Management Science Chapter 9

A probability near one indicates

an event is almost certain to occur.

A probability near zero indicates

an event is unlikely to occur.

The optimistic approach would be used by

an optimistic decision maker.

An assignment problem seeks to

minimize the total cost assignment of m workers to m jobs, given that the cost of worker I performing job j is cij.

The risk profile for a decision alternative shows

the possible payoffs for the decision alternative along with their associated probabilities.

A supply chain describes

the set of all interconnected resources involved in producing and distributing a product.

Frequently, decision makers have preliminary or prior probability assessments for

the states of nature that are the best probability values available at the time.

Even when a careful decision analysis has been conducted,

the uncertain future events make the final consequence uncertain.

An assignment problem is a special case of a

transportation problem in which all supplies and demands are equal to 1; hence assignment problems may be solved as linear programs.

Transshipment problems are

transportation problems in which a shipment may move through intermediate nodes, transshipment nodes, before reaching a particular destination.

The expected value of perfect information provides an

upper bound on the expected value of any sample or survery information.

Those that control the supply chain must make decisions such as

where to produce a product, how much should be produced, and where it should be sent.

For each of the problems, if the right hand side of the linear programming formulations are all integers, the optimal solution

will be in terms of integer values for the decision variables.

Decision making with probabilities: Expected value approach

If probabilistic information regarding the states of nature is available, one may use the expected value EV approach.

Special Case: If total supply exceeds total demand

No modification of lp formulation is necessary.

Assignment problems assume

all workers are assigned and each job is performed.

Linear programming can be used to help marketing managers

allocate a fixed budget to various advertising media. The objective is to maximize reach, frequency, and quality of exposure.

One application of linear programming in marketing is

media selection.

The decision chosen is

the one corresponding to the minimum of the maximum regrets.

Probability values are always assigned on a scale from

0 to 1.

The approach used to determined the optimal decision strategy is based on a backward pass through the decision tree using the following steps

1. At chance nodes, compute the expected value by multiplying the payoff at the end of each branch by the corresponding branch possibilities. 2. At decision nodes, select the decision branch that leads to the best expected value. This expected value becomes the expected value at the decision node.

Most linear programming problems have some common features

1. Decision variables. 2. Objective function. 3. Constraints.

Phase 2 of the guidelines for linear programming formulation

1. Define the decision variables precisely. 2. Write the objective function in terms of the decision variables. 3. Write the constraints in terms of the decision variables. 4. Simplify the constraints if necessary. 5. Add non negativity constraints.

Each decision tree has two types of nodes

1. Round nodes corresponds to the states of nature. 2. Square nodes corresponds to the decision alternatives.

Risk analysis helps the decision maker recognize the difference between

1. The expected value of a decision alternative. 2. The payoff that might actually occur.

Three commonly used criteria for decision making when probability information regarding the likelihood of the states of nature is available are

1. The optimistic approach. 2. The conservative approach. 3. The minimax regret approach Also the laplace approach.

Supply Chain models

1. Transportation problem. 2. Transshipment Problem.

Phase 1 of the guidelines for linear programming formulation

1. Understand the problem thoroughly. 2. Describe the objective. 3. Describe each constraint.

Remarks on constraints

1. Units on both sides. 2. At least, at most, no more than, exactly equal. 3. Constraint simplification.

Special Case: If total demand exceeds total supply

Add a dummy origin with supply equal to the shortage amount. Assign a zero shipping cost per unit. The amount shipped from the dummy origin will not actually be shipped.

Special Case: unacceptable route

Remove the corresponding decision variable.

Special Case: The objective is maximizing profit or revenue

Solve as a maximization problem.

A decision tree is

a chronological representation of the decision problem.

The conservative approach would be used by

a conservative decision maker.

The risk associated with any decision alternative is

a direct result of the uncertainty associated with the final consequences.

As the EVPI provides an upper bound for the EVSI, efficiency is always

a number between 0 and 1.

A decision strategy is

a sequence of decision and chance outcomes where the decisions chosen depend on the yet to be determined outcomes of chance events.

The decision yielding the

best expected return is chosen.

This is done by

calculating for each state of nature the difference between each payoff and the largest payoff for that state of nature.

Decision analysis

can be used to develop an optimal strategy when a decision maker is faced with several decision alternatives and an uncertain or risk filled pattern of future events.

This new information, often obtained from sampling,

can be used to revise the prior probabilities so that the final decision is based on more accurate probabilities for the states of nature.

Linear programming can be used in financial decision making that involves

capital budgeting, make or buy, asset allocation, portfolio selection, financial planning and more.

Portfolio selection problems involve

choosing specific investments, for example, stocks and bonds, from a variety of investment alternatives.

The decision with the largest possible payoff is

chosen.

A decision problem is characterized by

decision alternatives, states of nature, and resulting payoffs.

If the payoff table was in terms of costs, the

decision with the lowest cost would be chosen.

If the payoff was in terms of costs, the maximum costs would be determined for

each decision and then the decision corresponding to the minimum of these maximum costs is selected. Hence, the maximum possible cost is minimized.

The states of nature refer to

future events, not under the control of the decision maker, which may occur. States of nature should be defined so that they are mutually exclusive and collectively exhaustive.

Expected value of sample information

is the additional expected profit possible through knowledge of the sample or survey.

A firm conducts marketing research to

learn about consumer characteristics, attitudes, and preferences.

The transportation problem seeks to

minimize the total shipping costs of transporting goods from m origins, each with a supply si, to n destinations, each with a demand di, when the unit shipping cost from an origin, I, to a destination, j, is cij.

An important application of linear programming is

multi period planning such as production scheduling.

Transportation, transshipment, assignment, shortest route, and maximal flow problems are all examples of

network problems.

Probability is the

numerical measure of the likelihood that an event will occur.

A network model is

one which can be represented by a set of nodes, a set of arcs, and functions, examples are costs, supplies, demands... associated with the arcs and or nodes.

A table showing payoffs for all combinations of decision alternatives and states of nature is a

payoff table

The consequence resulting from a specific combination of a decision alternative and a state of nature is a

payoff.

At the end of each limb of a tree are

payoffs attained from the series of branches making up that limb.

These revised probabilities are called

posterior probabilities.

Linear programming can be used in operations management to aid in decision making about

product mix, production scheduling, staffing, inventory control, capacity planning, and other issues.

Payoffs can be expressed in terms of

profit, cost, time, distance, or any other appropriate measure.

Efficiency of sample information is the

ratio of EVSI to EVPI

Minimax regret approach

requires the construction of a regret table or an opportunity loss table.

Good decision analysis includes

risk analysis that provides probability information about the favorable as well as the unfavorable consequences that may occur.

In general, supply chains are designed to

satisfy customer demand for a product at minimum cost.

Here the expected return for each decision is calculated by

summing the products of the payoff under each state of nature and the probability of the respective state of nature occurring.

To make the best possible decision,

the decision maker may want to seek additional information about the states of nature.

The decision alternatives are

the different possible strategies the decision maker can employ.

The branches leaving around each round node represent

the different states of nature while the branches leaving around each square node represent the different decision alternatives.

The expected value of perfect information is

the increase in the expected profit that would result if one knew with certainty which state of nature would occur.

Then, using this regret table,

the maximum regret for each possible decision is listed.

For each decision the

the minimum payoff is listed and then the decision corresponding to the maximum of these minimum payoffs is selected. Hence the minimum possible payoff is maximized.