ARE 155 FINAL (Theory Questions)

Provide an example of a manufacturing or employee staffing application discussed in the class(based on chapter 3). State the business problem; name the decision variables; define the objective function; explain sources of the linear constraints in this application.

Example: Labor Planning Problem (Hong Kong Bank of Commerce and Industry) Decision variables: F= number of full-time tellers to use (all starting at 9am) P1= number of part-timers to use, starting at 9am (leaving at 1pm) P2= number of part-timers to use, starting at 10am (leaving at 2pm) P3= number of part-timers to use, starting at 11am (leaving at 3pm) P4= number of part-timers to use, starting at noon (leaving at 4pm) P5= number of part-timers to use, starting at 1pm (leaving at 5pm) Objective function: minimize total daily personnel cost = $90F + $28 (P1+P2+P3+P4+P5) Constraints: F+P1 >= 10 (9am - 10am requirement) F+P1+P2 >= 12 (10am - 11am requirement) 0.5F+P1+P2+P3+P4 >= 14 (11am - 12 noon requirement) 0.5F+P1+P2+P3+P4+P5 >=16 (12noon-1pm requirement) F+P2+P3+P4+P5 >=18 (1pm - 2pm requirement) F+P3+P4+P5 >= 17 (2pm-3pm requirement) F+P4+P5>= 15 (3pm-4pm requirement) F+P5>=10 (4pm-5pm requirement)

Provide an example of a marketing or transportation application discussed in the class (based on chapter 3). State the business problem; name the decision variables; define the objective function; explain sources of the linear constraints in this application.

Example: Media Selection Problem (Win Big Gambling Club) - marketing Decision variables: T=number of 1-minute TELEVISION SPOTS taken each week N=number of full-page daily NEWSPAPER ADS taken each week P =number of 30-second PRIME TIME RADIO SPOTS taken each week A=number of 1-minute AFTERNOON RADIO SPOTS taken each week (THE NEW PLAYERS ARISE) Objective function: maximize audience coverage = 5,000T+8,500N+2,400P+2,800A Constraints: T<=12 (maximum TV spots/week) N<=15 (maximum newspaper ads/week) P<=25(maximum prime time radio spots/week) A<=40 (maximum afternoon radio spots/week) 800T+400N+500P+600A <= 8000 (weekly advertising budget) P+A >= 5 (minimum radio spots contracted) 200P+300a <= 1,800 (maximum dollars spent on radio) T,N,P,A >= 0 (nonegativity)

Provide an example of a finance or blending application discussed in the class (based on chapter 3). State the business problem; name the decision variables; define the objective function; explain sources of the linear constraints in this application.

Example: Portfolio Selection Problem (International City Trust) Decision variables: T= dollars invested in trade credit B = dollars invested in corporate bonds G = dollars invested in gold stocks P = dollars invested in platinum stocks M= dollars invested in mortgage securities C= dollars invested in construction loans (TEDDY BEAR GETS PRETTY MAD CUTE) Objective function: maximize dollars of interest earned = 0.07T + 0.10B + 0.19G + 0.12P + 0.08M + 0.14C Constraints: T+B+G+P+M+C <= 5,000,000 T<=0.25 (T+B+G+P+M+C) B<=0.25 (T+B+G+M+C) G<=0.25 (T+B+G+M+C) P<=0.25 (T+B+G+M+C) M<=0.25 (T+B+G+M+C) C<=0.25 (T+B+G+M+C)

Provide an example of a multi-period application discussed in the class (based on chapter3). State the business problem; name the decision variables; define the objective function;explain sources of the linear constraints in this application.

Example: Production Scheduling Problem (Greenberg Motors) Decision variables: Pat = number of model GM3A motors produced in month t Pbt = number of model GM3B motors produced in month t Iat = level of on-hand inventory for GM3A motors at end of month t Ibt = level of on-hand inventory for GM3B motors at end of month t Objective function: minimize total costs = 10Pa1 + 11Pa2+12Pa4 + 10Pb1+11Pb2+12b3+13B4 +13Ia1+14la2+15la3+16la4 +12lb1+13lb2+14lb3+15lb4

What is the difference between the expected utility decision model and expected monetary value decision model? What characteristic of a decision maker does the shape of the utility function capture? Define a certainty equivalent for a lottery. Define the constant absolute risk aversion utility function.

