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Introduction to Management Science
Management Science – A scientific approach to solving management problems using quantitative analysis and mathematical modeling to support decision-making across various organizational contexts.
Problem Solving – The systematic process of identifying differences between current and desired states and resolving them using logical methods.
Scientific Method – A structured process involving observation, problem definition, model construction, solution, and implementation to solve management problems.
Observation – The first step of the scientific method; identifying problems in the organization through ongoing monitoring.
Problem Definition – The second step; clearly and precisely stating the problem and organizational objectives to guide model development.
Model Construction – The third step; developing a mathematical or abstract representation of the problem using variables, parameters, and functional relationships.
Model Solution – The fourth step; solving the constructed model using suitable mathematical techniques to find values for decision variables.
Implementation – The final step in the process; applying the model’s solution in the organization. Often overlooked, but critical for impact.
Feedback Loop – A concept indicating that failure in implementation may require re-evaluation, bringing the process back to earlier stages.
Decision Variable – A symbol used in a model to represent a controllable input, the value of which is determined during optimization.
Objective Function – A formula representing the goal of the model, such as maximizing profit or minimizing cost.
Constraint – An equation or inequality in a mathematical model that imposes restrictions on decision variables.
Variable – A symbol representing a quantity that can change or assume different values in a model.
Parameter – A known constant value in a model, often serving as coefficients for variables, derived from data.
Functional Relationship – A mathematical connection between variables, where one variable is dependent on another (e.g., profit as a function of units sold).
Mathematical Model – A representation of a real problem using equations and numerical relationships among variables and parameters.
Profit – The difference between total revenue (price × volume) and total cost (fixed + variable costs).
Break-even Analysis – A technique used to determine the point at which total revenue equals total cost, resulting in zero profit.
Break-even Point – The volume (V) where TR = TC; helps determine how many units must be sold to avoid loss.
Fixed Cost – Costs that remain unchanged regardless of production levels (e.g., rent, salaries).
Variable Cost – Costs that vary depending on the level of production or activity (e.g., raw materials).
Cost-Volume-Profit (CVP) Analysis – An analytical model examining the relationship between cost, volume, and profit.
Sensitivity Analysis – A technique used to assess how sensitive a model's outcomes are to changes in parameters or input values.
Risk – The probability and consequences of negative outcomes associated with uncertain events.
Uncertainty – The lack of certainty about future outcomes or events; not all variables are known.
Spreadsheet – A digital tool (e.g., Excel) used for modeling, data manipulation, and sensitivity or break-even analysis.
Excel QM – An Excel add-in used for solving management science problems like break-even analysis, volume analysis, and graphical modeling.
Excel QM Break-even Setup – Includes naming the company, inputting parameters under "Option 1," and generating a CVP graph.
Linear Programming – A mathematical technique for optimization where relationships are linear; used to achieve an objective under constraints.
Integer Programming – A linear programming method where some or all decision variables must be integers.
Total Integer Model – A model in which all decision variables must be integers; used when fractional solutions are not acceptable.
0–1 Integer Model – A model using binary (0 or 1) decision variables, typically for yes/no decisions.
Mixed Integer Model – A model that includes both integer and continuous variables.
Goal Programming – A variation of linear programming that handles multiple objectives by prioritizing goals.
Simplex Method – An algorithm used to solve linear programming problems efficiently.
Transportation Method – A technique used to minimize cost in distributing goods from sources to destinations.
Assignment Method – Used to assign resources/tasks on a one-to-one basis to optimize outcomes.
Transshipment Model – A distribution model that includes intermediate transfer points for goods between origin and destination.
Branch and Bound Method – A method used for solving integer and combinatorial optimization problems.
Network Techniques – Techniques using visual diagrams to model systems (e.g., shortest path, project scheduling).
Decision Analysis – A probabilistic method of evaluating decision alternatives under uncertain future conditions.
Queuing Theory – A method used to analyze waiting lines or queues to improve service efficiency.
