BIT Final EXAM Study Guide PDF

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BIT 2406 FINAL EXAM

Midterm Exam One (see Module One Files) Chapter 3 – Sensitivity Analysis Know how to read both an Answer Report and a Sensitivity Report See Worksheet 1 solution -

Standard Form: requires all variables in the constraint equations to appear on the left of the inequality and all numeric values to be on the right hand side

Beaver Creek Pottery Example Sensitivity Analysis - Sensitivity Analysis: determines the effect on the optimal solution of changes in parameter values of the objective function and constraint equations o Changes may be reactions to anticipated uncertainties in the parameters or to new or changed information concerning the model - Sensitivity Range: the sensitivity range for an objective function coefficient is the range of values over which the current optimal solution point will remain optimal Objective Function Coefficient Ranges Beaver Creek Example Sensitivity Report

Changes in Constraint Quantity Values Sensitivity Range - The sensitivity range for a right-hand-side value is the range of values over which the quantity’s value can change without changing the solution variable mix, including the slack variables Constraint Quantity Value Ranges by Computer Excel Sensitivity Range for Constraints

BIT 2406 FINAL EXAM Other Forms of Sensitivity Analysis - Changing individual constraint parameters - Adding new constraints - Adding new variables Shadow Prices (Dual Variable Values) - Defined as the marginal value of one additional unit of resource - The sensitivity range for a constraint quantity value is also the range over which the shadow price is valid

Example Problem:

BIT 2406 FINAL EXAM

Midterm Exam Two (see Module Two Files) -

Chapter 6 – Transportation, Transshipment, and Assignment Problems Be able to set up each of these three types of problems as an LP model Part of a class of LP problems known as network flow models Special mathematical features that permit very efficient, unique solution methods (variation of traditional simplex procedure)

The Transportation Model: Characteristics - A product is transported from a number of sources to a number of destinations at the minimum possible cost - Each source is able to supply a fixed number of units of the product and each destination has a fixed demand for the product - The linear programming model has constraints for supply at each source and demand at each destination - All constraints are equalities in a balanced transportation model where supply equals demand - Constraints contain inequalities in unbalanced models where supply does not equal demand Example: The Transshipment Model: Characteristics - Extension of the transportation model - Intermediate transshipment points are added between the sources and destinations - Items may be transported from: o Sources through transshipment points to destinations o One source to another o One transshipment point to another o One destination to another o Directly from sources to destinations o Some combination of these - Extension of the transportation model in which intermediate transshipment points are added between sources and destinations Example: The Assignment Model: Characteristics - Special form of linear programming model similar to the transportation model - Supply at each source and demand at each destination limited to one unit - In a balanced model supply equals demand - In an unbalanced model supply does not equal demand Example:

BIT 2406 FINAL EXAM

Midterm Exam Three (see Module Three Files) Chapter 7 – Network Flow Models Know Shortest Route determination – see Quiz 4 solution Know Minimal Spanning Tree determination – see Quiz 5 solution Know Maximal Flow determination – see Quiz 6 solution Network Components - A network is an arrangement of paths (branches) connected at various points (nodes) through which one or more items move from one point to another - The network is drawn as a diagram providing a picture of the system, thus enabling visual representation and enhanced understanding - A large number of real-life systems can be modeled as networks which are relatively easy to conceive and construct - Network diagrams consist of nodes and branches - Nodes (circles) represent junction points, or locations - Branches (lines) connect nodes and represent flow o Origin and destination o Values assigned to branches The Shortest Route Problem - Determine the shortest routes from the origin to all destinations Solution Approach - The permanent set indicates the nodes for which the shortest route has been found o Determine all nodes directly connected to the permanent set o Redefine the permanent set - Determine the network with optimal routes from the origin to all destinations o Shortest travel time from origin to each destination Solution Method Summary 1. Select the node with the shortest direct route from the origin 2. Establish a permanent set with the origin node and the node that was selected in step 1 3. Determine all nodes directly connected to the permanent set nodes 4. Select the node with the shortest route from the group of nodes directly connected to the permanent set nodes 5. Repeat steps 3 & 4 until all nodes have joined the permanent set The Minimal Spanning Tree Problem - Connect all nodes in a network so that the total of the branch lengths are minimized - Start with any node in the network and select the closest node to join the spanning tree - Select the node not presently in the spanning area - Continue to select the closest node not presently in the spanning area - Continue - Continue - Optimal Solution Solution Method Summary: 1. Select any starting node (conventionally, node 1) 2. Select the node closest to the starting node to join the spanning tree

BIT 2406 FINAL EXAM 3. Select the closest node not currently in the spanning tree 4. Repeat step 3 until all nodes have joined the spanning tree The Maximal Flow Problem - Maximize the amount of flow items from an origin to a destination - Step 1: arbitrarily choose any path through the network from origin to destination and ship as much as possible - Step 2: re-compute branch flow in both directions - Step 3: select other feasible paths arbitrarily and determine maximum flow along the paths until flow is no longer possible Solution Method Summary 1. Arbitrarily select any path in the network from the origin to the destination 2. Adjust the capacities at each node by subtracting the maximal flow for the path selected in step 1 3. Add the maximal flow along the path to the flow in the opposite direction at each node 4. Repeat steps 1, 2, and 3 until there are no more paths with available flow capacity Example

