# 代写代考 GBA468 – cscodehelp代写

Why Build Models?

• Represent (and often simplify) business situations

• Develop insight into the dynamics of complicated operations • Identify patterns in empirical data

• Use historical data to make future predications

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• Analyze potential outcomes of decisions alternatives

• Build proof of concept and hypothetical scenarios

• Visualize risk & uncertainty

“All models are wrong, but some are useful.” –

Decision Analysis

Summary of Decision Rules Under Conditions of Uncertainty

Maximax rule

Identify best outcome for each possible decision & choose decision with maximum payoff.

Maximin rule

Identify worst outcome for each decision & choose decision with maximum worst payoff.

Minimax regret rule

Determine worst potential regret associated with each decision, where potential regret with any decision & state of nature is the improvement in payoff the manager could have received had the decision been the best one when the state of nature actually occurred. Manager chooses decision with minimum worst potential regret.

Expected Monetary Value Rule (EMV)

Choose decision with maximum expected value (start by assuming all outcomes equally likely)

Expected Opportunity Loss (EOL)

Choose decision with the minimum expected regret (expected opportunity loss).

Mohr – GBA468

Summary of Decision Rules Under Conditions of Risk

Choose decision with maximum expected value

Mean- variance rules

Given two risky decisions A & B:

• If A has higher expected outcome & lower variance than B, choose decision A

• If A & B have identical variances (or standard deviations), choose decision with higher expected value

• If A & B have identical expected values, choose decision with lower variance (standard deviation)

Coefficient of variation rule

Choose decision with smallest coefficient of variation

Mohr – GBA468

Manager’s Attitude Toward Risk

• Risk averse

If faced with two risky decisions with equal expected profits, the less risky decision is chosen

Diminishing MUprofit

• Risk loving

Expected profits are equal & the more risky decision is chosen Increasing MUprofit

• Risk neutral

Indifferent between risky decisions that have equal expected profit Constant MUprofit

Roll Back Analysis for Decision Tree Model

• First step

• Calculate cumulative cash flow for each node as sum of all cash flow along the branch ending at that node.

• Second step (roll back, or backward induction)

• Starting at the leaf and working backwards (right to left), calculate EMV for each node

• For Event node:

• EMV = expected cumulative cash flow for branches extending from that node

• For Decision node:

• EMV = maximum cumulative cash flow for all branches extending from that node

60% – High R & D Costs -60000 16000

40% – Low R & D Costs

-30000 46000

20% – High R & D Costs

29000 -70000 5000 7

80% – Low R & D Costs

-40000 35000

10% – High R & D Costs

Black: Additional cash flow at each node

Red: Cumulative cash flow at each node

Blue: Rollback EMV calculation at each node

Green: Choice of next node @ Decision points

46000 5000

Receive Grant

85000 80000

-5000 75000

Submit Proposal

-5000 -5000 13500

2 Don’t Submit

Don’t Receive

-4000 76000

-80000 -4000 8

90% – Low R & D Costs -40000 36000

Proposal 00

Decision Analysis Examples

• Single Stage Decision examples

• Non-probabilistic examples

• Magnolia Inn facility location choice

• Fish House product sourcing

• Probabilistic examples

• Auction sales contract (self-paced)

• Atlanta-Boston-Cleveland comparison

• Expected utility examples

• Atlanta-Boston-Cleveland comparison

• Insurance example

• Multi-stage Decision examples

• OSHA grant decision

• Game theory strategic competitor interaction examples

• QC testing sequence

Constrained Optimization & Linear Programming

Mathematical Programming/Optimization

• MP is a field of management science that finds the optimal, or most efficient, way of using limited resources to achieve the objectives of an individual of a business.

• Applications

Determining Product Mix Manufacturing

Routing and Logistics

Financial Planning

Linear Programming (LP) Problems

MAX (or MIN): Subject to:

c1X1 + c2X2 + … + cnXn

a11X1 + a12X2 + … + a1nXn <= b1
ak1X1 + ak2X2 + ... + aknXn >=bk

am1X1 + am2X2 + … + amnXn = bm

• Decisions

• Constraints • Objectives

Linear Optimization Applications

• Resource Allocation

Amount Used < Amount Available
Product Mix Problems
Capital Budgeting/Portfolio Design Problems
• Cost-Benefit-Tradeoff
Amount Achieved/Produced > Minimum Amount Required

AdvertisingMixProblems Scheduling

• Mixed Constraints

Resource (<), Benefit (>) and Fixed Constraints (=)

Logistic Optimizations

Blending Problems

Assignment Problems Etc…

Shadow Prices

Amounts by which the objective function value will change given a one-unit change in the right-hand side of the constraint (all other values held constant).

Python PuLP

Microsoft Excel 15.0 Sensitivity Report

Worksheet: [Opt_HotTubs_Sensitivity.xlsx]Model Expanded Report Created: 2/18/2018 10:49:57 AM

Variable Cells

Final Cell Name Value $B$10 Production Level Required 122

Reduced Cost

Objective Allowable Allowable Coefficient Increase Decrease

350 100 20 300 50 40 320 13.33333333 1E+30

Constraint Allowable Allowable R.H. Side Increase Decrease

200 7 26 1566 234 126 2880 1E+30 168

$C$10 Production Level Hydro-Lux $D$10 Production Level Typhoon

Constraints

$F$6 Pumps Used

$F$7 Labor Used

$F$8 Tubing Used

0 -13.33333333

Final Value 200 1566 2712

16.66666667 0

Excel Solver sensitivity report

Linear Programming Examples

• Blue Ridge hot tubs (resource allocation)

• Phone survey (cost-benefit)

• Lunch menu (blending)

• School assignment (assignment + blending) • Logistics optimization (assignment)

• Optimal route

• Leases (set covering) (self-paced)

• Fire stations (set covering)

• Transmitters (set covering)

• Production planning (resource allocation & cost-benefit)

• with sensitivity analysis

Simulation Models

Simulation & Modeling

• In many business models, the value for one or more cells representing independent variables is unknown or uncertain.

• As a result, there is uncertainty about the value the dependent variable will assume:

Y = f(X1, X2, …, Xk)

• Simulation can be used to analyze these types of models.

Simulation

• To properly assess the risk inherent in the model we need to use simulation.

• Simulation is a 4 step process:

1) Identify the uncertain cells in the model.

2) Implement appropriate RNGs for each uncertain cell.

3) Replicate the model n times, and record the value of the bottom-line performance measure.

4) Analyze the sample values collected on the performance measure.

Simulation Examples

• Coin Flip Game

• Example distributions

• Endowment with Scholarship • Reservation Management

• Queuing model

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