Expected utility in decision theory, the expected value of an agent action to an agent, calculated by multiplying the value to the agent of each possible outcome of the action by the probability of that outcome occurring and then summing those numbers. Expected monetary value (EMV) is a ballpark figure that shows how much money a plaintiff can reasonably expect in meditation. Think of it as an average of the best and the worst case scenarios. It accounts not only for the dollar figure assigned to each outcome but also for the likelihood of that outcome occurring. Constant absolute risk aversion or CARA utility is a class of utility functions. Also called exponential utility, has the form, for some positive constant 'a'. Under this specification, the elasticity of marginal utility is equal to -ac, and the instantaneous elasticity of substitution is equal to 1/ac.

What are the main three steps in budgeting process? Explain difference between budget using earliest latest starting times. How can one compute cost overrun in any given moment of project implementation?

Answer a. In simple terms, budgeting is a process or plan to determine how to use your money, it could be for business or personal purpose. It is a process or system to plan for effective use of the money on projects or any process. It is not about spending little but spending effectively to get the optimum result of the project There are three main steps in the budgeting process that are as per below, a. Planning and Centralizing of Budget Process: Planning is one of the main steps of budgeting and it happens at the starting of the project. The project manager would calculate the total budget of the project by historical costs, getting fresh quotations, allocation by the management, etc. The budget should be included the overall expenditure for raw materials, equipment, workforce compensation, reserve analysis, and cost of quality in the budget. Budget planning is basically the allocation of money on different aspects to get the optimum results from the project. It should not be less or high as per the project structure. The budget process should be centralized that means the project manager will be the sole responsibility to make the base plan for the budget and will get feedback and suggestions from the other team members such as purchase authority, technical team, supply chain team to add all type of costs in the budget. b. Mastering in Spreadsheets or any budgeting tools: Today their so many online or offline tools that can help the project manager to calculate and analysis of the budget before implementation. It is very important to analyze the budget and allocation of funds to ensure the best quality outcomes at the lowest cost. This step of budgeting is basically analyzing and brainstorming of the budget funds. The project manager will seek help from all his core member team if they think there are some changes are required in the budgeting. Various spreadsheet tools and other online tools are available to make the budget plan that shows the proper results or variations as per the historical data. In the end, the project manager will get approval from his senior authority to get the funds to be spent in the project. c. Tracking and Focus on Budget: Tracking post-implementation of the budget is important and essential for the project manager as it will help in controlling unexpected costs and ensure that the project is not going beyond the expected budget. The project manager should track each and every cost in the budget to make sure that they are spending as per the expected budget and they are not adding any additional costs that were not the part of the initial budget planning. The project manager should be focused on the budget at each step of the project post-implementation and ensure the project is finishing within the planned budget with the projected objective. Answer b. This is the responsibility of the project manager to manage and control the project like the client and organizational requirement to get the optimum results or outcomes from the project. There are differences when constructing a budget in terms of the earliest and latest start time. The earliest start time refers to the earliest time that activity in a project can be started and assuming that all the activities prior to this activity have already been started. In this type of schedule, all the activities would be started earliest possible of time as soon as possible. The latest start time refers to the lates time the activity in the project can be started but not lengthening the project time duration. In this project schedule, each activity would be delayed in starting as long as possible but the project would be finished in the minimum possible time. Answer c. Cost overrun is basically cost increase as compared to the planned budget. There are various reasons expected or unexpected that result in exceeding our planned budget. A project will not always run as per our planned scheduled or budget, due to unforeseen schedules, unexpected costs, the cost of the budget at any point in time could increase that lea the project over budget. So it is the duty and responsibility of the project manager to control the unexpected costs by negotiating, using his expertise and computing costs at any given point of time after project implementation. Cost overrun is very common in technological, construction, and infrastructure building projects. Cost overrun is basically calculated on the daily burn rate in the project. But there is not a concept of daily loss in the project management. The reason behind it is most of the projects cost centric but not profit central. Cost is the main factor to be successful of any project. We can just calculate the expenses spending on various activities and need to analyze if we are on track as per the budget plan. We need to analyze the Earned value and actual cost and compare it with the planned value as per the projected budgeting planning. Planned Value refers to the approved value of the work to be finished at a given period of time, that could be tracked from the project planning document. i. Planned value = (% of planned work completed as per the schedule)* BAC where BAC = Budget at completing of the project or total budget of the project. ii. Earned value refers to the work actually completed at a given period of time. Earned value = % of completed work * BAC iii. The actual cost is the total cost spend on the project at a given period of time. This will be calculated from the money spent on the project to date. This can be calculated from the invoices and tools to track the expenses. These three elements can be used to calculate the cost overrun at any given point of time in the project.

