ME-703-A Operation Research and Supply Chain - Nov 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. 14 Marks
   A small manufacturer employs 5 skilled men and 10 semi-skilled men and makes an article in two qualities, a deluxe model and an ordinary model. The making of a deluxe model requires 2 hours work by a skilled man and 2 hours work by a semi-skilled man. The ordinary model requires 1 hour work by a skilled man and 3 hours work by a semi-skilled man. By union rules no man can work more than 8 hours per day. The manufacturer's clear profit of the deluxe model is Rs. 10 and of the ordinary model Rs. 8. Formulate the model of the problem.
   How to answer

   • Define decision variables for deluxe and ordinary models
   • Formulate objective function for profit maximization: Max Z = 10x1 + 8x2
   • Formulate skilled and semi-skilled hour constraints with 40 and 80 hours availability
   • Add non-negativity constraints x1, x2 >= 0
2. 14 Marks
   Solve by Simplex method: Maximize $Z = 2x_1 + x_2$ Subject to $x_1 + 2x_2 \le 10$ $x_1 + x_2 \le 6$ $x_1 - x_2 \le 2$ $x_1 - 2x_2 \le 1$ $x_1, x_2 \ge 0$
   How to answer

   • Convert inequalities to standard form with slack variables
   • Construct initial simplex tableau
   • Iterate pivot operations to optimality
   • State optimal values of $x_1, x_2$ and max $Z$
3. 7 Marks
   aCan degeneracy occur in a transportation problem? Justify your answer.
   How to answer

   • Define degeneracy in transportation problem (m+n-1 allocations)
   • Explain when degeneracy occurs at initial and optimal stages
   • Justify with condition and resolution using epsilon
4. 7 Marks
   bFind the initial basic feasible solution to the following transportation problem by North-West corner rule.

   

   How to answer

   • Tabulate cost, supply and demand
   • Apply North-West corner allocations sequentially
   • Compute number of allocations and total cost
   • State initial basic feasible solution
5. 7 Marks
   aExplain what is Bull-whip effect in SCM?
   How to answer

   • Define bullwhip effect and its origin in SCM
   • Explain causes like demand distortion and order batching
   • Describe consequences on inventory and costs
6. 7 Marks
   bDiscuss what is cross docking? What are its disadvantages?
   How to answer

   • Define cross docking concept
   • Explain working with example
   • List disadvantages like coordination need and capital cost
7. 14 Marks
   A company uses 1,200 units per month of an electronic component each costing Rs. 3. Placing each order costs Rs. 60 and the carrying cost is 8% per year of the average inventory.

   1. i)Find EOQ
   2. ii)If the company gets 5% discount on single order, should it accept the discount offer.
   3. iii)Find discount percentage which matches EOQ ordering for a single order.
   How to answer

   • Compute annual demand, ordering and carrying costs and EOQ formula
   • Evaluate total cost with and without 5% discount
   • Decide on discount acceptance and find break-even discount percentage
8. 7 Marks
   aHow competitive advantages can be achieved using MRP?
   How to answer

   • Define MRP and its functions
   • Explain how MRP reduces inventory and lead time
   • Link to competitive advantage with example
9. 7 Marks
   bHow SCM is linked with e-business? Explain.
   How to answer

   • Define SCM and e-business linkage
   • Explain information sharing and integration
   • Give examples of e-procurement and e-logistics
10. 7 Marks
    aDefine a queue and explain the various queue disciplines.
    How to answer

    • Define queue and queuing system elements
    • List disciplines: FCFS, LCFS, SIRO, priority
    • Explain each with example
11. 7 Marks
    bIn a bank, 20 customers on the average, are served by a cashier in an hour. If the service time has exponential distribution. What is the probability that it will take more than 15 minutes to serve a customer.
    How to answer

    • Identify service rate mu = 20 per hour exponential
    • Apply exponential probability P(T > t) = e^{-mu t}
    • Compute for t = 15 minutes = 0.25 hour
12. 7 Marks
    aWhat does a critical path actually signify? In what ways does it differ from any other path.
    How to answer

    • Define critical path and its zero slack property
    • Explain significance for project duration
    • Differentiate from non-critical paths with float
13. 7 Marks
    bPERT calculations yield a project length of 60 weeks with variance of 9. Within how many weeks would you expect the project to be completed with probability of 0.99?
    How to answer

    • Note mean = 60 weeks, variance = 9 so sigma = 3
    • Use normal deviate for 0.99 probability Z ~ 2.33
    • Compute X = mean + Z*sigma