Project Management (CPM/PERT) – Tools used for planning, scheduling, and controlling projects using network diagrams.
Analytical Hierarchy Process (AHP) – A structured decision-making technique using pairwise comparisons in a hierarchy.
Simulation – A technique that imitates real-world systems to analyze behavior under different scenarios; useful when other techniques fail.
Forecasting – Predicting future demand or trends based on historical data to improve planning and reduce costs.
Non-linear Programming – Optimization where relationships between variables are not linear; used in complex models.
Game Theory – A method for analyzing competitive scenarios where outcomes depend on strategies of multiple players.
Markov Analysis – A probabilistic method used to model state transitions over time in a system.
Decision Support System (DSS) – A computer-based tool that aids decision-makers by integrating data, models, and a user interface.
Data-Oriented DSS – A DSS focusing on data collection and analysis to support decisions.
Model-Oriented DSS – A DSS emphasizing analytical models and mathematical techniques for decision-making.
Online Analytical Processing (OLAP) – A type of DSS focused on complex, multidimensional data analysis for business decisions.
Western Clothing Company Example – Used in the file to illustrate break-even analysis using Excel QM by modeling cost, revenue, and profit.
Linear Programming
Linear Programming – A mathematical technique used to determine the optimal outcome in a system modeled with linear relationships involving decision variables, constraints, and an objective function.
Objective Function – A linear formula representing the goal of the model, either to maximize or minimize a particular value, such as profit or cost.
Decision Variable – A symbolic representation of controllable elements whose values are determined in the optimization process to achieve the objective.
Constraints – Linear conditions that restrict the possible values of decision variables, often due to limited resources or required specifications.
Parameters – Fixed numerical values that define the coefficients in the objective function and constraints, representing resources or contributions.
Model Formulation – The structured process of converting a real-world problem into a linear programming model composed of decision variables, an objective function, and constraints.
Feasible Solution – A set of values for decision variables that satisfies all constraints in the model.
Infeasible Solution – A set of values for decision variables that violates one or more constraints.
Optimal Solution – The feasible solution that results in the most favorable value of the objective function, whether maximum or minimum.
Nonnegativity Constraint – A condition requiring decision variables to be zero or greater, reflecting realistic conditions such as nonnegative production levels.
Maximization Model – A linear programming model in which the objective function is designed to achieve the highest possible value, such as maximum profit.
Minimization Model – A model aimed at achieving the lowest possible value of the objective function, typically minimizing costs or losses.
Slack Variable – A variable added to a ≤ constraint to convert it into an equation, representing unused resources.
Surplus Variable – A variable subtracted from a ≥ constraint to transform it into an equation, representing excess above the requirement.
Standard Form – A version of a linear programming model where all constraints are equations and decision variables are nonnegative.
Graphical Solution – A visual method used to solve linear programming problems with two decision variables by plotting constraints and identifying the feasible region and optimal solution.
Feasible Region – The area on a graph where all constraints overlap, representing all combinations of decision variables that satisfy the constraints.
Extreme Point – A corner point of the feasible region where the optimal solution is often found in a graphical method.
Product Mix Problem – A common type of linear programming application where a firm determines the optimal combination of products to produce within resource limits to maximize profit.
Sensitivity Analysis – An evaluation of how changes in model parameters (such as resource availability or profit coefficients) affect the optimal solution.
Binding Constraint – A constraint that forms part of the optimal solution boundary and is fully utilized in the solution.
Nonbinding Constraint – A constraint that does not affect the optimal solution directly, as it is not fully used at the optimal point.
Shadow Price – The amount by which the objective function value would improve if there were one more unit of a binding resource.
Graphical Method Limitations – Constraints of the graphical method, which only works for problems with two decision variables and cannot handle higher dimensions.
Slope of Objective Function – The rate at which the objective function increases or decreases, used in graphical solutions to move the objective line to its optimal position.
Multiple Optimal Solutions – A condition where more than one point on the boundary of the feasible region yields the same optimal value.
Degeneracy – A condition where more than one optimal solution occurs at the same extreme point due to overlapping constraints.