Chapter 8 – Project Management o Know PERT/CPM calculations and the use of probabilistic activity times to calculate both expected time and estimated variance for an activity o know how to perform both a forward pass and a backward pass in order to find both the length of the project and the critical path o know how to determine the project variance and standard deviation and how to calculate a zscore o know how to determine which activity to crash for a project o See Worksheet 3 solution Overview - Network representation is useful for project analysis - Networks show how project activities are organized and are used to determine time duration of projects - Network techniques used are: o CPM (critical path method) o PERT (Project Evaluation and Review Technique) Project Management - Management is generally perceived as concerned with planning, organizing, and control of an ongoing process or activity - Project management is concerned with control of an important activity for a relatively short period of time after which management effort ends - Primary elements of project management to be discussed: o Project planning o Project return o Project team o Project control - Project scheduling

BIT 2406 FINAL EXAM o Project schedule evolves from planning documents, with focus on timely completion o Critical elements in project management are the source of most conflicts and problems o Gnatt chart and CPM/PERT techniques can be useful

Gnatt Chart - Direct precursor of CPM/ PERT for monitoring work progress - A visual display of project schedule showing activity start and finish times where extra time is available The Project Network CPM/ PERT - Activity-on Arc Network o A branch reflects an activity of a project o A node represents the beginning and ends of activities, referred to as events o Branches in the network indicate precedence relationships o When an activity is completed at a node, it has been realized Concurrent Activities - Activities can occur at the same time - Network aids in planning and scheduling - Time duration of activities shown on branches Activity on Node Network - A node represents an activity with its label and time shown on the node - The branches show the precedence relationships - Convention used in Microsoft Project software The Critical Path - The critical path is the longest path through the network; the minimum time the network can be completed Activity Scheduling: Earliest Times - ES is the earliest time an activity can start - EF is the earliest start time plus the activity time Activity Scheduling: Latest Times - LS is the latest time an activity can start without delaying critical path time - LF is the latest finish time Activity Slack Time - Slack is the amount of time an activity can be delayed without delaying the project - Slack Time exists for those activities not on the critical path for which the earliest and latest start times are not equal - Shared slack is slack available for a sequence of activities Probabilistic Activity Times - Activity time estimates usually cannot be made with certainty - PERT used for probabilistic activity times - In PERT, three time estimates are used: o Most likely time

BIT 2406 FINAL EXAM o The optimistic time o And the pessimistic time - These provide an estimate of the mean and variance of a beta distribution Example and Formula:

Expected Project Time and Variance - Expected project time is the sum of the expected times of the critical path activities - Project variance is the sum of the critical path activities’ variances - The expected project time is assumed to be normally distributed (based on central limit theorem) - In example, expected project time and variance interpreted as the mean and variance of a normal distribution: Probability Analysis of a Project Network - Using the normal distribution, probabilities are determined by computing the number of standard deviations (Z) a value is from the mean - The Z value is used to find the corresponding probability in the table Project Crashing and Time-Cost Trade-Off Overview - Project duration can be reduced by assigning more resources to project activities - However, doing this increases project cost - Decision is based on an analysis of trade-off between time and cost - Project crashing is a method for shortening project duration by reducing one or more critical activities to a time less than normal activity time - Crash cost and crash time have a linear relationship - As activities are crashed, the critical path may change and several paths may become critical General Relationship of Time and Cost - Project crashing costs and indirect costs have an inverse relationship - Crashing costs are highest when the project is shortened - Indirect costs increase as the projects duration increases - The optimal project time is at the minimum point on the total cost curve

The CPM/ PERT Network Formulating as a Linear Programming Model - The objective is to minimize the project duration (critical path time)

BIT 2406 FINAL EXAM

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A shadow price of 1 indicates the critical path The objective is to minimize the cost of crashing Example

BIT 2406 FINAL EXAM

Module Four Material Chapter 9 – Multicriteria Decision Making o Know general concepts that were covered in class and from the lecture slides o Goal Programming – know how to set up Goal Programming model o Analytical Hierarchy Process – see Quiz 7 Excel solution One with pieces missing Scoring Models – review Worksheet 5 solution Chapter 12 – Decision Analysis o Know general concepts that were covered in class and from the lecture slides o Decision Making without Probabilities – Know how to manually solve for Maximax, Maximin, Hurwicz, Equal Likelihood, and Minimax Regret o Decision Making with Probabilities – Know how to manually solve for Expected Value (EV) and Expected Opportunity Loss (EOL) o Know how to manually solve for Expected Value of Perfect Information and the Total Worth in the System o Know how to manually work through Sequential Decision Making with Decision Trees Review Quiz 8 Excel solution and Quiz 9 Excel solution Chapter 15 – Forecasting o Smoothing Methods – Know how to manually calculate Moving Average (MA) forecast, Weighted Moving Average (WMA) forecast, and Exponential Smoothing forecast o Forecast Error Measurements – Know how to manually calculate Forecast Error, MAD, MSE, and MAPD o Trend Forecasting – Know how to manually calculate both Slope and Intercept in order to develop the Trend Forecasting equation o Seasonal Forecasting – Know how to calculate the Seasonal Average and the Seasonal Index in order to Deseasonalize data; be able to develop the Trend Forecasting equation from the deseasonalized data; be able to Reseasonalize the trend forecast Review Quiz 10 Excel solution and Quiz 11 Excel solution

BIT 2406 FINAL EXAM...