CE-604-D Operation Research - May 2023 Question Paper

Under each question, How to answer lists the points an answer should cover, outlined by CampusPrep from the syllabus. Check the details against your textbook.

1. 7 Marks
   aExplain the Phases of Operation Research.
   How to answer

   • Define Operation Research and need for phased approach
   • List phases: problem formulation, model construction, solution, validation, implementation
   • Brief explanation of each phase
   • Flow among phases
2. 7 Marks
   bDefine Model. Discuss the steps of modeling.
   How to answer

   • Define model in OR context
   • Types/purpose of models
   • Steps of modeling: define, formulate, solve, validate, implement
   • Example
3. 14 Marks
   Solve the following travelling salesman problem.

   

   How to answer

   • State 6-city symmetric cost matrix with infinities on diagonal
   • Apply assignment / TSP branch and bound to find lower bound
   • Eliminate subtours and obtain feasible tour
   • Report optimal tour length and sequence
4. 7 Marks
   aExplain Economic order quantity model with suitable example.
   How to answer

   • Define EOQ, assumptions of basic model
   • Derive $Q^* = \sqrt{2DS/H}$ and total cost components
   • Explain trade-off ordering vs holding cost with diagram
   • Illustrate with suitable numerical example
5. 7 Marks
   bIn the basic EOQ model, if $D = 6000$ per year, $S = \$150$, and holding cost - $\$15$ per unit per month, Unit cost $\$5$, what is the economic order quantity?
   How to answer

   • Convert holding cost $15 per unit per month to annual $H$
   • Apply $EOQ = \sqrt{2DS/H}$
   • Substitute D=6000, S=150
   • Compute EOQ value and interpret
6. 7 Marks
   aDefine Queue. Explain Queuing systems with neat sketch.
   How to answer

   • Define queue, queueing system components
   • Explain arrival, service, servers, discipline
   • Draw neat sketch of single/multi-server system
   • Give examples
7. 7 Marks
   bA television repairman finds that the time spent on his jobs has exponential distribution with a mean of 30 minutes. If he repairs the sets in the order in which they came in, and if the arrival of sets follows a Poisson distribution with an approximate average rate of 10 per 8-hour day, what is repairman expected idle time each day?
   How to answer

   • Identify M/M/1 with lambda=10 per 8-hr day, mu from 30 min mean
   • Compute traffic intensity rho=lambda/mu
   • Compute idle probability P0=1-rho
   • Compute expected idle time = 8*P0 hours
8. 14 Marks
   The owner of a chain of four grocery stores has purchased six crates of fresh strawberries. The estimated probability distribution of potential sales of the strawberries before spoilage differs among the four stores. The following table gives the estimated total expected profit at each store, when it is allocated various numbers of crates. For administrative reasons, the owner does not wish to split crates between stores. However he is willing to distribute zero crates to any of his stores.

   

   How to answer

   • Formulate as DP resource allocation: 6 crates to 4 stores
   • Use profit table as stage returns
   • Perform forward/backward recursion for optimal allocation
   • Report optimal distribution and maximum total profit
9. 14 Marks
   Write short notes on the following:

   1. a)PERT
   2. b)Pay off matrix
   3. c)Saddle Point
   4. d)Zero Sum Game
   How to answer

   • Define PERT, three-time estimates and expected time
   • Define pay-off matrix with example
   • Define saddle point and optimality condition
   • Define zero-sum game with example
10. 14 Marks
    Draw a network diagram and find the critical path of diagram.

    

    How to answer

    • Construct network from predecessor list A-N
    • Perform forward pass for earliest times
    • Perform backward pass for latest times and floats
    • Identify critical path and project duration
11. 14 Marks
    Write about the following:

    1. a)Stochastic inventory models
    2. b)Minimal spanning tree
    How to answer

    • Define stochastic inventory models, demand uncertainty
    • Explain single/multi-period models, safety stock
    • Define minimal spanning tree, cut property
    • Explain Prim/Kruskal algorithm with example