SCM 411 Exam Review PDF

09 Spreadsheet Models (6 Questions) 10 Optimization and Linear Programming (10 Questions) 11 Sensitivity Analysis (6 Questions) 12 Network Modeling (6 Questions) 13 Integer Linear Programming (6 Questions) 14 Aggregate Planning (6 Questions) 15 Simulation (5 Questions) 16 Decision Analysis (5...

09 Spreadsheet Models (6 Questions) 10 Optimization and Linear Programming (10 Questions) 11 Sensitivity Analysis (6 Questions) 12 Network Modeling (6 Questions) 13 Integer Linear Programming (6 Questions) 14 Aggregate Planning (6 Questions) 15 Simulation (5 Questions) 16 Decision Analysis (5 Questions) Spreadsheet Models - Spreadsheet models are mathematical and logic based model often referred to as what-if models - Spreadsheet models are without question the most used business analytics too because 1. They provide easy-to-use sophisticated mathematical and logical functions 2. They allow for easy instantaneous recalculation of the output for a change in model inputs 3. They are less expensive than specialized software packages 4. They often come preloaded on computers 5. They are reasonable and easy to use Make-versus-Buy Decision - The total cost of manufacturing a product can be defined as the sum of two portions: 1. The fixed cost does not depend the the production unity and remains the same no matter how much is produced 2. The variable cost is the proportion of the total cost dependent on and varies with the productions quantity - A make-versus-buy decision involves comparing the costs of manufacturing inhouse to the cost of outsourcing production to another firm Influence Diagram for Nowlin Plastics - An influence diagram is a visual representation of which entities influence others in a model - Influence in the model is depicted by the arrow connecting the nodes - The influence diagram to the right compares manufacturing versus outsourcing costs for bowling plastics - This modular approach simplifies the modeling process General Principles of Spreadsheet model Design and Construction - The following three general principles of spreadsheet model design and constriction should always be followed 1. Separate the parameter from the model - we can update the model parameters without risk of mistakenly creating an error in a formula 2. Document the model and use proper formatting and color as needed - a good spreadsheet models is well documented has clear labels, and proper formatting and alignment facilitate navigation and understanding 3. Use simple formulas - we can reduce errors and make maintaining the spreadsheet easier by using clear and simple formulas. Long and complex calculations should always be divided into several cells Descriptive and Predictive Spreadsheet Models - Decision making is difficult because of uncertainty and an overwhelming number of choices - Spreadsheet what if models are descriptive models. Basic what-if spreadsheet models can be extended to help deal with uncertainty or the many alternatives a decision maker may face - Predictive models can be estimated from data in spreadsheets using tools provided by excel: The regression tool and other data analysis tools, such as exponential smoothing and moving average allow us to develop predictive models based on data in the spreadsheet. Prescriptive Spreadsheet models  - Simulation and optimization models are examples of prescriptive models - Monte carlo simulation automates a manual what if model by replacing static input parameters with a random generation of values for these uncertain inputs - Optimizing models characterized by having an objective to be maximized or minimized can be used to help make smart decision - Excel includes a special tool called solver that solves optimization models. Solver is used to finding an optimal course of action that maximizes or minimizes the objective on a what if model whale satisficing a set of constraints 10 Optimization and Linear Programming Introduction - Every decisions can be considered an optimization problem - We generally try to make the best decision possible under the circumstances - We face decision about how to use limited resources such as 1. Class schedules 2. Oil in the earth 3. Land for dumps 4. Time 5. Money 6. Workers Characteristics of Optimization Problems - An optimization model or mathematical program consists of 1. Input Parameters: data that is given and fixed 2. Decision Variables: variables that represent decisions to be made 3. Objective functions : function of the decision variables to be maximized or minimized 4. Constraints: restrictions or limitation on the decision variables - Variable bounds: specify the values for which the decision variables have meaning - General constraints: specify all other restriction, requirement, and interaction that could limit the values of the decision variable LP Problems: Spreadsheets - Solving linear programming (LP) problems graphically is only possible when there are two decision variables - Few real-world LP have only two decision variables - Fortunately we can now use spreadsheets to solve LP problems Spreadsheet Design guidelines (I) - Organize the data, then build the model around the dta - Do not embed numeric constraints in formulas - Things which are logically related should be physically related - Use formulas that can be copied - column/rows totals should be close to the columns/rows being totaled Spreadsheet Design guidelines (II) - The english reading eye scans left to right, top to bottom - Use color, shading,, borders, and protection to