Decision Modeling Exam Prep
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Simulate the city's weather for 7 days and determine the total days without rain.
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Use random numbers to simulate daily weather outcomes.
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Formulate the motorcycle seat production problem as a GP model.
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Create a goal programming model for production scheduling.
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Calculate the minimum time for the renovation project.
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Determine the minimum duration based on activity sequencing.
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What is queueing theory? Explain the Kendalls Notation. Explain in detail different types of queue disciplines.
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Queueing theory studies waiting lines, and Kendall's Notation classifies queue systems.
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1(b) Solve the model and interpret the results.
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Use simplex method to find optimal solution and interpret.
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2(b)(i) Determine the expected queue size (average number of trains in the queue).
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Use queueing theory formulas to calculate expected queue size.
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2(b)(ii) Find the probability that the queue size exceeds 10.
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Calculate using Poisson distribution for queue size.
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4(b) Determine whether a saddle point exists, find the optimal strategies for both players and the value of the game.
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Analyze the payoff matrix for saddle point and optimal strategies.
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Construct the state-transition matrix that describes the problem at hand.
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The state-transition matrix shows client transitions among advocates based on gains and losses.
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For the network shown below, use the augmenting path algorithm to find the flow pattern giving the maximum flow from the source to the sink.
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Apply the augmenting path algorithm to determine maximum flow in the network.
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5(a) Find the loss or profit for the company for next 5 days. Use random number table for random numbers.
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Calculate total profit/loss based on demand and production.
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5(b) How many units should be ordered to get maximum benefit?
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Determine optimal order quantity using cost-benefit analysis.
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6(a) Draw the network diagram for the project.
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Illustrate the project activities and their precedence relationships.
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6(b) Determine the earliest and latest occurrence times for each event.
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Calculate earliest and latest times using forward and backward pass.
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6(c) Identify the critical path and compute the total project duration.
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Identify critical path and total duration using network analysis.
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6(d) Calculate the total and free floats of activities for each activity.
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Determine float times using project scheduling techniques.
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Use the following sequence of random numbers to simulate the demand for the next 10 days. Also, estimate the daily average demand for the cakes based on the simulated data.
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Simulate demand using random numbers and calculate the average from the results.
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Determine the optimal shipping distribution for the company.
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Minimize shipping costs using linear programming.
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Derive the steady-state probability distribution of the queuing system.
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Use queuing theory to derive the steady-state probabilities.
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1(a) Formulate the goal programming model.
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Define decision variables, constraints, and objective function.
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Construct the arrow diagram for the fast-food restaurant project.
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Draw a diagram representing the project activities and dependencies.
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7(b)(i) Determine the steady-state probabilities of the system.
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Solve for steady-state probabilities using transition matrix.
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Determine the optimum strategy using the Hurwicz principle if α = 0.8.
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Apply the Hurwicz principle to find the optimal decision.
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3(a)(i) Obtain an initial basic feasible solution using Vogel's Approximation Method (VAM).
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Apply VAM to find initial feasible solution.
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3(a)(ii) Test optimality using MODI method with help of basic feasible solution above.
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Use MODI method to check for optimality.
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3(b) Find the maximum flow from source to sink for the network shown in Figure 1 using the Ford-Fulkerson algorithm.
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Apply Ford-Fulkerson algorithm to determine maximum flow.
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Calculate the payoff table for the seller selling books on taxation laws.
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Construct a table showing payoffs for different demand scenarios.
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Calculate the regret table for the seller selling books on taxation laws.
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Create a table showing regrets for different demand scenarios.
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What should Mr. Sethi decide, using the pessimistic criterion, optimistic criterion, equally likely criterion and regret criterion?
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Analyze investment options using decision-making criteria to choose the best strategy.
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Calculate the critical path and expected project completion time.
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Identify the critical path and calculate the total duration.
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7(a) State the Basic Limit Theorem for an aperiodic Markov chain.
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In an aperiodic Markov chain, the state probabilities converge to a steady state.
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7(b)(ii) Compute the expected per day cost of maintenance.
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Calculate expected cost using steady-state probabilities.
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Determine the probability of completing the project in 52 days.
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Calculate the probability using project duration analysis.
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Calculate the average number of patients waiting and getting treatment.
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Determine the average using queuing theory formulas.
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What strategy will the company and labor union adopt?
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Analyze the cost matrix to determine optimal strategies.
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4(a) Explain the maximin and minimax principles.
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Maximin is maximizing the minimum gain, minimax is minimizing the maximum loss.
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Calculate the probability that 4 patients will arrive in the next 2 hours.
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Use Poisson distribution to find the probability.
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4(a) Under what condition does a saddle point exist?
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A saddle point exists when the row minimum equals the column maximum.
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Calculate the EPPI for the seller selling books on taxation laws.
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Calculate the Expected Payoff under Perfect Information.
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Define (a) Reneging (b) Jockeying (c) Balking
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Reneging: leaving the queue; Jockeying: switching queues; Balking: refusing to join the queue.
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What is the utility of using Simulation?
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Simulation helps estimate performance under uncertainty by modeling real-world processes.
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2(a)(i) Define balking.
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Balking occurs when a potential customer decides not to join a queue.
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2(a)(ii) Define reneging.
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Reneging is when a customer leaves the queue before being served.
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2(a)(iii) Define jockeying.
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Jockeying is the act of switching from one queue to another.
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2(a)(iv) Define queue discipline.
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Queue discipline refers to the rules determining the order of service.
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4(a) Define a saddle point in a game.
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A saddle point is where the strategy of both players intersect at optimal value.
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7(a) Define a Markov chain.
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A Markov chain is a stochastic process with memoryless property.
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