Certainty Assumption – The presumption in linear programming that all coefficients in the model are known and fixed.
Additivity – A property where the total effect of all decision variables is the sum of their individual effects.
Proportionality – A linear programming assumption that the contribution of each decision variable is directly proportional to its level.
Divisibility – An assumption that decision variables can take on any fractional value, allowing continuous solutions.
Integer Linear Programming – A variation of linear programming where some or all decision variables are restricted to integer values.
Balanced Transportation Model – A transportation problem where total supply equals total demand, and all constraints are equalities.
Unbalanced Transportation Model – A model where supply does not equal demand, leading to inequality constraints.
Model Components – The essential parts of a linear programming model: decision variables, objective function, and constraints.
Model Summary – A concise representation of a linear programming model including variables, objective, and constraints.
Model Interpretation – The analysis of a model’s results to guide real-world decision-making and understand the implications of the solution.
QM for Windows – A software used for solving linear programming models through graphical and simplex methods.
Excel Solver – A Microsoft Excel add-in tool used to define and solve linear programming problems by specifying objective functions, variables, and constraints.
Dual Value – Also called shadow price, it indicates how much the objective function will change with a one-unit increase in a resource.
Ranging – A sensitivity analysis method used to determine the range of values over which an objective coefficient or right-hand side value can vary without changing the optimal solution.
Systematic Format – A structured approach to model formulation involving sequential steps: defining variables, formulating objective function, and setting constraints.
Modeling Example – A practical case used to illustrate linear programming concepts by applying them to a real or hypothetical scenario.
Constraint Line – A graphical representation of a constraint equation showing the boundary between feasible and infeasible areas.
Intersection Point – A point on the graph where two constraint lines meet, often representing a potential optimal solution.
Inactive Constraint – A constraint that does not limit the feasible solution space at the optimal point and thus does not impact the solution.
Binding Resource – A resource that is fully utilized at the optimal solution point, limiting the achievement of a better outcome.
Excess Capacity – The amount of a resource that is not fully used in the optimal solution, represented by slack variables.
Idle Resource – A resource that is available but not used in the solution due to optimality considerations.
Inequality Types in LP – The three types of inequalities used in linear programming: ≤ (less than or equal to), = (equal to), and ≥ (greater than or equal to).
Integer Programming
Integer Programming – An optimization method where some or all decision variables are constrained to integer values.
Total Integer Model – A model in which all decision variables must be integers, used when fractional values are not acceptable.
0–1 Integer Model – A model using binary decision variables that can only be 0 or 1 to represent yes/no choices.
Mixed Integer Model – A model combining integer and continuous decision variables within the same formulation.
Decision Variable – A variable representing a controllable input in the model whose value is determined during optimization.
Objective Function – The formula that defines the goal of the model, such as maximizing profit or minimizing cost.
Constraint – A condition that decision variables must satisfy, reflecting limits like capacity or budget.
Feasible Solution – A solution that satisfies all constraints and integrality conditions of the model.
Optimal Solution – The best feasible solution according to the objective function.
Graphical Solution Method – A visual technique to solve two-variable linear models by plotting constraints and feasible regions.
Branch and Bound Method – A solution algorithm that breaks integer problems into subproblems and evaluates them systematically.
Binary Variable – A variable restricted to 0 or 1, used for inclusion/exclusion decisions.
Mutually Exclusive Constraint – A restriction ensuring only one variable in a group can be 1 at a time.
Conditional Constraint – A rule linking binary variables, such that one choice depends on another.
Corequisite Constraint – A condition that forces binary variables to be equal, ensuring joint inclusion or exclusion.
Slack – The unused portion of a ≤ constraint, representing spare capacity or resources.
Suboptimal Solution – A feasible but non-optimal solution that doesn't yield the best value of the objective function.
Set Covering Model – A binary model that selects the minimum number of options to cover all requirements.
Capital Budgeting Model – A 0–1 model used to choose projects under a budget constraint to maximize return.