Define covering problem, its objective function, decision variables and constraints. DefineMixed integer model and provide a business case application of the model. Provide corresponding objective function, decision variables and constraints

Covering problems are linear programming problem Linear programming is a mathematical techique, in which a linear function is either maximised or minmised and which is subjects to set of constraints with an objective function It is mainly useful for quantitative decision in business planning in industrial decisions making process etc i. Graphical method Graphical method is used for Linear programming objective function with two constraints. For using graphical method first set a LP problem Then construct a graph and plot the constraint line Find the value of on each point of constraint lines Then identify the feasible solution region. Then find the optimum point ii. Simplex method We use simplex method to solving linear programming method which has more than two variables. By using simplex method, we can approach linear programming by hand using slack variables, tableaus and pivot variables as way to find a solution to optimization problem Excel solver Under this method, we can solve linear programming problem with excel. It consists separate columns for values and coefficients

What is the difference between decision under uncertainty and risk? Define expected monetary value decision model. How to transform payoffs to regrets? What is the value with perfect information? Why is it different from the expected monetary value ? What is the value with survey information?

Difference between decision under uncertainty and risk: Decision taken under risk is calculated decision as in risk possibility of a future outcome is predictable while uncertainty is uncontrolled and hence no prior decision can be taken in case of uncertainty. Risk is calculative but uncertainty is not. With proper planning and measures, it can be controlled as it is the potential outcomes but uncertainty is beyond control due to its unpredictable nature. A decision under uncertainty occurs when there are many unknowns and no possibility of knowing what could happen in the future to change the outcome of a decision. Define the expected monetary value decision model: The expected monetary value decision model is defined as how much money one can expect to make from a certain decision. This model is based on probability and there is not any quick and easy formula for it.EMV is part of risk management and is generally used to perform Quantitative Risks Analysis process. The expected monetary value decision model involves mathematical calculations. How to transform payoffs to regrets? The maximum regret criteria are being used to transform payoff to regrets.It examines the opportunity cost or loss resulting when a particular situation occurs and the payoff of the selected alternatives is smaller than the payoff that could have been attained with a particular situation. The regret corresponding to a particular payoff is defined as Ras = Xs(max) - Xas where Xs (max) is the minimum payoff attainable under the state. What is the value with perfect information? The value with perfect information is said to be the amount of profit bygone because of uncertain conditions that affect the selection of a path of action. Given a piece of perfect information, the decision-making body is aware of which particular state of nature will be in effect, hence an optimal course of action is chosen but due to uncertainty deviation strikes. Why is it different from the expected monetary value? The expected monetary value is the amount of money one can expect to make from a certain decision. It differs from expected monetary value due to uncertainty. What is the value of the survey information? Survey information helps to tap into what customer is thinking and provide them with that so that maximum profit can be ascertained. It is a tool for collecting information and in order to improve customer satisfaction.

Explain how to represent a project as a network. What is earliest and latest start and finish times for a task? Explain the algorithm to compute the times. What is a slack time for an activity? What is a critical path and how is related to the total time requirement for a project?

Explain how to represent a project as a network A project network can be represented using two forms - Activity On Arrow (AOA) and Activity ON Node (AON). When the AOA form is used, the activities i.e. project tasks are the arrows joining the two nodes. In this case, the nodes at the two ends of an activity arrow are termed as 'events'. The AON network is a little more easy and handy to construct because it uses the nodes itself for the activities and the joining arrows are used for the precedence relationships. What are the earliest and latest start and finish times for a task? The earliest start (ES) time is the earliest time a project task that can be started. For a starting activity, it is always zero. For the intermediate and ending activities, it is the maximum of the earliest finish (EF) time of its immediate predecessors. The earliest finish time of any activity will be its earliest start plus the duration. The latest start (LS) time is the upper limit of the time a task can be started without delaying the project duration. It can be computed by subtracting the duration from the latest finish (LF) time. For any activity except the ending ones, the latest finish time is the minimum of the latest start times of its immediate successors. The ending activities' LF, is the maximum of all activities' EF and gives the overall duration of the project as well. The relationships that are described above can be written in the equation form as follows: -ES of the starting activities = 0 -ES of all other activities = Max. (EF of their immediate predecessors) -EF of an activity = Its ES + Its duration -LF of ending activities = Max (All EFs) -LF of all other activities = Min. (LS of their immediate successors) -LS of an activity = Its LF - Its duration What is slack time for an activity? The slack time is the time an activity can be delayed without delaying the entire project. The total slack of an activity can be computed by subtracting the EF from its LF (or, ES from its LS). What is a critical path and how is it related to the total time required for a project? A critical path is the longest path on the project. So, the duration of the critical path(s) is the same as that of the entire project. For the same reason, the activities on the critical path will have zero slack. So, these activities cannot be delayed without delaying the project. If a critical activity is delayed, the project will also be delayed by an equal amount.

