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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

DeterministicInputs

StochasticInputs

Process Output

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Simulation - Random Variables

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Simulation - A Corporate Health Insurance Example

Lisa Pon has just been hired as an analyst in the corporate planning department ofHungry Dawg Restaurants. Her first assignment is to determine how much money thecompany needs to accrue in the coming year to pay for its employees' health insuranceclaims. Hungry Dawg is a large, growing chain of restaurants that specializes intraditional southern foods. The company has become large enough that it no longer buysinsurance from a private insurance company. The company is now self-insured, meaningthat it pays health insurance claims with its own money (although it contracts with anoutside company to handle the administrative details of processing claims and writingchecks).

The money the company uses to pay claims comes from two sources: employeecontributions (or premiums deducted from employees' paychecks), and company funds(the company must pay whatever costs are not covered by employee contributions). Eachemployee covered by the health plan contributes $125 per month. However, the numberof employees covered by the plan changes from month to month as employees are hiredand fired, quit, or simply add or drop health insurance coverage. A total of 18,533employees were covered by the plan last month. The average monthly health claim percovered employee was $250 last month.

Case Problem (R) p. 517

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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 @Riskfile

Change @Risksettings

Add selectedcells as @Riskoutputs

Displayinputs byoutputs table

Run Simulation

Show main@Risk window

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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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SimulationSpreadsheet 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 newmagnetic resonance (MRI) system. The system costs $1,500,000, and the hospital wouldhave to spend another $1,000,000 for site preparation and installation. Since the systemwould be installed in the hospital, the space to be used has a very low, or zero, marketvalue to outsiders, and thus no opportunity cost has been assigned to account for thevalue of the space.

The MRI site is estimated to generate weekly usage (volume) of 40 scans, andeach scan would, on average, cost the hospital $15 in supplies. The site is expected tooperate 50 weeks a year, with the remaining 2 weeks devoted to maintenance. Theestimated average charge per scan is $500, but 25 percent of this amount, on average, isexpected to be lost to indigent patients, contractual allowances, and bad debt losses.

The MRI site would require two technicians, resulting in an incremental increasein annual labor costs of $50,000, including fringe benefits. Cash overhead costs wouldincrease by $10,000 annually if the MRI site is activated. The equipment would requiremaintenance, 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 sitewill 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 thehospital’s master plan calls for a brand-new imaging facility. The hospital plans to sellthe MRI system at that time for an estimated $750,000 salvage value, net of removalcosts. 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, andthus the hospital’s current 10 percent cost of capital is the appropriate project cost ofcapital.

We will illustrate Monte Carlo simulation by specifying the distributions for onlytwo key variables (this is a simplification): weekly volume and salvage value. Weeklyvolume is not expected to vary by more than + 10 scans from its expected value of 40scans. We will assume a normal distribution to represent the uncertainty inherent involume. Salvage value uncertainty will be modeled with a triangular distribution with alower 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

Laura Tanner is the owner of Computers of Tomorrow (COT), a retail computerstore in Austin, Texas. Competition in retail computer sales is fierce-both in terms ofprice and service. Laura is concerned about the number of stockouts occurring on apopular type of computer monitor. This monitor is priced competitively and generates amarginal profit of $45 per unit sold. Stockouts are very costly to the business becausewhen customers cannot buy this item at COT, they simply buy it from a competing storeand COT loses the sales (there are no backorders). Laura measures the effects ofstockouts on her business in terms of service level, or the percentage of total demand thatcan be satisfied from inventory.

Laura has been following the policy of ordering 50 monitors whenever her dailyending 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 thenext day. Orders are delivered at the beginning of the day and, therefore, can be used tosatisfy demand on that day. For example, if the ending inventory position on day 2 is lessthan 28, Laura places the order at the beginning of day 3. If the actual time between orderand delivery, or lead time, turns out to be 4 days, then the order arrives at the start of day7. 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 onany given day can vary. By reviewing her sales records for the past several months, Lauradetermined that the actual daily demand for this monitor is a random variable that can bedescribed by the following probability distribution:

Units Demanded: 0 1 2 3 4 5 6 7 8 9 10Probability: 0.01 0.02 0.04 0.06 0.09 0.14 0.18 0.22 0.16 0.06 0.02

The manufacturer of this computer monitor is located in California. Although ittakes an average of 4 days for COT to receive an order from this company, Laura hasdetermined that the lead time of a shipment of monitors is also a random variable that canbe described by the following probability distribution:

Lead Time (days): 3 4 5Probability: 0.2 0.6 0.2

One way to guard against stockouts and improve the service level is to increase thereorder point for the item so that more inventory is on hand to meet the demand occurringduring the lead time. Laura wants to determine the reorder point that results in an averageservice level of 99%

Case Problem - (R) p. 539

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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