Fixed-Charge Model – A model with fixed setup costs plus variable costs, used in logistics and facility planning.
Rounding Down – A heuristic that floors fractional values, possibly resulting in feasible but suboptimal outcomes.
Rounding Up – A heuristic that ceilings fractional values, potentially causing infeasibility.
Enumeration Method – A brute-force method that checks all possible combinations of integer variables.
Solver (Excel) – A tool in Excel for solving optimization problems using linear and integer programming.
QM for Windows – Software used for modeling and solving various operations research problems, including integer programming.
Cutting Plane Method – An algorithm that adds linear constraints iteratively to eliminate non-integer solutions.
Constraint Violation – Occurs when a proposed solution does not satisfy one or more constraints.
Feasible Region – The set of all decision variable values that satisfy all constraints.
Operating Room Allocation Model – An integer programming application for assigning surgical time slots efficiently.
Scheduling Problem – An application where events or tasks are assigned to time slots or locations under constraints.
Multiple-Choice Constraint – A restriction requiring exactly one choice among a group of binary variables.
Investment Model – An optimization model that allocates capital among investment options under constraints.
Real-World Application – A practical use of integer programming in fields like logistics, finance, or healthcare.
Facility Location Problem – A model to find optimal facility sites minimizing fixed and transportation costs.
Set Covering Problem – A binary model aiming to cover all targets with the fewest selected sets or resources.
Real Variable – A decision variable that can assume any non-negative continuous value.
Budget Constraint – A restriction ensuring total costs do not exceed available funds.
Space Constraint – A limit on the amount of physical resource usage like area or volume.
Profit Maximization – An objective that seeks to maximize the difference between revenue and costs.
Constraint Coefficient – The multiplier of a decision variable in a constraint or objective function.
Integer Feasibility – A condition where all integer variables in a solution have valid integer values.
Infeasible Solution – A solution that violates one or more model constraints.
Enumeration Tree – A branching structure used in branch and bound to explore solution paths.
Optimality Gap – The difference between the best-known and best-possible solution values.
Constraint Binding – A constraint that holds as an equality and directly influences the optimal solution.
Transportation, Transshipment, and Assignment Models
Transportation Problem – A model to minimize shipping costs from multiple sources to destinations under supply and demand constraints.
Balanced Transportation Model – A transportation model where total supply equals total demand.
Unbalanced Transportation Model – A model with unequal supply and demand, requiring dummy nodes for balance.
Supply Constraint – Ensures shipments from a source do not exceed its available supply.
Demand Constraint – Ensures that the total received at a destination meets its demand.
Objective Function (Transportation) – A function that minimizes the total shipping cost across all routes.
Prohibited Route – A route that cannot be used, modeled by assigning a large cost or excluding the variable.
Transportation Tableau – A tabular format representing costs, supply, and demand in a transportation problem.
Transshipment Problem – A variant of the transportation problem with intermediate nodes between sources and destinations.
Transshipment Constraint – Requires that inflow equals outflow at intermediate transshipment points.
Network Flow Problem – A class of LP problems involving routing flow through a network of nodes and arcs.
Assignment Problem – A special case where each supply and demand is 1, and agents are matched to tasks.
Balanced Assignment Model – An assignment model where the number of agents equals the number of tasks.
Objective Function (Assignment) – A function that minimizes total assignment costs or maximizes efficiency.
Decision Variable (Assignment) – A binary variable equal to 1 if an agent is assigned to a task, 0 otherwise.
Linear Programming Formulation – A structured LP model with linear objective and constraints for optimization.
QM for Windows – Software for solving quantitative models like transportation, transshipment, and assignment.
Excel Solver – A spreadsheet tool for solving LP and IP problems including transportation and assignment models.
Excel QM – An Excel add-in that simplifies model setup and solution for quantitative problems.
Initial Solution Methods (Transportation) – Techniques like Northwest Corner, Minimum Cell Cost, and VAM used to generate starting feasible solutions.
