COMMERCE 3QA3 Final: 3QA3 Exam Formula Sheet
4 Jun 2018
School
Department
Course
Professor
Chapter 1
Input variables = white, Unknown input variables = blue, Decision variables = yellow, Output variables / results = green
Chapter 2
Chapter 4
Binding or nonbinding, slack or surplus variable for a constraint:
- A constraint is binding when the left-hand-side (LHS) value and the right-hand-side (RHS) value are equal.
- A constraint is nonbinding (or not binding) when the LHS value and the RHS value are not equal.
- If a ostrait is the LHS + s = ‘HS ad s is called the slack.
- If a ostrait is the LHS = ‘HS + s ad s is alled the surplus Eel alls this slak ut e sa surplus.
- If a constraint is binding then the LHS = RHS so the slack or surplus, s, is zero.
- If a constraint is nonbinding the the LHS ≠ ‘HS so the slak or surplus, s, is greater tha zero.
Reduced cost or shadow price for non-negativity constraint = marginal contribution - marginal worth of resources used
Range of feasibility for the RHS of a constraint
Range of optimality for the coefficient of a decision variable in the objective function
Computer output for answer report
100% Rule for changing constraint RHSs
(Allowable change is from sensitivity report below)
Chapter 6
Cell reference for integer = int / cell reference for binary = bin (Binary is 0 or 1, Integer is whole #)
Chapter 8
Break-even analysis
Break-even quantity: quantity at which Total Revenue = Total Cost
Total Revenue = price × quantity sold = pQ
Total Cost = fixed cost (i.e. cost that does not vary with volume) + variable cost (i.e. cost that varies linearly with volume)
= F + cQ
Total Revenue = Total Cost -> pQ = F + cQ and solve for Q
Choice between two alternatives A and B
Total Revenue is the same for Alternative A and Alternative B. Total Revenue = pQ.
Total Cost for Alternative A = FA+ cAQ. Total Cost for Alternative B = FB+ cBQ
We are indifferent between A and B when: FA+ cAQ = FB+ cBQ
Decision making under uncertainty
(a) Maximax – Choose the alternative that has the best payoff if the best event occurs (optimistic).
(b) Maximin – Choose the alternative that has the best payoff if the worst event occurs (pessimistic).
(c) Equally Likely (Laplace) – Each possible future outcome has an equal probability of occurrence; choose the alternative
that has the best weighted payoff.
If there are n possible outcomes then the probability of each outcome is 1/, for each alternative calculate:
(d) Criterion of Realism (Hurwicz) – Choose the alternative that has the best realism payoff.
(e) Minimax Regret (opportunity loss) – ‘egret = est paoff – atual paoff; Choose the alteratie ith the sallest
maximum regret.
Decision making under risk—one stage: payoff table
(f) Expected monetary value (EMV). Select the alternative with the best expected payoff.
Expected payoff for alternative i = ∑ payoff, × Probability(outcome)
Expected Value of Perfect Information (EVPI)
EVwPI = ∑ best payoff × Probability (outcome) , where i is an outcome
Expected value of perfect information (EVPI): EVPI = EVwPI – best EMV
(g) Expected opportunity loss (EOL) select alternative w lowest expected opportunity loss
Expected opportunity loss for alternative i = ∑ regret, × Probability(outcome)
Note: EMV + EOL = EVwPI
Decision making under risk— 2 stages: decision trees
1. At each outcome node, we calculate the expected payoff (usually the expected monetary value, EMV or the expected
utility, EU).
2. At each decision node, we select the alternative with the best EMV or EU.
Expected Value of Sample Information, EVSI
EVSI = EMV of best decision with sample information when cost of sample information is $0 – EMV of best decision
without any information
Efficiency of sample information = EVSI/EVPI
(i) Using Certainty Equivalents (CEs) to derive a decision makers Utility Function ()
-The decision maker is a risk avoider when the risk premium is positive.
-The decision maker is risk indifferent whenever the risk premium is zero.
-The decision maker is a risk seeker whenever the risk premium is negative
Risk premium = EMV of a decision – Certainty Equivalent of a decision
(ii) Using an Exponential Utility Function U()
x is payoff
If we know a utility value U, we can calculate the corresponding payoff X from:
Expected utility EU = utility * probability -> (multiply branch and add between branches like typical tree)
Chapter 10
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Input variables = white, unknown input variables = blue, decision variables = yellow, output variables / results = green. Break-even quantity: quantity at which total revenue = total cost. Total revenue = price quantity sold = pq. Total cost = fixed cost (i. e. cost that does not vary with volume) + variable cost (i. e. Total cost = fixed cost (i. e. cost that does not vary with volume) + variable cost (i. e. cost that varies linearly with volume) Total revenue = total cost -> pq = f + cq and solve for q. Total revenue is the same for alternative a and alternative b. Total cost for alternative a = fa+ caq. Total cost for alternative b = fb+ cbq. We are indifferent between a and b when: fa+ caq = fb+ cbq. Decision making under risk one stage: payoff table (f) expected monetary value (emv). Select the alternative with the best expected payoff.