What problem does goal programming approach solves? Explain what is a deviation from the goal. Why would one use weighted goals? Provide one example of a business case application.Discuss goals, weights, objective function, decision variables and constraints.

GOAL PROGRAMMING is a branch of multiobjective optimization which in turn is a branch of mcda it can be thought of as an extension or generalisation of linear programming to handle multiple normally conflicting objective measure .each of the measure is given a goal or target value to be achieved.deviations are measured from these goal bothe above and below the target .unwanted deviation from the this set of target values are then minimised in an achievement function.this can be a vector or a weighted sum dependent on the goal programming variant used . as setisfaction of the target is deemed to setisfy the decision maker and underlying satisfaction philosophy is assumed goal programming is used to perform three type of analysis. GOAL PROGRAMMING WAS FIRST USED BY CHARNES Cooper and ferguson in 1955 although the actual name first appeared in a 1961 text by charnes and cooper seminal work by lee ignizio and cavalier and romero followed schniederjans gives in a bibliography of a large number of pre 1995 articles relating to goal programming and jones and tamiz givan an annotated bibligraphy of the period 1990-2000 a recent textbook by jones and tamiz gives a comprehensive overview of the state of the art in goal programming. VARIANTS the initial goal programming formulations ordered the unwanted deviations into a number of priority levels with the minimisation of a deviation higher priority level being infinitely more importent then any deviation in lower priority levels this is known as lexicographic or pre emptive goal programming ignizio gives an algorithm showing how a lexicographic goal programme can be solved as a series of linear programmes lexicographic goal programming is used when exists a clear priority ordering amongst the goals to be achieved. if the decision market is more interested in direct comparisons of the objective then weight or non pre emptive goal programming should be used in this case all the unwanted deviations are multiplied by weight reflecting their relative importance and added together as a single sum to from the achievement function deviation measured in different units cannot be summed directly due to the phenomenon of incommensurability.

Define the transshipment model. Define supply, demand, and transshipment nodes. What are the decision variables, the objective function and constraints? What is the difference between the balanced and unbalanced model?

In a TRANSSHIPMENT model, a point can have shipments that both arrive and leave. - example: a warehouse where shipments arrive from factories and leave for retail outlets Balanced model: a model in which total demand (at all destinations) is equal to total supply (at all origins) Unbalanced model: a situation in which total demand is NOT equal to total supply.

Explain difference between linear and non-linear programs (NLP)? What are the difficulties involved in a solution of a NLP? Give an economic example of NLP. What are the objective function, decisions vars and constraints in the example.

Linear Programming is a method which to used to achieve the best outcome in a mathematical model whose requirements have a linear relationship between them. It aims at finding the best possible solution of a problem by using linear constraints. It is a bit easy to solve because of the linearity. Non-linear Programming is a method of solving an optimization problem where either the objective function or constraints or both are non-linear in nature. It aims at finding the best possible solution of a problem by using non-linear constraints. Some of the non linear programmings are a complex to solve. DIFFICULTIES INVOLVED IN SOLUTION OF NLP 1. Non linear programming is quite complex and hard to solve because unlike linear programming, there is no single algorithm that can efficiently solve every non-linear programming problem, therefore, researchers need to apply the stochastic search algorithm to find the nearest optimal solution of a general NLP. 2. It is difficult to distinguish between a local optimum and a global optimum. 3. There can exist multiple feasible regions in a non-linear programming problem. 4. Unlike linear programming, optima are not just restricted to extreme points in non-linear programming. 5. It can have multiple starting points and different starting point may lead to a different solution. 6. Different solvers and different algorithms mat provide a different solution or outcome to a same formulation. EXAMPLE: Maximize: Z = 6x + 35y^3 + 14x^2 - 29 subject to: x^3 + 5y^2 = 25 x - 2y = 31 Here, the objective function is :​ Maximize: Z = 6x+ 35y^3 + 14x^2 - 29 Decision variables are x and y. Constraints are: x^3 + 5y^2 = 25 x-2y = 31

Define a linear programming model (or problem) and its components. Discuss which 3 properties a planning problem needs to meet to be modeled as a LP.

Linear programming (LP) can be defined as a problem of maximizing or minimizing a linear function which is having a linear constraints. Components: 1. Decision variables 2. Constraints 3. Data 4. Objective Functions Three properties must be met: 1. The decision variables are continuous 2. The objective function is a linear function 3. The constraints should also be a linear function

Discuss advantage of using integer linear programming when compared to rounding off solutions of LP. How one can find optimum of an integer program without a solver? Define and provide business case examples of general and binary integer variables.

