insurance
claims. Hungry Dawg is a large, growing chain of restaurants that specializes in
traditional southern foods. The company has become large enough that it no longer buys
insurance from a private insurance company. The company is now self-insured, meaning
that it pays health insurance claims with its own money (although it contracts with an
outside company to handle the administrative details of processing claims and writing
checks).
The money the company uses to pay claims comes from two sources: employee
contributions (or premiums deducted from employees' paychecks), and company funds
(the company must pay whatever costs are not covered by employee contributions). Each
employee covered by the health plan contributes $125 per month. However, the number
of employees covered by the plan changes from month to month as employees are hired
and fired, quit, or simply add or drop health insurance coverage. A total of 18,533
employees were covered by the plan last month. The average monthly health claim per
covered employee was $250 last month.
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Simulation - A Corporate Health
Insurance Example
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Simulation - A Corporate Health
Insurance Example
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Simulation - @Risk
Open @Risk
file
Save @Risk
file
Change
@Risk
settings
Display
inputs by
outputs
table
Add selected
cells as @Risk
outputs
Show main
@Risk window
Run
Simulation
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Simulation - A Corporate Health
Insurance Example
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Simulation - A Corporate Health
Insurance Example
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Simulation - A Corporate Health
Insurance Example
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Simulation - A Corporate Health
Insurance Example
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Simulation - A Corporate Health
Insurance Example
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Simulation - A Corporate Health
Insurance Example
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Simulation - A Corporate Health
Insurance Example
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Simulation
Spreadsheet Models
• Develop the model equations
and enter them into a
spreadsheet
• Identify input variables that are
uncertain
• Assign a probability distribution
to each uncertain input variable
• Run the model
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Risk Simulation - Applications
A Capital Budgeting Example
From Gapenski, p. 408
Bayside Memorial Hospital, a not-for profit hospital, is evaluating a new
magnetic resonance (MRI) system. The system costs $1,500,000, and the hospital would
have to spend another $1,000,000 for site preparation and installation. Since the system
would be installed in the hospital, the space to be used has a very low, or zero, market
value to outsiders, and thus no opportunity cost has been assigned to account for the
value of the space.
The MRI site is estimated to generate weekly usage (volume) of 40 scans, and
each scan would, on average, cost the hospital $15 in supplies. The site is expected to
operate 50 weeks a year, with the remaining 2 weeks devoted to maintenance. The
estimated average charge per scan is $500, but 25 percent of this amount, on average, is
expected to be lost to indigent patients, contractual allowances, and bad debt losses.
The MRI site would require two technicians, resulting in an incremental increase
in annual labor costs of $50,000, including fringe benefits. Cash overhead costs would
increase by $10,000 annually if the MRI site is activated. The equipment would require
maintenance, which would be furnished by the manufacturer for an annual fee of
$150,000, payable at the end of each year of operation. For book purposes, the MRI site
will be depreciated by the straight-line method over a five-year life.
The MRI site is expected to be in operation for five years, at which time the
hospital’s master plan calls for a brand-new imaging facility. The hospital plans to sell
the MRI system at that time for an estimated $750,000 salvage value, net of removal
costs. The inflation rate is expected to affect all revenues and costs except depreciation.
Bayside’s managers initially assume that projects under evaluation have average risk, and
thus the hospital’s current 10 percent cost of capital is the appropriate project cost of
capital.
We will illustrate Monte Carlo simulation by specifying the distributions for only
two key variables (this is a simplification): weekly volume and salvage value. Weekly
volume is not expected to vary by more than + 10 scans from its expected value of 40
scans. We will assume a normal distribution to represent the uncertainty inherent in
volume. Salvage value uncertainty will be modeled with a triangular distribution with a
lower limit of $500,000, a most likely value of $750,000, and an upper limit of
$1,000,000.
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Risk Simulation - Applications
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Risk Simulation - Applications
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Risk Simulation - Applications
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Risk Simulation - Applications
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Risk Simulation - Applications
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Risk Simulation - Applications
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Risk Simulation - Applications
Sensitivity Analysis
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Risk Simulation - Applications
Scenario Analysis
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Risk Simulation - Applications
Correlated Inputs
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Risk Simulation - Applications
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Risk Simulation - Applications
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Risk Simulation - Applications
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Simulation
An Inventory Control Example
Case Problem - (R) p. 539
Laura Tanner is the owner of Computers of Tomorrow (COT), a retail computer
store in Austin, Texas. Competition in retail computer sales is fierce-both in terms of
price and service. Laura is concerned about the number of stockouts occurring on a
popular type of computer monitor. This monitor is priced competitively and generates a
marginal profit of $45 per unit sold. Stockouts are very costly to the business because
when customers cannot buy this item at COT, they simply buy it from a competing store
and COT loses the sales (there are no backorders). Laura measures the effects of
stockouts on her business in terms of service level, or the percentage of total demand that
can be satisfied from inventory.
Laura has been following the policy of ordering 50 monitors whenever her daily
ending inventory position (defined as ending inventory on hand plus outstanding orders)
falls below her reorder point of 28 units. Laura places the order at the beginning of the
next day. Orders are delivered at the beginning of the day and, therefore, can be used to
satisfy demand on that day. For example, if the ending inventory position on day 2 is less
than 28, Laura places the order at the beginning of day 3. If the actual time between order
and delivery, or lead time, turns out to be 4 days, then the order arrives at the start of day
7. The current level of on-hand inventory is 50 units and no orders are pending.
COT sells an average of 6 monitors per day. However, the actual number sold on
any given day can vary. By reviewing her sales records for the past several months, Laura
determined that the actual daily demand for this monitor is a random variable that can be
described by the following probability distribution:
Units Demanded:
Probability:
0
0.01
1
0.02
2
0.04
3
0.06
4
0.09
5
0.14
6
0.18
7
0.22
8
0.16
9
0.06
10
0.02
The manufacturer of this computer monitor is located in California. Although it
takes an average of 4 days for COT to receive an order from this company, Laura has
determined that the lead time of a shipment of monitors is also a random variable that can
be described by the following probability distribution:
Lead Time (days):
Probability:
3
0.2
4
0.6
5
0.2
One way to guard against stockouts and improve the service level is to increase the
reorder point for the item so that more inventory is on hand to meet the demand occurring
during the lead time. Laura wants to determine the reorder point that results in an average
service level of 99%
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Simulation
An Inventory Control Example
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Simulation
An Inventory Control Example
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Simulation
An Inventory Control Example
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Simulation
An Inventory Control Example
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Simulation
An Inventory Control Example
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Simulation
An Inventory Control Example
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Simulation
An Inventory Control Example
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