Degeneracy (Transportation) – A condition with fewer occupied cells than required, possibly causing cycling.
Sensitivity Analysis (Transportation) – Examining how changes in inputs affect the optimal solution.
Integer Variables in Transportation – Used when fractional shipments are not allowed, though many models assume divisibility.
Multiple Optimal Solutions – Occurs when different feasible solutions yield the same optimal cost.
Dummy Source or Destination – A fictitious node added to balance an unbalanced problem, usually with zero cost.
Network Flow Models
Network – A system of paths (branches) connected at points (nodes) through which items flow from one location to another.
Node – A junction or point in a network, typically representing cities, terminals, or intersections.
Branch – A connection between nodes that represents a path with an associated cost, time, or capacity.
Network Flow Model – A class of models that represent the flow of items through a network to optimize distance, time, or quantity.
Shortest Route Problem – A network model that determines the minimum path length between origin and destination nodes.
Minimal Spanning Tree Problem – A model that connects all nodes with the least total branch length, without creating cycles.
Maximal Flow Problem – A model that determines the greatest amount of flow from an origin to a destination given capacity constraints.
Directed Branch – A one-way connection between two nodes allowing flow in only one direction.
Undirected Branch – A two-way path between nodes allowing flow in either direction.
Flow Capacity – The maximum amount of flow that can pass through a network branch.
Conservation of Flow – A rule stating that flow into a node must equal flow out of the node, except at the source and destination.
Decision Variable (xij) – A value indicating whether branch i–j is part of the route or the amount of flow through it.
Objective Function (Shortest Route) – Minimize the total travel time or distance for selected branches.
Objective Function (Maximal Flow) – Maximize total flow from origin to destination under capacity constraints.
0–1 Integer Programming – A modeling approach using binary decision variables to select network paths.
Linear Programming (LP) – A mathematical method used to model and solve network problems in Excel or Solver.
Permanent Set – A group of nodes for which the shortest path from the origin is already determined.
Slack (Network Flow) – Unused flow capacity on a branch or flexibility in path choice.
Solver (Excel) – An Excel tool used to build and solve optimization models for network flow problems.
QM for Windows – Software for solving network models, including shortest route, minimal spanning tree, and maximal flow.
Excel QM – An Excel add-in that automates modeling of network problems using templates.
Dummy Node or Branch – A placeholder used in network diagrams to maintain logical or structural consistency without real flow.
Spanning Tree – A sub-network that connects all nodes with the minimal total length and no cycles.
Steps (Shortest Route Solution) – Iteratively select nodes with minimum temporary values and move to permanent set until destination is reached.
Steps (Minimal Spanning Tree) – Start at any node and add the shortest connection to a new node until all nodes are included.
Steps (Maximal Flow) – Select a feasible path, push maximum flow through it, and update residual capacities until no further flow is possible.
Residual Capacity – Remaining capacity available on a branch after flow has been assigned.
Backward Flow – Flow in the reverse direction of a branch, used in adjusting net flow in maximal flow problems.
Iteration (Maximal Flow) – One cycle of selecting a path, assigning flow, and updating capacities.
Path Selection (Maximal Flow) – The process of arbitrarily choosing a path with available capacity from origin to destination.
Flow Adjustment – Updating branch values in both directions after assigning flow to a path.
Healthproof Pharma Example – A shortest route problem where travel time is minimized between cities for sales routing.
Metro Cable TV Example – A minimal spanning tree problem connecting suburbs with the least cable length.
Scott Tractor Company – A maximal flow problem determining the max number of railroad cars from Omaha to St. Louis.
CSX Railway Application – A real-world network model used to optimize empty railcar distribution, saving millions in cost and emissions.
Milk Collection Problem (Italy) – A route optimization model minimizing travel time and fleet size while satisfying constraints like milk type and truck capacity.
Constraint (Maximal Flow) – Ensures that the net flow into and out of each node (except source/sink) is zero.
Branch Capacity Constraint – Limits the amount of flow on a branch to its maximum allowable capacity.