Linear programming aids in the most efficient utilisation of productive resources. It also shows how a decision-maker can successfully use his productive elements by selecting and distributing (allocating) them. Techniques like linear programming help to improve the quality of decisions. The user's decision-making style becomes more objective and less subjective as a result of this technique. Because there may be other constraints working outside the problem that must be taken into account, linear programming approaches provide plausible and practical solutions. The fact that we can create a large number of units does not imply that they can be sold. As a result, for the sake of convenience to the decision-maker, necessary modifications to its mathematical answer are required The most notable benefit of this technique is that it highlights bottlenecks in production processes. When a bottleneck occurs, for example, some machines are unable to meet demand while others sit idle for a period of time. Linear programming can also be used to re-evaluate a fundamental strategy in response to new circumstances. If conditions change while the plan is being implemented in part, they can be determined so that the remainder of the plan can be adjusted for the optimal results. There is no guarantee that we will get integer-valued solutions while solving an LP model. A non-integer valued solution, for example, will be worthless in determining how many workers and machines are necessary to execute a specific job. The solution will not be optimal if it is rounded off to the nearest integer. In such instances, integer programming is utilised to assure that the decision variables have integer values.

Define Maximal-flow and shortest-path models. What are the decision variables, the objective function and constraints for each of them? Provide a business case for each of the two models.

Maximal-flow model finds the maximum flow that can occur from the origin to the destination through this network. This model can be used to determine, the maximum number of vehicles that can go through a network of roads from one location to another. Shortest-path model finds the shortest path or route through this network from the origin to the destination.

What is PERT and how it is used? What is the main modeling assumption about a random variable that represents an activity time ? Which parameters one needs to provide to determine expected time and variance for an activity? Explain how to compute the expected completion time for the entire project and the variance for the total time. How to estimate probability of project completion before a certain deadline.

PERT is 1. Stands for Program (or Project) Evaluation and Review Technique 2. Project Management planning tool 3. Used for calculation of time to finish the project 4. Some charts used in it is used to schedule and plan for the task. (Gantt Chart) The main modelling assumption about a random variable that represents an activity time is Every activity's completion time is a random variable with a special distribution. This special distribution is called PERT-beta. And taking this as a base, the expected completion time and its variance for each project can be determined by the help of formulas. The parameters one needs to provide to determine 1. expected time Σ = Expected Time or Expected Duration Σ (sigma) = [O+ 4M +P] / 6 2. Variance for an activity Variance (σ²) = ((P-O)/6)^2 Where O = Optimistic time P = Pessimistic time M = Most Likely time We have been given with the activities and their predecessors as well as its three times O = Optimistic time, P = Pessimistic time and M = Most Likely time. It is also denoted as to , tp, and tm respectively. For the calculation of the expected completion time for the entire project and the variance for the total time as well as estimation of the probability of project completion before a certain deadline, we take an example. The problem is given with the Activities, its Predecessors, three times -Optimistic time, Pessimistic time and Most Likely time. Now we need to calculate the expected completion time of the project and then the variance of the total time. Estimate the probability of project completion before a certain deadline i.e. less than 40 days in this case.

What is project crashing ? What are the 4 steps involved in the project crashing? Explain.What is the LP formulation of the project crashing problem? What are the decision variables, constraints and the objective function of the LP formulation of crashing problem?

Project crashing is the method for shortening the project duration by reducing the time of one or more critical activities to less than their normal time. 4 steps involved: 1. Crashing expending: reducing project time by expending additional resources 2. Crash time: an amount of time an activity is reduced 3. Crash cost: cost of reducing activity time 4. Goal: reduce project duration at minimum cost LP formulation of project crashing problem: 1. We have to know the project network with activity time, which can be achieved from PERT and CPM. 2. To what extent an activity can be crashed. 3. The crash cost associated with per unit of time for all activities (check rest of answers on CHEGG)

Explain what is sensitivity analysis of changes in right hand side of the constraints? Pro-vide example of a business case where such analysis is relevant. Explain difference between binding and non-binding constraints in the sensitivity analysis. Define shadow prices for the constraints.

Sensitivity analysis is the analysis of RHS of constraints and is used to find out the amount by which the RHS of a constraint might be changed without affecting the optimal basis of solution. THis provides a range of values under which the solution remains unaffected. There are a number of examples where sensitivity analysis can be used to find this range. An example is a process where profitability of a firm depends on the profits produced by two products that company makes. These products consume different values of electricity and the supply of electricity is a constraint. If the optimum solution is X units of one product and Y units of other, the sensitivity analysis helps he company to identify the range under which the value of available electricity can be changed so that there is no change in the optimum solution. Binding constraints are the one which affect the optimum solution, by even a small change in the constrait value, while the change in non binding constraints don't change the optimal solution over a limit. Shadow price is the rate by which the optimal solution changes with marginal change in the RHS of constraint.

