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COMMERCE 2DA3 - Decision Making with Analytics
study guide solution complete update McMaster
University
Decision Analysis - A systematic approach to the study of decision making.
- clearly define the problem
- list all possible alternatives
- identify all possible outcomes for each alternative
- identify the payoff for each alternative and outcome combination
- use a decision modelling technique to choose an alternative - The five steps of decision making are... Decision making under certainty - A type of decision making where we know the consequence of all alternatives. Decision making under uncertainty - A type of decision making where we can list the possible future outcomes but cannot estimate the probability that a specific outcome will occur. Decision making under risk - A type of decision making where we have some idea about the probabilities of each outcome. ...maximax, maximin, realism, equally likely, and minimax regret - The five different decision-making criteria that can be used to make a decision under uncertainty are... Maximax - A type of decision-making criteria where you choose the alternative with the best payoff, if the best outcome happens. First for each alternative, find the maximum payoff over all possible
outcomes. Next, find the maximum of them. Choose the alternative whose maximum payoff gives this maximum. Maximin - A type of decision-making criteria where you choose the alternative with the best payoff, if the worst outcome happens. First for each alternative, find the minimum payoff over all possible outcomes. Next, find the maximum of them. Choose the alternative whose minimum payoff gives this maximum. Criterion of Realism - A type of decision-making criteria where you calculate the realism payoff for each alternative and select the alternative with the highest realism payoff. Coefficient of Realism (a) - A number from 0 to 1 such that when a is close to 1, the decision criterion is optimistic, and when a is close to zero, the decision criterion is pessimistic. Equally Likely - A type of decision making criteria where you calculate the average payoff for each alternative and select the alternative with the highest average payoff. Minimax Regret - A type of decision making criteria where you find the alternative that minimizes the maximum regret for each alternative. First find the regrets for all outcome-alternative combination. Next, find the maximum regret for all alternatives and choose the minimum among them. Opportunity loss/Regret - The amount lost by not picking the best alternative, calculated as the difference between the optimal payoff for an outcome and the actual payoff for an outcome. Expected Opportunity Loss (EOL) - The expected cost of not picking the best solution, calculated as the weighted average of all the regrets. We select the alternative with the smallest value of this. Expected Monetary Value (EMV) - The weighted average of all possible payoffs, where the weights are the probabilities of outcomes. We select the alternative with the largest value of this.
...all outcomes that could occur at that node. Only one outcome will actually occur. The decision maker has no control over which outcome will actually occur. - The lines originating from an outcome node represent... ...terminal node. - Each path of decision alternatives and outcomes in the decision tree ends at a... ...finding the difference between the expected monetary value of the best decision with sample information when its cost is $0 and the expected monetary value of the best decision without any information. - We calculate the expected value of sample information (EVSI) by... ...dividing the expected value of sample information by the expected value of perfect information (EVSI/EVPI) - We calculate the efficiency of sample information by... Prior probability - A type of probability that exists before additional information is gathered. Posterior probability - A type of probability that can be computed based on prior probabilities and additional information. ...at each outcome node we calculate the expected monetary value (EMV), and at each decision node we select the alternative with the best expected monetary value (EMV). - Folding back the decision tree involves 2 parts. These parts are... ...goes down (EMV + EOL = EVwPI) - If EMV increases, then the EOL.. ...goes up (EMV + EOL = EVwPI) - If the EMV decreases, the the EOL... ...always the same. - The alternative suggested by the maximum expected monetary value (max EMV) and the alternative suggested by the minimum expected opportunity loss (min EOL) is...
Single-stage problems - Treeplan problems with only 1 set of alternatives and outcomes. Multistage problems - Treeplan problems with a sequence of alternatives and outcomes. Utility Theory - A theory that allows decision makers to incorporate a person's attitude toward risk, and a person's value for money into decision modelling. ...best payoff. - In utility theory, a number of 1 is assigned to the... ...worst payoff. - In utility theory, a number of 0 is assigned to the... ...accept more risks. - For small monetary amounts, people generally... ...act more conservative. - For large monetary amounts, people generally... Certainty Equivalent - The minimum guaranteed amount a person is willing to accept to avoid the risk associated with a gamble. Risk Avoider - A person with a decreasing marginal utility for money. Risk Seeker - A person with an increasing marginal utility for money. Risk Neutral - A person with a fixed marginal utility for money. Risk Premium - The expected monetary value (EMV) that a person is willing to give up in order to avoid the risk associated with a gamble. Calculated as the difference between the expected monetary value and the certainty equivalent (EMV - CE).
- it is straightforward and flexible
- it can handle large and complex systems
- it allows "what-if questions"
- it does not interfere with real-world systems
- it studies interactions among variables
- "time compression" is possible
- it handles complications that other methods can't - The seven advantages of simulation are...
- it can be expensive and time consuming
- it does not generate optimal solutions
- managers must generate all conditions and constraints
- each model is unique so nothing can be generalized. - The four disadvantages of simulation are...