Integer Constraint – Restricts decision variables to whole numbers, typically used in flow models requiring discrete units.
Objective Function (General) – A mathematical expression of the model’s goal—either maximizing flow or minimizing travel/time cost.
Solver Constraint Formula – A formula expressing conservation and capacity constraints in spreadsheet-based models.
Dijkstra’s Algorithm – A solution procedure for shortest route and minimal spanning tree problems developed by E.W. Dijkstra.
Ford–Fulkerson Algorithm – The original procedure for solving maximal flow problems using path augmentation, developed by L.R. Ford Jr. and D.R. Fulkerson.
Project Management
Project Management – The process of planning, organizing, and controlling resources to achieve specific goals within a defined time frame.
CPM (Critical Path Method) – A project analysis technique using deterministic time estimates with activities shown as nodes.
PERT (Program Evaluation and Review Technique) – A project analysis method using probabilistic time estimates, with activities shown as arrows between nodes.
CPM/PERT – A hybrid technique combining CPM and PERT to analyze project duration and identify critical paths.
Project Objectives – A clear description of what a project aims to accomplish, including time frame, cost, and expected outcomes.
Project Scope – The boundaries of a project, detailing what is included and what constitutes project success.
Contract Requirements – Managerial, reporting, and performance obligations defined for staff, suppliers, and subcontractors.
Schedules (Project Planning) – Lists of events and tasks, organized into a master schedule.
Resources (Project Planning) – Budgeted materials, labor, and other assets required to complete a project.
Personnel (Project Planning) – The recruitment and assignment of skilled individuals to the project team.
Control (Project Planning) – Monitoring systems to evaluate progress, cost, and schedule performance.
Risk and Problem Analysis – The identification of potential delays or failures and plans to address them.
Return on Investment (ROI) – A metric used to evaluate project gain relative to cost:
Soft Return – Intangible project benefits like employee satisfaction or public image improvement.
Project Team – A temporary group of individuals with diverse skills organized to execute a project.
Project Manager – The individual responsible for coordinating project activities and ensuring timely completion within budget.
Scope Statement – A document outlining project justification, goals, deliverables, and success criteria.
Statement of Work (SOW) – A detailed work description for team members or subcontractors specifying duties and deliverables.
Work Breakdown Structure (WBS) – A hierarchical decomposition of the project into modules, activities, and tasks.
Organizational Breakdown Structure (OBS) – A chart linking project tasks to responsible organizational units.
Responsibility Assignment Matrix (RAM) – A table assigning responsibility, performance, and support roles to project members.
Project Scheduling – The process of defining, sequencing, and timing project activities to ensure timely completion.
Gantt Chart – A bar chart displaying project activities against time, used for simple project scheduling and tracking.
Slack – The time an activity can be delayed without affecting the overall project duration.
Project Control – Ensuring the project progresses as planned, addressing deviations in schedule, cost, and performance.
Time–Cost Trade-off – Adjusting time and resources to maintain project schedule, often at higher cost.
Performance Management – Tracking progress against goals, using metrics and status reports.
Earned Value Analysis (EVA) – A method that compares planned and actual performance to determine schedule and cost variances.
Schedule Variance (SV) – The difference between work scheduled and work performed.
Cost Variance (CV) – The difference between the budgeted cost and actual cost of work performed.
Network Diagram – A graphical representation of project activities and precedence relationships.
Activity-on-Node (AON) – A network method where nodes represent activities and arrows show dependencies.
Activity-on-Arrow (AOA) – A network method where arrows represent activities and nodes represent events.
Dummy Activity – A placeholder in an AOA network that shows precedence without consuming time or resources.
Critical Path – The longest duration path in a network that determines the shortest possible project duration.
Forward Pass – A method to calculate the earliest start and finish times for project activities.
Backward Pass – A method to calculate the latest start and finish times for project activities.
Earliest Start (ES) – The earliest time an activity can begin without delay.
Earliest Finish (EF) – ES plus activity duration; the soonest an activity can end.