Explain what is sensitivity analysis of changes in objective function coefficients? Provide example of a business case where such analysis is relevant. Explain what are the allowable change limits for OFC. What happens to the optimal solution when these limits are exceded and when they are not exceded.

Sensitivity anlysis of change in objective function coefficient is an exercise to identify the range of variation in the coefficients of objective function under which the optimal basis does not change. An example is a business where there are two manufactured products,a table and a chair. If producing a table yields a profit of 50 and producing chair yields 40 as profit, the objective of maximising the profit will make the objective function as 50X+40Y where X is the number of tabels made while Y is the number of chairs made. If the cost of raw materials for table goes up and the profit needs to be reduced ( to ensure that sales don't decline) he sensitivity analysis helps to identify the range to which the profit be reduced to keep the current combination of X and Y optimal. For example if 30 chairs and 25 tables is the optimal solution, the value of objective function at different alternatives will determine the range upto which these values of X and Y will remain optimal. The change limits upto which the current optimal solution rmains optimal is the allowable limits. If they are not exceeded, the optimal solution will remain the same and current mix ( of X and Y) will remain optimal. If those limits are exceeded. some other combination will be more optimal than this mix.

What is simultaneous change in the constraints? Provide example of a business case where such scenario is relevant. Explain what 100% rule mean? Explain how to analyze impact of a new decision variable. Provide example of a business case where such scenario is relevant.

Simultaneous change in constraint refers to the change in two or more constraints at the same time. Consider the example of the following LP Max 5x + 4y ST 2x + 8y <= 25 7x + 3y <= 30 x,y >= 0 In this problem if the value of 25 is changed to any other value and at the same time value of 30 is also change to any other value then it is called simultaneous change in constraints. In many business cases, we often have limiting resource where we need to maximize benefit (profit). These limiting resources are often labor hours, budget, equipment, etc. In case of a merger/acquisition, there may be simultaneous increase in several resources. This results in simultaneous change in our model. 100% rule allows us to determine if simultaneous change in constraint (or the coefficients of decision variables) will result in overall change in solution. In case of constraints, an LP's feasible region is affected. This means if the sum of fractions of "change/allowable change" for the simultaneous constraints under question results in more than 1 then we know that the overall feasible regions shape will change and thus the optimal points will change as well.

Describe 7 main steps in the scientific decision making. Illustrate the steps using a specific-management problem (for example, choice of inputs for a PC with minimal costs ).

Steps in scientific decision making- 1. Identify the decision- At this step, Business identify and define the problem or question we need to answer. For example- Our company has shortage of PC in our company so we need to make a decision how we purchase PC at minimal cost. 2. Gather relevant information Once you have identified your decision, it's time to gather the information relevant to that choice. Do an internal assessment, seeing where your organization has succeeded and failed in areas related to your decision. Also, seek information from external sources, including studies, market research, and, in some cases, evaluation from paid consultants. For example- I would gather information for Past purchases done by company. Gather information from Our suppliers etc. 3. Identify the alternatives With relevant information now at your fingertips, identify possible solutions to your problem. There is usually more than one option to consider when trying to meet a goal. for example- We either purchase from wholesaler or we can purchase directly from Company like HP, HCL,Lenovo etc. 4. Weigh the evidence Once you have identified multiple alternatives, weigh the evidence for or against said alternatives. At this step, we would see what brand or company is giving the best offer. our decision would be weigh on cost, service, response,quality etc. 5. Choose among alternatives Here is the part of the decision-making process where you, you know, make the decision. for example- we choose HP because this company offer high quality PC at low cost and deliver on time. 6. Take action At this stage, we take action where we make plan of action. for example- we decide to go for HP to purchase PC directly from the company. so we would create purchase request and send to company and initiate the payment on delivery. 7-Evaluate the decision- At this stage, we evaluate and review our decision. For example- The purchased PC are according to our expectation and standard so our decision was good.

Define the task assignment model. How is it related to the transportation model? What are the decision variables, the objective function and constraints. Provide a business case where this model is applicable.

The assignment model seeks to find the optimal one-to-one assignment of people to projects, jobs to machines, and so on. Th objective is to minimize total cost or total time of performing the tasks at hand. An important characteristic of assignment models is that each job or worker can be assigned to at most one machine or project and vice versa. Transportation models deal with distribution of goods from supply points to demand points at minimum cost. Common objective is to minimize costs from destination to destination.