- establish the probability distribution for each random variable
- use random numbers to generate random values
- repeat for some number of replications - The 3 steps of Monte Carlo simulation are... Flow Chart Diagram - A visual representation that shows the sequence in which activities occur in the real system and the impact of each activity's outcome on subsequent activities. Drawing these can help ensure that a simulation represents the real system being analyzed. Deterministic environment - An environment in which input data values must be fixed, and the consequence of each decision must be fixed and identifiable. Discrete-event Simulation - A type of simulation where changes in the state of the system occur at random points in time. Outcome values are whole numbers.
Continuous Simulation - A type of simulation where changes in the state of the system occur continuously over time. Outcome values are decimal numbers. Discrete uniform distribution - A type of distribution where outcomes are discrete and the probabilities of all outcomes are the same. Discrete general distribution - A type of distribution where outcomes are discrete and the probabilities of outcomes are different. Monte Carlo Simulation - A simulation that experiments with probabilistic elements of a system by generating random numbers to create values for those elements. Binomial distribution - A discrete distribution giving the probability of obtaining a specified number of successes in a finite set of independent trials in which the probability of a success remains the same from trial to trial. Each trial has a boolean-valued outcome: success or failure. Queue - A waiting line at a service point to receive a service. This happens when there is a temporary imbalance between the demand for a service and the capacity of a service system.
- Single queue - Single server - Single phase
- Single queue - Single server - Multiple phases
- Single queue - Multiple servers - Single phase
- Multiple queues - Multiple servers - Single phase
- Single queue - Multiple servers - Multiple phases. - The five main queue types are... ...simulation and analytical modelling. - The two main methods to analyze a queuing system are... ...arrivals, queue, and service. - The 3 main parts of a queuing system are...
...lambda (๐). - In queuing models, the average arrival rate or the average number of arrivals per unit of time is denoted by... ...x (๐ฅ) - In queuing models, when using the Poisson Formula the number of arrivals per unit of time is denoted by... ...A is the arrival probability distribution, B is the service time probability distribution, and s is the number of servers. - In queuing models, Kendall's Notation is denoted by A/B/s where... ...M for Markovian (Poisson for arrivals/A or exponential for service time/B), D for Degenerate (i.e. constant rate), or G for general distribution. - In queuing models, Kendall's Notation is denoted by A/B/s. The possible choices for A and B are... ...L is the length of the queue and N is the size of the arrival population. - In queuing models, Kendall's Notation can be expanded to A/B/s/L/N where... ...rho (๐). - In queuing models, the utilization factor of the system or the probability that all servers are busy is denoted by... ...L sub q (๐ณ๐) - In queuing models, the average length of the queue or the number of customers in the queue is denoted by... ...L (๐ณ) - In queuing models, the average number of customers in the system calculated as the number in the queue plus the number being served is denoted by... ...W sub q (๐พ๐) - In queuing models, the average time that each customer spends in the queue is denoted by... ...W (๐พ) - In queuing models, the average time that each customer spends in the system calculated as the time spent waiting plus the time spent being served is denoted by...
...P sub 0 (๐0) - In queuing models, the probability that there is no customer in the system or the probability that the service facility will be idle is denoted by... ...P sub n (๐๐) - In queuing models, the probability that there are exactly n (๐) customers in the system is denoted by... ...C sub s (๐ถ๐ ) - In queuing models, the cost of providing service per unit of time is denoted by.. ...C sub w (๐ถ๐ค) - In queuing models, the waiting cost per unit of time is denoted by...
- Average number of customers in the system (L)
- Average time spent in the system (W)
- Average number in the queue (Lq)
- Average time in the queue (Wq)
- Utilization factor (ฯ)
- Percent idle time (Po)
- Probability there are exactly n customers in the system (Pn) - The seven important operating characteristics of a queuing system are...
- Queue discipline is FIFO.
- There is no balking or reneging.
- Arrivals are independent.
- Arrivals are Poisson.
- Service times are independent.
- Average service rate exceeds average arrival rate. - The six assumptions underlying common queuing models are...
- If alternative A is preferred to B, the utility of A is greater than the utility of B: A>B=U(A)>U(B)
- If a decision maker is indifferent between A for certain and B with a probability of p for success and probability 1-p for failure then: U(A)=pU(B)+(1-p)U(B)
- If A>B>C then the Certainty Equivalent or B is minimum guaranteed amount you are willing to accept to avoid the risk associated with a gamble: U(B)=pU(A)+(1-p)U(C) - The 3 principles of utility theory are... Risk Avoider - This type of decision maker will have a CE<EMV during a gamble. Risk Seeker - This type of decision maker will have a CE>EMV during a gamble. Risk Neutral - This type of decision maker will have a CE=EMV during a gamble. ...EMV minus the CE. - The risk premium is calculated as the... ...the model is complex and there is no hope of finding an analytical (exact) solution. - We should use simulation if... ...the model is simple enough that we can find an analytical (exact) solution. - We should not use simulation if... ..manually (very time-consuming and can only be applied to small problems) or using a computer. - The 2 ways to simulate are... ...L-Lq - In queuing models, the average number of customers being served is calculated by...
...W-Wq - In queuing models, the average time that each customer spends being served is calculated by... ...minimizing the total expected cost which is calculated by service cost+waiting cost. - In queuing models, managers can find the optimal service level by...
