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Chapter 2 - An Introduction to Linear Programming

1. Obtain an overview of the kinds of problems linear programming has been used to solve.
2. Learn how to develop linear programming models for simple problems.
3. Be able to identify the special features of a model that make it a linear programming model.

4. Learn how to solve two variable linear programming models by the graphical solution procedure.

5. Understand the importance of extreme points in obtaining the optimal solution.

6. Know the use and interpretation of slack and surplus variables.

7. Be able to interpret the computer solution of a linear programming problem.

8. Understand how alternative optimal solutions, infeasibility and unboundedness can occur in linear programming problems.

9. Understand the following terms:
   • problem formulation
     
   • feasible region
     
   • constraint function
     
   • slack variable
     
   • objective function
     
   • standard form
     
   • solution
     
   • redundant constraint
     
   • optimal solution
     
   • extreme point
     
   • nonnegativity constraints
     
   • surplus variable
     
   • mathematical model
     
   • alternative optimal solutions
     
   • linear program
     
   • infeasibility
     
   • linear functions
     
   • unbounded
     
   • feasible solution
     

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Chapter 3 - Linear Programming: Sensitivity Analysis and Interpretation of Solution

1. Be able to conduct graphical sensitivity analysis for two variable linear programming problems.

2. Be able to compute and interpret the range of optimality for objective function coefficients.

3. Be able to compute and interpret the dual price for a constraint.

4. Learn how to formulate, solve, and interpret the solution for linear programs with more than two decision variables.

5. Understand the following terms:
   • sensitivity analysis
     
   • range of optimality
     
   • dual price
     
   • reduced cost
     
   • range of feasibility
     
   • 100 percent rule
     
   • sunk cost
     
   • relevant cost

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Chapter 4 - Linear Programming Applications

1. Learn about applications of linear programming that have been encountered in practice.

2. Develop an appreciation for the diversity of problems that can be modeled as linear programs.

3. Obtain practice and experience in formulating realistic linear programming models.

4. Understand linear programming applications such as:
   • media selection
     
   • production scheduling
     
   • portfolio selection
     
   • work force assignments
     
   • financial mix strategy
     
   • blending problems
     
   • data envelopment analysis
     
   • revenue management

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Chapter 5 - Linear Programming: The Simplex Method

1. Learn how to find basic and basic feasible solutions to systems of linear equations when the number of variables is greater than the number of equations.

2. Learn how to use the simplex method for solving linear programming problems.

3. Obtain an understanding of why and how the simplex calculations are made.

4. Understand how to use slack, surplus, and artificial variables to set up tableau form to get started with the simplex method for all types of constraints.

5. Understand the following terms:
   • simplex method
     
   • net evaluation row
     
   • basic solution
     
   • basis
     
   • basic feasible solution
     
   • iteration
     
   • tableau form
     
   • pivot element
     
   • simplex tableau
     
   • artificial variable

6. Know how to recognize the following special situations when using the simplex method to solve linear programs.
   • infeasibility
     
   • unboundedness
     
   • alternative optimal solutions
     
   • degeneracy

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Chapter 6 - Simplex-Based Sensitivity Analysis and Duality

1. Be able to use the final simplex tableau to compute ranges for the coefficients of the objective function.

2. Understand how to use the optimal simplex tableau to identify dual prices.

3. Be able to use the final simplex tableau to compute ranges on the constraint right-hand sides.

4. Understand the concepts of duality and the relationship between the primal and dual linear programming problems.

5. Know the economic interpretation of the dual variables.

6. Be able to convert any maximization or minimization problem into its associated canonical form.

7. Be able to obtain the primal solution from the final simplex tableau of the dual problem.

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Chapter 7 - Transportation, Assignment, and Transshipment Problems

1. Be able to identify the special features of the transportation problem.

2. Become familiar with the types of problems that can be solved by applying a transportation model.

3. Be able to develop network and linear programming models of the transportation problem.

4. Know how to handle the cases of (1) unequal supply and demand, (2) unacceptable routes, and (3) maximization objective for a transportation problem.

5. Be able to identify the special features of the assignment problem.

6. Become familiar with the types of problems that can be solved by applying an assignment model.

7. Be able to develop network and linear programming models of the assignment problem.

8. Be familiar with the special features of the transshipment problem.

9. Become familiar with the types of problems that can be solved by applying a transshipment model.

10. Be able to develop network and linear programming models of the transshipment problem.

11. Be able to utilize the minimum-cost method to find an initial feasible solution to a transportation problem.

12. Be able to utilize the transportation simplex method to find the optimal solution to a transportation problem.

13. Be able to utilize the Hungarian algorithm to solve an assignment problem.

14. Understand the following terms.
    • transportation problem
      
    • modified distribution (MODI) method
      
    • origin
      
    • assignment problem
      
    • destination
      
    • Hungarian method
      
    • network flow problem
      
    • opportunity loss
      
    • transportation tableau
      
    • transshipment problem
      
    • minimum cost method
      
    • capacitated transshipment problem
      
    • stepping-stone path

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Chapter 8 - Integer Linear Programming

1. Be able to recognize the types of situations where integer linear programming problem formulations are desirable.

2. Know the difference between all-integer and mixed integer linear programming problems.

3. Be able to solve small integer linear programs with a graphical solution procedure.

4. Be able to formulate and solve fixed charge, capital budgeting, and distribution system design problems as integer linear programs.

