ME-703-A Operation Research and Supply Chain - Jun 2025 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
   Use simplex method to solve the following LP problem. Maximize $Z = x_1 + x_2 + 3x_3$ Subject to $3x_1 + 2x_2 + x_3 \le 3$ $2x_1 + x_2 + 2x_3 \le 2$ $x_1, x_2 \ge 0$
   How to answer

   • Convert to standard form with slack variables
   • Construct initial simplex tableau
   • Iterate pivot on most negative Zj-Cj till optimality
   • Read optimal $x_1,x_2,x_3$ and max $Z$
2. 4 Marks
   aExplain degeneracy in a transportation problem and how to resolve it?
   How to answer

   • Define degeneracy in transportation: occupied cells < m+n-1
   • Causes and effect on MODI/UV loop
   • Resolution by epsilon allocation to least cost unoccupied cell
   • Maintain independence of allocations
3. 10 Marks
   bConsider the following problem where unit transportation costs are given in Indian Rupees : Destinations J, K, L, M Availability; Factories A: 5, 3, 7, 2 : 40; B: 6, 4, 2, 8 : 70; C: 3, 1, 5, 7 : 50; Requirements: 75, 20, 50, 30 Due to shortage problems, some requirements may not be fulfilled. In such case, unfulfilled requirements may be levied penalties of Rs.2, Rs.5, Rs.3 and Rs.4 for the destinations J, K, L and M respectively. Determine the optimal allocation to minimize the transportation and penalty costs.

   

   How to answer

   • Check total availability 160 vs requirement 175 - unbalanced with shortage
   • Add dummy factory with penalty costs 2,5,3,4 as costs
   • Find initial basic feasible solution e.g. Vogel's method
   • Optimize with MODI/UV to minimize transportation + penalty cost
4. 7 Marks
   aExplain Bull-Whip effect in supply chain management and its uses.
   How to answer

   • Define Bullwhip effect: demand variance amplification upstream
   • Causes: order batching, price fluctuation, rationing, forecast error
   • Effects on inventory and cost
   • Mitigation/uses: information sharing, VMI, coordination
5. 7 Marks
   bDiscuss development of MRP to ERP system and SCM.
   How to answer

   • Origin of MRP for dependent demand
   • Evolution to MRP-II and ERP integration
   • Extension to SCM modules
   • Benefits for planning and coordination
6. 7 Marks
   aExplain the importance of outbound logistics in SCM.
   How to answer

   • Define outbound logistics in SCM
   • Role in distribution, customer service, delivery
   • Cost and lead time impact
   • Examples of warehousing, transportation
7. 7 Marks
   bDiscuss the role of inventory in the logistics supply chain system.
   How to answer

   • Define inventory in logistics
   • Functions: decoupling, safety, cycle stock
   • Trade-off holding vs shortage cost
   • Impact on supply chain efficiency
8. 14 Marks
   A manufacturer has to supply his customer with 600 units of his products per year. Shortages are not allowed and storage cost amounts to 60 paise per unit per year. The set up cost is Rs 80.00. Find- (i) EOQ (ii) The minimum average yearly cost. (iii) The optimum number of orders per year. (iv) The optimum period of supply per optimum order.
   How to answer

   • Apply EOQ formula $Q^*=\sqrt{2DS/H}$ with D=600, H=0.6, S=80
   • Compute minimum average yearly cost = ordering + carrying
   • Compute number of orders N=D/Q*
   • Compute cycle time T=Q*/D in years/months
9. 7 Marks
   aExplain ABC and VED analysis. What are their advantages?
   How to answer

   • Define ABC classification by annual usage value
   • Define VED by criticality: Vital, Essential, Desirable
   • Procedure and examples
   • Advantages for control, cost, service level
10. 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

    • Service rate mu=20/hr, exponential parameter
    • Use $P(T>t)=e^{-\mu t}$ with t=15 min=0.25 hr
    • Compute $e^{-5} \approx 0.0067$
    • Interpret as very low probability
11. 7 Marks
    aA project schedule has the following characteristics. Draw the network diagram and find the critical path. Activity: 1-2, 1-3, 2-4, 3-4, 3-5, 4-5, 4-6, 5-6 Time (days): 6, 5, 10, 3, 4, 6, 2, 9
    How to answer

    • Draw nodes 1 to 6 with given activity durations
    • Perform forward pass for EST and backward pass for LFT
    • Identify zero-slack path as critical path
    • State project duration and critical activities
12. 7 Marks
    bExplain in detail about various phases of project management.
    How to answer

    • List phases: initiation, planning, execution, monitoring, closure
    • Explain objectives of each phase
    • Tools and deliverables per phase
    • Importance for time-cost-quality control
13. 14 Marks
    Write short note on (Any two)

    1. a)PERT
    2. b)Heuristic and Meta-Heuristic Algorithms
    3. c)Network logics
    How to answer

    • Select any two topics from PERT, Heuristic/Meta-Heuristic, Network logics
    • Define and explain key terms with diagram/flow
    • Give applications and advantages
    • Conclude with example