distinguish changeable parameters from other models elements - Use text boxes and cell notes to document various elements of the model Make vs. Buy Decisions - LP is particularly well suited to problems where scarce or limited resources must be allocated or used in an optimal manner - For example, LP might be used to determine how the various components of a job should be assigned to multipurpose machines in order to minimize the time it takes to complete the job - As another example, a company might receive an order for several items that it cannot fill entirely with its own production capacity - In such as case, the company must determine which items to produce and which items to subcontract from an outside supplier Investment Problem  - There are numerous problems in the area of finance for which various optimization techniques can be applied - These problems often involve attempting to maximize the return on an investment while meeting certain cash flow requirements and risk constraints - Alternatively, we may want to minimize the risk on an investment while maintain a certain level of return Transportation Problem - Many transportation and logistics problems businesses face fall into a category known as network flow problems - The transportation problem is a special type of linear programming problem where the objective is to minimize the cost of distributing a product from am number of sources or origins to a number of destinations - The problems assumes demand requirements and supply limitations Blending Problem - Many business problems involve determining an optimal mix of ingredients. For example, major oil companies must determine the least costly mix of different crude oils and other chemicals to blend together to produce a certain grade of gasoline. Lawn care companies must determine the least costly mix of chemicals and other products to blend together to produce different types of fertilizers - Blending problems are typical applications of mixed integer-linear programming (MILP). They involve blending several resources or materials to create one or more products corresponding to a demand. Mixed integer linear programs are linear programs in which some variable are required to take integer values 11 Sensitivity Analysis  - Businesses rarely know with certainty what costs will be incurred or the exact amounts of resources that will be consumed or available in each situation or time period - Thus optimal solutions obtained using models that assume all relevant factors are know with certainty might be viewed with skepticism by management - Sensitivity analysis can help overcome this skepticism and provide a better picture of how the solution to a problem will change if different factors in the model change - Sensitivity analysis also can help answer several practical managerial questions that might arise about the solution to an LP problem Purpose of Sensitivity analysis - Al the coefficients in the model represent numeric constraints (the ci, aij, and bi) - In the real world, these coefficients might change from day to day or minute to minute - For example the price a company charges for its product can change on a daily, weekly, or monthly basis. Similarly if a skilled machinist call in sick a manufacturer might have less capacity to price items on a given machine that was originally planned The purpose of sensitivity analysis - Realizing that such uncertainties exist, a manager should consider how sensitive an LP models solution s to changes or estimation errors that might occur in: 1. The objective function coefficients (the ci) 2. The constraint coefficients (the aij) 3. The right hand side (RHS) values for the constraints (the bi) - A manger also might ask “What if” questions about these values - For example what if the cost of a production increased by 7% what if a reduction in setup time allows for additional capacity on a given machine? What if a workers suggestion results in a product requiring only 2 hours of labor rather than 3 - Sensitivity analysis addresses these issues by assessing the sensitivity of the solutions to uncertainty or estimation errors in the model coefficients as well as the solutions sensitive to change in model coefficients that occur because of human intervention Approaches to sensitivity analysis - Solver also provides some sensitivity information after solving an LP problem - Solver sensitivity report answer question about: 1. Amounts by which objective functions coefficients can change without changing the optimal solution 2. The impact on the optimal objective function values of changes in constrained resources 3. The impact on the optimal objective function values of forced changes in decision variables 4. The impact changes in constraint coefficients will have on the optimal solution A warning about degeneracy - The solution to an LP problem is degenerate if the allowable increase or decrease on any constraint is zero - When the solution is degenerate 1. The methods mentioned earlier for detecting alternative optimal solutions cannot be relied upon  2. The reduced costs for the changing cells may not be unique. Also the objective function coefficients for changing cells must change by at least as much as their respective reduced costs before the optimal solution would change 3. The allowable increases and decrease for the objective function coefficients still hold and in fact the coefficients may have to be changed beyond the allowable increase and decrease limits before the optimal solution changes 4. The