Latest Start (LS) – The latest an activity can begin without delaying the project.
Latest Finish (LF) – The latest time an activity can end without extending project duration.
Activity Slack – The difference between LS and ES (or LF and EF), indicating scheduling flexibility.
Shared Slack – Total slack shared across sequential, non-critical activities.
Probabilistic Time Estimates – Estimations including optimistic (a), most likely (m), and pessimistic (b) times used in PERT.
Beta Distribution – A probability distribution used in PERT to model activity durations.
Expected Activity Time (t) – Calculated using the formula:
Activity Variance (v) – Used to measure uncertainty in duration:
Project Duration Variance – The sum of variances of all activities on the critical path.
Central Limit Theorem – Justifies the use of normal distribution for project duration with enough independent activities.
Standard Deviation (σ) – The square root of the project duration variance.
Z-Value – Used to calculate the probability of meeting a specific project duration:
Microsoft Project – A software tool used for project planning, scheduling, and CPM/PERT analysis.
Excel QM – An Excel add-in that simplifies project scheduling and evaluation tasks.
QM for Windows – A user-friendly software suite used for modeling and solving quantitative management problems.
Modular Construction (T5 Case Study) – A method where project components are prefabricated off-site to reduce construction time and complexity.
Project Crashing – The process of reducing project duration by expending additional resources to shorten the time of critical activities.
Responsibility Assignment Matrix (RAM) – A chart that assigns levels of responsibility (overall, performance, or support) for tasks to individuals or departments.
Organizational Breakdown Structure (OBS) – A chart mapping the work in a WBS to the organizational units responsible for completing it.
Dummy Activity – A placeholder in an AOA diagram that shows dependency between tasks without requiring time or resources.
Deterministic Time Estimate – A single-value estimate for activity duration, assuming no variation or uncertainty.
Probabilistic Time Estimate – A technique (used in PERT) that incorporates optimistic, most likely, and pessimistic times to estimate mean and variance.
Beta Distribution – A probability distribution used in PERT for modeling activity durations based on three time estimates.
Normal Distribution (Project Analysis) – A continuous distribution assumed for total project duration when computing probabilities in CPM/PERT.
Z-Score (Project Management) – A standardized value indicating how far a given completion time is from the expected time, used to calculate probabilities.
Shared Slack – Slack that is collectively available across a sequence of non-critical activities, which cannot all be delayed by their full individual slack.
Schedule Variance (SV) – In EVA, the difference between the value of work performed and the value of work scheduled.
Cost Variance (CV) – In EVA, the difference between the budgeted and actual cost of completed work.
Crashing Goal (CPM) – The target time for project completion that is shorter than the normal duration, often achieved by expediting activities.
AOA Network (Activity-on-Arrow) – A network diagram where activities are represented by arrows and nodes represent events.
AON Network (Activity-on-Node) – A network diagram where activities are shown as nodes, with arrows representing dependencies.
Time–Cost Trade-Off – The balance between speeding up activities (crashing) and increased costs, often necessary to meet project deadlines.
Soft Return – Intangible project benefits that are difficult to quantify, such as improved employee morale or public image.
Critical Activities – Activities on the critical path that cannot be delayed without affecting the project completion time.
Project Scope Statement – A document that outlines the justification, objectives, deliverables, and success criteria for the project.
Statement of Work (SOW) – A formal document detailing the tasks, deliverables, and responsibilities assigned to project personnel or vendors.
Project Manager Challenges – Includes managing diverse teams, tight deadlines, fixed budgets, and high stakes under uncertainty.
Cultural Considerations in Global Projects – Differences in communication, hierarchy, and values (e.g., U.S. individualism vs. Chinese guanxi) that affect teamwork.
Microsoft Project – Project management software used for planning, scheduling, and tracking project tasks and resources.
Crashing via Excel Solver – A method of determining the least-cost way to reduce project duration using optimization models in Excel.
Application Areas for CPM/PERT – Includes R&D, construction, defense, infrastructure, event planning, and space exploration.
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