5. See how zero-one integer linear variables can be used to handle special situations such as multiple choice, k out of n alternatives, and conditional constraints.

6. Be familiar with the computer solution of MILPs.

7. Understand the following terms:
   • all-integer
     
   • mutually exclusive constraint
     
   • mixed integer
     
   • k out of n alternatives constraint
     
   • zero-one variables
     
   • conditional constraint
     
   • LP relaxation
     
   • co-requisite constraint
     
   • multiple choice constraint

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Chapter 9 - Network Models

1. Know the basic characteristics of the shortest route problem.

2. Know the basic characteristics of the minimal spanning tree problem.

3. Know the basic characteristics of the maximal flow problem.

4. Be able to use network-based algorithms to solve shortest route, maximal flow, and minimal spanning tree problems.

5. Be able to formulate and solve a maximal flow problem as a linear program.

6. Understand the following terms:
   • shortest route
     
   • tentative label
     
   • permanent label
     
   • spanning tree
     
   • minimal spanning tree
     
   • maximal flow
     
   • source node
     
   • sink node
     
   • arc flow capacities

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Chapter 10 - Project Scheduling: PERT/CPM

1. Understand the role and application of PERT/CPM for project scheduling.

2. Learn how to define a project in terms of activities such that a network can be used to describe the project.

3. Know how to compute the critical path and the project completion time.

4. Know how to convert optimistic, most probable, and pessimistic time estimates into expected activity time estimates.

5. With uncertain activity times, be able to compute the probability of the project being completed by a specific time.

6. Understand the concept and need for crashing.

7. Be able to formulate the crashing problem as a linear programming model.

8. Learn how to schedule and control project costs with PERT/Cost.

9. Understand the following terms:
   • network
     
   • beta distribution
     
   • PERT/CPM
     
   • path
     
   • activities
     
   • critical path
     
   • event
     
   • critical activities
     
   • optimistic time
     
   • slack
     
   • most probable time
     
   • crashing
     
   • pessimistic time
     

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Chapter 11 - Inventory Models

1. Learn where inventory costs occur and why it is important for managers to make good inventory policy decisions.

2. Learn the economic order quantity (EOQ) model.

3. Know how to develop total cost models for specific inventory systems.

4. Be able to use the total cost model to make how-much-to-order and when-to-order decisions.

5. Extend the basic approach of the EOQ model to inventory systems involving production lot size, planned shortages, and quantity discounts.

6. Be able to make inventory decisions for single-period inventory models.

7. Know how to make order quantity and reorder point decisions when demand must be described by a probability distribution.

8. Learn about lead time demand distributions and how they can be used to meet acceptable service levels.

9. Be able to develop order quantity decisions for periodic review inventory systems.

10. Understand the following terms:
    • inventory holding costs
      
    • backorder
      
    • cost of capital
      
    • quantity discounts
      
    • ordering costs
      
    • goodwill costs
      
    • economic order quantity (EOQ)
      
    • probabilistic demand
      
    • constant demand rate
      
    • lead time demand
      
    • reorder point
      
    • service level
      
    • single-period inventory model
      
    • lead time demand
      
    • periodic review
      
    • cycle time
      
    • safety stock

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Chapter 12 - Waiting Line Models

1. Be able to identify where waiting line problems occur and realize why it is important to study these problems.

2. Know the difference between single-channel and multiple-channel waiting lines.

3. Understand how the Poisson distribution is used to describe arrivals and how the exponential distribution is used to describe services times.

4. Learn how to use formulas to identify operating characteristics of the following waiting line models:
   1. Single-channel model with Poisson arrivals and exponential service times
      
   2. Multiple-channel model with Poisson arrivals and exponential service times
      
   3. Single-channel model with Poisson arrivals and arbitrary service times
      
   4. Multiple-channel model with Poisson arrivals, arbitrary service times, and no waiting
      
   5. Single-channel model with Poisson arrivals, exponential service times, and a finite calling population

5. Know how to incorporate economic considerations to arrive at decisions concerning the operation of a waiting line.

6. Understand the following terms:
   • queuing theory
     
   • steady state
     
   • queue
     
   • utilization factor
     
   • single-channel
     
   • operating characteristics
     
   • multiple-channel
     
   • blocking
     
   • mean arrival rate
     
   • infinite calling population
     
   • mean service rate
     
   • finite calling population
     
   • queue discipline
     

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Chapter 13 - Simulation

1. Understand what simulation is and how it aids in the analysis of a problem.

2. Learn why simulation is a significant problem-solving tool.

3. Understand the difference between static and dynamic simulation.

4. Identify the important role probability distributions, random numbers, and the computer play in implementing simulation models.