given shadow prices and their ranges may still be interpreted in the usual way but they may not be unique that is a different set of shadow prices and ranges may also apply to the problem 12 Network Modeling Topics - Describe the characteristics of network flow problems - Draw network representation of a variety of decision problems - Explain the balance of flow rules - Differentiate between transshipment shortest path and transportation assignment problems - Expand the term side constraint - Describe the generalized network flow problem and the unique modeling issues it presents - Explained the use of artificial nodes and arcs - Describe the max flow problem - Describe the minimum spanning tree problem The shortest path problem - In many decision problems we need to determine the shortest (or least costly) route or path through a network from a starting node to an ending node - This is special case of transient problem where 1. There is one supply node with a supply of -1 2. There is one demand node with a demand of +1 3. All other nodes have supply/demand of +0 The transportation/Assignment Problem - The transportation problem is a special type of linear programming problem where the objective is to minimize the cost of distributing a product from a number of sources or origins to a number of destinations - The problem assumes demand requirements and supply limitations The generalized network flow problem - In all of the network problems we have considered so far, the amount of flow that exited an arc was always the same as the amount that entered the arc - However there are numerous examples of network flow problems in which a gain or loss occurs on flow across arcs The maximum flow problem - The maximal flow problem involves determining the maximum amount of material that can flow for money pout to antler in a network - Examples of this type of problem include determining the maximum number of cars that can flow through a highway system the maximum amount of a liquid that can flow through a series of pipers, the maximum number of cell-phone calls that can pass through a series of cell towers, and the maximum amount of data that can flow through a computer network The Minimal spanning tree problem - Another type of network problems is knows as the minimal spanning tree problem - This type of problem cannot be solved as an LP problem, but it is solved easily using a simple manual algorithm - A minimum spanning tree is special kind of tree that minimized the lengths of the edges of the tree - An example is a cable company wanting to lay line to multiple neighborhoods by minimizing the amount of cable laid the cable company will save 13 Integer Linear Programming Introduction - When some or all of the decision variables in a linear programming problem are restricted to assuming only integer values, the resulting problem is referred to as an integer linear programming (ILP) problem Integrality Conditions  - An integrality condition indicates that some (or all) of the variables in the formulation must assume only integer values. We refer to such variables as the integer variables in a problem - In contrast variables that are not required to assume strictly integer values are referred to as continuous variables - Although it is easy to state integrality conditions for a problem such conditions often make a problem more difficult to solve Relaxation - The only difference between the ILP and its LP relaxation is that all integrity conditions imposed by the ILP are dropped in the relaxation - However this change has a significant impact on the feasible regions for the two problems - As a general rule, the optimal solutions to the LP relaxation of the ILP problem is not guaranteed to produce an integer solutions - In such cases, the other techniques must be applied to find the optimal integer solution for the problem being solved Bounds - Before discussing how to solve the ILP problem,s an important point must be made about the relationship between the optimal solution to an ILP problem and the optimal solution to its LP relaxation; The objective function value for the optimal solution to the ILP problem can never be better than the objective function value for the optimal solution to its LP relaxation Rounding - In general this does not work reliably: - The rounded solution may be feasible - The rounded solution may be suboptimal Branch and Bound - The branch and bound algorithm can be used to solve ILP problems - It requires the solution of a series of LP problems termed “candidate problems” - Theoretically this can solve any ILP. Practically it often takes large amount of computational effort (and time) Stopping Rules - Because B&B can take sol ong, most ILP package allow you to specify a suboptimality tolerance factor - This allows you to stop once an integer solutions is found that is within some % of the global optimal solution - Bounds obtained from LP relaxation are helpful here Ex.  - LP relaxation has an optimal objective value of $64,306 - 95% of $64,306 is $61,090 - Thus an integer solution with objective value of $61,090 or better must be within 5% of the optimal solutions 14. Aggregate Planning Introduction - Imagine a work in which manufacturing, transportation, warehousing and even information capacity are all limitless and free. Imagine a lead time of zero, allowing goods to be produced and delivered instantaneously. In this world, there is no need to plan in anticipation of demand, because whenever a customer demands a product, the demand is instantly satisfied. In this world, aggregate planning plays no role - In the real world, however, capacity has a cost, and lead time are often long. therefor , companies must make decisions regarding capacity levels, productions levels, outsourcing, and promotions well before demand is known - A company must anticipate demand and determine in advance of that demand and how to meet The Aggregate Planning Problem - Given the demand forecast for each period in the planning horizon, determine the production level, inventory level, and the capacity level for each period that maximizes the firm's profit over the planning horizon - Specify the planning horizon (typically 3-18 months) - Specify the duration of each period - Specify key information required to develop and aggregate plan Information Needed for An Aggregate Plan - Aggregate demand forecast Ft for each period t over T periods - Production costs - Labor costs, regular time and overtime - Subcontracting costs - Costs of changing capacity - hiring or layoff, adding or reducing machine capacity - labor/machine hours required per unit - Inventory holding costs - Stockout or backlog costs - Constraints - overtime, layoffs, capital available, stock outs, backlogs, from suppliers Output of Aggregate Plan - Production quantity from regular time, overtime, and subcontracted time - Inventory held - Backlog/stockout quantity - Workforce hired/laid off - Machine capacity increase/decrease  - A poor aggregate plan can result in lost sales, lost profit, excess inventory, or excess capacity 15 Simulation - Simulation refers to a broad collections of methods and applications to mimic the behavior of real systems usually on a computer with appropriate software - The process of designing a model of a real system and conducting experiments with this model for the purpose of understanding the behavior of the system and or evaluating various strategies for the operation of the system Simulation: Advantages - Flexibility to model things as they are (even if messy and complicated) - Allows uncertainty. Nonstationary in modeling - The only thing that for sure: nothing is for sure - Danger of ignoring system variability - Model validity Simulatio: Disadvantages - Don't get exact answers, only approximations, estimates - Also true of many other modern methods - Can bound eros by machine round off - Get random output (RIRO) from stochastic simulations - Statistical design, analysis of simulation experiments - exploit : noise control, replicability, sequential sampling, variance reduction techniques - Catch “standard” statistical methods seldom work When to use Simulation?  - A complete mathematical formulation of the problem does not exist or analytical methods of solving the mathematical model does not exist - When analytical methods exist, but solution procedures are very complex - The physical system cannot be experimented upon conveniently or at reasonable costs, or there is need for reproducible experimentation Process of Simulation Define problem → introduce important variables → construct simulation model → specify values of variables to be tested → conduct the simulation → examine the results → select best course of action Monte Carlo Simulation - Uncertainty pervades decision making in business, government, and our personal lives - Monte Carlo simulation: used to evaluate the impact of uncertainty on a decision - When systems contain elements that exhibit chance in their behavior the monte carlo method of simulation can be applied - The basis of the Monte carlo simulation is experimentation on the probabilistic elements through random sampling 1. Inventory demand 2. Lead time for inventory 3. Time between machine breakdowns 4. Time between arrivals 5. Service times 6. Time to complete project activities 7. Number of employees absent Monte Carlo Simulation - based on these five steps 1. Establishing a probability distribution for important input variables 2. Building a cumulative probability distribution for each variable in step 1 3. Establishing an interval of random numbers for each variable 4. Generating random numbers 5. Simulating a series of trials Monte Carlo simulation - Probability distribution: represents not only the range of possible values but also the relative likelihood of various outcomes - A simulation model extends the spreadsheet modeling approach by replacing the use of single values for parameters with a probability distribution of possible values - Parameters that are known with a high degree of certainty are called random, or uncertain variables - The values for random variables are randomly generated from the specified probability distributions  - Simulation results help us to make decisions recommendations for the controllable inputs that address not only the average output ut also the variability of the output Verification and Validation - Verifications: the process of determining that the computer procedure that performs the simulation calculations is logically correct - In some cases, an analyst may compare computer results fo a limited number of events with independent hand calculations - In other cases, test may be performed to verify that the random variables are being generated correctly and that the output from the simulation model seems reasonable - The verifications step is not complete initial the user develops a high degree of confidence that the computer procedure is error free - Validations: the process of ensuring that the simulations model provides an accurate representations