Define feasible set and its corner points. Explain how one can find the combinations of the decision variables corresponding to the corner points. How one can use the corner points to find the optimal solution?

The feasible solution region or the set on the graph is the one which is satisfied by all the constraints. It could be viewed as the intersection of the valid regions of each constraint line as well. Choosing any point in this area would result in a valid solution for our objective function. The corner points are the vertices of the feasible region. Once you have the graph of the system of linear inequalities, then you can look at the graph and easily tell where the corner points are. You may need to solve a system of linear equations to find some of the coordinates of the points in the middle. We solve each of the corner points (or extreme points) to find the objective value that it yields and choose the one that is highest or lowest based on the objective function value.

What are the five steps in decision analysis? Illustrate the steps with a business case. List the three types of decision making environments. Explain the differences between them.

The five steps in decision analysis At the point when decision making, there are numerous means that can be taken; however, when making great decisions there are extremely just five stages that should be thought of. These means are as per the following: ‍ Stage 1: Identify Goal One of the best decision-making techniques is to watch out for your goal. Does this basically mean distinguishing the motivation behind your decision by asking yourself what precisely is the issue that should be illuminated? Furthermore, for what reason does this difficult should be tackled? Making sense of what's generally imperative to you will assist you with making great decisions. At the point when you know the motivation behind why you have settled on a specific decision; it will better serve you in remaining with it, and protecting it. ‍ Stage 2: Gather Information for Weighing Options When making great decisions it is ideal to accumulate important information that is legitimately identified with the issue. Doing this will assist you with bettering comprehend what should be done in tackling the issue, and will likewise assist with creating thoughts for a potential arrangement. When gathering information it is ideal to make a rundown of each conceivable other option; even ones that may at first solid senseless or appear to be ridiculous. Continuously look for the assessments of individuals that you trust or address specialists and experts since it will assist you with coming up with an assortment of arrangements when gauging every one of your alternatives for an ultimate conclusion. You will need to accumulate however many assets as could be allowed so as to settle on the best decision. ‍ Stage 3: Consider the Consequences This progression can be similarly as significant as stage one since it will assist you in deciding how your ultimate conclusion will affect yourself, as well as others, included. In this progression, you will ask yourself what is probably going to be the consequence of your decision. By what method will it influence you now? What's more, in what manner will it influence your future? This is a basic advance since it permits you to audit the advantages and disadvantages of the various alternatives that you recorded in the past advance. It is additionally significant on the grounds that you need to feel great with every one of your choices and the conceivable result of whichever one you pick. ‍ Stage 4: Make Decision Since you have recognized your goal, accumulated all fundamental information, and gauged the outcomes, the time has come to settle on a decision and really execute your official choice. Understanding that this progression can cause a few people a great deal of nervousness is significant in light of the fact that this is the place you need to heed your gut feelings. In spite of the fact that you may in any case be somewhat hesitant about your official choice, you need to consider how this affects you. Ask yourself, does it feel right? What's more, accomplishes this decision work best for you now, and later on? At the point when you answer those inquiries back, you should like the outcome. ‍ Stage 5: Evaluate Decision When you have settled on your official conclusion and placed it vigorously, it is important to assess the decision and the means you have taken to guarantee that it works. This last advance is most likely similarly as significant as stage one, if not increasingly significant on the grounds that it will assist you with furthering build up your decision-making abilities for future issues. This progression is additionally principal since it might expect you to search out new information and roll out certain improvements en route. Keep in mind, this progression requires some tolerance and it can likewise support diligence. Why? Since it might require some investment to see the ultimate result. Perceiving that if the principal decision isn't working, you may need to return to stage two and pick another choice. Example: In the event that a real estate development company is settling on whether to manufacture another strip mall in an area, they may look at a few bits of contribution to help in their decision-production process. These might remember traffic at the proposed area for different days of the week on various occasions, the notoriety of comparable malls in the territory, money related socioeconomics, neighborhood rivalry, and favored shopping propensities for the zone populace. These things can be placed into a decision-analysis program and various recreations are run that help the company settle on a decision about the strip mall. Three types of decision-making environments The decisions are taken in various sorts of environments. The kind of condition likewise impacts the manner in which the decision is made. There are three kinds of environments in which decisions are made. 1. Certainty: In this kind of decision-making condition, there is just one sort of occasion that can occur. It is extremely hard to track down total certainty in a large portion of the business decisions. In any case, in numerous normal sorts of decisions, practically complete certainty can be taken note. These decisions, by and large, are of next to no centrality to the achievement of the business. 2. Uncertainty: In the nature of uncertainty, beyond what one kind of occasion can occur and the decision-producer is totally in dim with respect to the occasion that is probably going to happen. The decision-creator isn't in a position, even to dole out the probabilities of happening of the occasions. Such circumstances for the most part emerge in situations where occurring of the occasion is dictated by outside elements. For instance, interest for the item, moves of contenders, and so forth are the components that include uncertainty. 3. Risk: Under the state of risk, there is more than one possible occasion that can happen. Be that as it may, the decision-creator has satisfactory data to appoint a likelihood to the occurrence or non-occurring of every conceivable occasion. Such data is commonly founded on past understanding. Essentially, every decision in a cutting edge business endeavor depends on the interaction of various elements. New apparatuses of investigation of such decision-making circumstances are being created. These instruments incorporate risk investigation, decision trees, and inclination hypothesis. Present-day information frameworks help in utilizing these strategies for decision making under states of uncertainty and risk. The difference between certainty, risk, and uncertainty In the environment of decision making under certainty, decision-makers know without a doubt (i.e., with certainty) the result for each decision elective. Normally, this implies there is just a single result for every other option. In decision making under uncertainty, decision-makers have no data at about the different results. That is, they don't have the foggiest idea about the probability (or likelihood) that a particular result will happen. In decision making under risk, decision-makers have some information with respect to the likelihood of event of every result. The likelihood could be an exact measure or a gauge. Despite how the probabilities are resolved, in decision making under risk, decision-makers endeavor to recognize the elective that advances their normal result.