5. Realize the relative advantages and disadvantages of simulation models.

6. Understand the following terms:
   • simulation
     
   • Monte Carlo simulation
     
   • simulation model
     
   • discrete-event simulation
     

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Chapter 14 - Decision Analysis

1. Learn how to describe a problem situation in terms of decisions to be made, chance events and consequences.

2. Be able to analyze a simple decision analysis problem from both a payoff table and decision tree point of view.

3. Be able to develop a risk profile and interpret its meaning.

4. Be able to use sensitivity analysis to study how changes in problem inputs affect or alter the recommended decision.

5. Be able to determine the potential value of additional information.

6. Learn how new information and revised probability values can be used in the decision analysis approach to problem solving.

7. Understand what a decision strategy is.

8. Learn how to evaluate the contribution and efficiency of additional decision making information.

9. Be able to use a Bayesian approach to computing revised probabilities.

10. Know what is meant by utility.

11. Understand why utility could be preferred to monetary value in some situations.

12. Be able to use expected utility to select a decision alternative.

13. Be able to use TreePlan software for decision analysis problems.

14. Understand the following terms:
    • decision alternatives
      
    • decision strategy
      
    • chance events
      
    • risk profile
      
    • states of nature
      
    • sensitivity analysis
      
    • influence diagram
      
    • prior probabilities
      
    • payoff table
      
    • posterior probabilities
      
    • decision tree
      
    • expected value of sample information (EVSI)
      
    • optimistic approach
      
    • efficiency of sample information
      
    • conservative approach
      
    • Bayesian revision
      
    • minimax regret approach
      
    • utility
      
    • opportunity loss or regret
      
    • lottery
      
    • expected value approach
      
    • expected utility
      
    • expected value of perfect information (EVPI)

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Chapter 15 - Multicriteria Decision

1. Understand the concept of multicriteria decision making and how it differs from situations and procedures involving a single criterion.

2. Be able to develop a goal programming model of a multiple criteria problem.

3. Know how to use the goal programming graphical solution procedure to solve goal programming problems involving two decision variables.

4. Understand how the relative importance of the goals can be reflected by altering the weights or coefficients for the decision variables in the objective function.

5. Know how to develop a solution to a goal programming model by solving a sequence of linear programming models using a general purpose linear programming package.

6. Know what a scoring model is and how to use it to solve a multicriteria decision problem.

7. Understand how a scoring model uses weights to identify the relative importance of each criterion.

8. Know how to apply the analytic hierarchy process (AHP) to solve a problem involving multiple criteria.

9. Understand how AHP utilizes pairwise comparisons to establish priority measures for both the criteria and decision alternatives.

10. Understand the following terms:
    • multicriteria decision problem
      
    • analytic hierarchy process (AHP)
      
    • goal programming
      
    • hierarchy
      
    • deviation variables
      
    • pairwise comparison matrix
      
    • priority levels
      
    • synthesization
      
    • goal equation
      
    • consistency
      
    • preemptive priorities
      
    • consistency ratio
      
    • scoring model

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Chapter 16 - Forecasting

1. Understand that the long-run success of an organization is often closely related to how well management is able to predict future aspects of the operation.

2. Know the various components of a time series.

3. Be able to use smoothing techniques such as moving averages and exponential smoothing.

4. Be able to use the least squares method to identify the trend component of a time series.

5. Understand how the classical time series model can be used to explain the pattern or behavior of the data in a time series and to develop a forecast for the time series.

6. Be able to determine and use seasonal indexes for a time series.

7. Know how regression models can be used in forecasting.

8. Know the definition of the following terms:
   • time series
     
   • mean squared error
     
   • forecast
     
   • moving averages
     
   • trend component
     
   • weighted moving averages
     
   • cyclical component
     
   • smoothing constant
     
   • seasonal component
     
   • seasonal index
     
   • irregular component
     

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Chapter 17 - Markov Processes

1. Learn about the types of problems that can be modeled as Markov processes.

2. Understand the Markov process approach to the market share or brand loyalty problem.

3. Be able to set up and use the transition probabilities for specific problems.

4. Know what is meant by the steady-state probabilities.

5. Know how to solve Markov processes models having absorbing states.

6. Understand the following terms:
   • state of the system
     
   • transition probability
     
   • state probability
     
   • steady-state probability
     
   • absorbing state
     
   • fundamental matrix

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Chapter 18 - Dynamic Programming

1. Understand the basics of dynamic programming and its approach to problem solving.

2. Learn the general dynamic programming notation.

3. Be able to use the dynamic programming approach to solve problems such as the shortest route problem, the knapsack problem and production and inventory control problems.

4. Understand the following terms:
   • stages
     
   • state variables
     
   • principle of optimality
     
   • stage transformation function
     
   • return function
     
   • knapsack problem

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