of a real system - Validations requires an agreement among analysts and managers that the logic and the assumptions used in the design of the simulations model accurately reflect how the real system operates - The first phases of the validation process is done prior to or in conjunction with development of the computer procedure for the simulation process - Validation continues with the analysis reviewing the simulation output to see whether the simulation results closely approximate the performance of the real system - An analyst can also have one or more individuals experience with the operation of the real system review the simulation output to determine whether it is a reasonable approximation of what would be obtained with the real system under similar conditions - Verifications can validations are key steps in any simulation study and are necessary to ensure that decisions and conclusions based on the simulation results are appropriate for the real system 16. Structure of Decisions - A decision maker - who is the manager - An aim that the manager wants to achieve - A number of alternative courses of actions - A decision of choosing the best alternative - After the decision has been mode, events occurring over which the manager has no control - Each combination of an alternative chosen being followed by an event happening, leading to an outcome that has some measurable consequence Types of Decisions-Making Environments - Decisions making under certainty - The decisions maker knows with certainty the consequences of every alternative or decision choice  - Decision making under certainty - The decision maker does not know the probabilities of the various outcomes - Decision making under risk - The decisions maker knows the probabilities of the various outcomes The Six Steps in Decision Making 1. Clearly define the problem at hand 2. List the possible alternatives 3. Identify the possible outcomes or states of nature 4. List the payoff of each combination of alternatives and outcomes 5. Select one of the mathematical decision theory models 6. Apply the model and make your decision Decision Making Under Uncertainty - Criteria for making decision under uncertainty 1. Maximax (optimistic) 2. Maximin (conservative) 3. Minimax Regret Maximax (optimistic) - The optimistic approach evaluates each decision alternative in terms of the bst playoff that can occur - For the PDC maximization problem, the optimistic approach leads to choosing the alternative corresponding to the largest profit value - For minimization problem this approach would lead to choosing the alternative with the smallest payoff among those belonging to the most desirable state of nature Maxmin (conservative) - The conservative approach evaluates each decision alternative in terms of the worst payoff that can occur - For the PDC maximization problem, the conservative approach leads to choosing the alternative corresponding to the largest profit value among those belongings to the least desirable state of nature - For minimization problems this approach would lead to choosing the alternative with the smallest payoff Minimax Regret - We define regret as the difference between the payoff associated with a given decision alternative (di) and the payoff associated with the decision that would have yielded the most desirable payoff for a given state of nature (sj). - Regret is often referred to as opportunity loss that is, how much potential payoff one would forgo by selecting a particular decision alternative give that a specific state of nature will occur - Formally we write regret as Rij = |Vj - Vij|  - Where Rij = the reget associated with di and sj Vj = the best payoff associated with sj Vij = the payoff corresponding to di and sj Decision making under risk - When there are several possible states are known - Most popular method - choose the alternative with the highest expected value (EV) - Decision trees - Any problem that can be presented in a decision table can be graphically represented in a decision tree - Most beneficial when a sequence of decision must be made - All decisions tree constrain decision points/nodes and state-of nature points/nodes - At decision nodes one of several alternatives may be chosen - At state of nature nodes one state of nature will occur Five Steps of Decision Tree Analysis 1. Define the problem 2. Structure or draw the decisions trees 3. Assign probabilities to the states of nature 4. Estimate payoff for each possible combination of alternatives and states of nature 5. Solve the problem by computing expected monetary values (EMVs) for each state of nature Risk Analysis for the PDC project  - Risk analysis helps recognize the difference between the expected value of a decision alternative and the payoff that may actually occur - The risk profile for a decision alternative shows the possible payoffs along with their associated probabilities Sensitivity Analysis - Sensitivity analysis can be used to determine how changes in the following inputs affect the recommendation decision alternative - Probabilities for the state of nature - Payoff values - Two possible scenarios - If a small change in the value of one of the inputs causes a change in the recommended decision alternative extra effort and care should be taken in estimating the input value - If a modest ot large change in the value of one of the inputs does not cause a change in the recommended decision alternative the solution to the decision analysis problem is not sensitive to that particular input