Define special situations: unbounded feasible set, infeasibility, alternate solutions, redundant constraints. Discuss what do these situations imply for the manager's planning problem. When do you need to and how do you avoid this situations?

Unbounded feasible set implies that there is a 100% scope of improvement in the objective function. This happens when either the model is mis-specified or the problem is optimized under wrong constraint. There is no MAXIMUM and a optimal feasible solution CANNOT be determined Infeasibility implies that there exists no solution to the problem stated which satisfies all the constraints. An alternate solution is the one which exists when a linear programming problem contains more than one optimal solution. It arises when the slope of the objective function is the same as the slope of the constraint. A redundant constraint CANNOT change the feasible region. All the above situations imply that either the model has been formulated incorrectly or the data collected for the model is not correct. To rectify this, the manager needs to re-gather the data and specify the problem again.

What is the difference between decision under uncertainty and risk? Define maximax, max-imin , criterion of realism, and equally likely criterion. What are the underlying assumptions about the probabilities of the outcome, that correspond to each of these criteria?

While making decisions under risks, we take the potential risks into account. The risks are of known type and thus making decisions is better. However, uncertainties could be good or bad for the project. They are unpredictable and hence making decisions on basis of same is not comfortable and certain. Maximax is a strategy used to select the alternative which maximizes the maximum output or benefits. The assumption is that there are certainties and no uncertainties. While, maximin is a strategy to select the alternate which maximizes the minimum attainable pay-off. The assumption is that there are certainties and no uncertainties. Criterion of realism is a decision rule used to arrive at a median between maximax and maximin. Equally likely criterion is decision rule which enables to find the alternative which enables to achieve the highest output. The assumption of this rule is that equally likely outcomes are applicable to all cases.

Explain what is sensitivity analysis of changes in right hand side of the constraints? Provide example of a business case where such analysis is relevant. Define shadow prices for the constraints. Explain what are the allowable change limits for RHS. What happens to the shadow price when these limits are exceded and when they are not exceeded

sensitivity analysis of changes in right hand side of the constraint. sensitivity analysis is the study of responsiveness or sensitiveness of solutions to the parameter changes. RHS values of constraints in sensitive analysis represents the positive side of an LPP. to be particular it analyses the available resources to the firm like the time, labour, machine time etc. eg:- consider a firm has 200 working hours a week and possible profit is 1000 dollar. if we increase the working our by 30 hours, to 230 hours. the optimal solution changes and the profit may varry to 1030 dollar. so the profit increased by 30 dollar to the change in additional 30 hours changes can be seen when we reduce the working hours too like let the hours be 170hours, then profit also will be reduced to $970. shadow price in above eg, 30 hours change leads to 30 dollar change in profit, that means $1/1 additional hours. this price is termed as shadow price it is the improvement in the value that results from the increase or decrease in the right hand side of the constraint the limit of which the profit can be changed without affecting the optimality of the present solution is termed as the allowable ranges of RHS the shadow price is valid only when the RHS is within the allowble limit. if it exceeds the price may change