ME-703-A Operation Research & Supply Chain - Dec 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. 7 Marks
   aSolve the following LPP by Simplex method. $Z_{min} = x_1 - 3x_2 + 2x_3$ Subject to, $3x_1 - x_2 + 2x_3 \le 7$ $-2x_1 + 4x_2 \le 12$ $4x_1 + 3x_2 + 8x_3 \le 10$
   How to answer

   • Convert to standard form with slack variables for maximization of -Z
   • Construct initial simplex tableau and identify entering/leaving variables
   • Iterate simplex pivots until optimality condition satisfied
   • Read optimal x1, x2, x3 and Z_min value
2. 7 Marks
   bDetermine an initial basic feasible solution to the following transportation problem by using Vogel's approximation method.

   

   How to answer

   • Compute row and column penalties (Vogel's) from cost matrix
   • Allocate to highest penalty cell with min cost exhausting supply/demand
   • Recalculate penalties after each allocation
   • Obtain IBFS and compute total transportation cost
3. 7 Marks
   aGive the mathematical formulation of an assignment problem. How does it differ form a transportation problem?
   How to answer

   • Define decision variables x_ij and cost c_ij with objective minimize sum
   • State assignment constraints: one job per person and vice versa, x_ij = 0/1
   • Explain square matrix, supply=demand=1 properties
   • Contrast with transportation: general m x n, fractional flows vs 1-to-1 assignment
4. 7 Marks
   bDescribe the flow of materials, money, and information in a typical supply chain with an example.
   How to answer

   • Define supply chain stages from supplier to customer
   • Explain forward material flow and reverse returns
   • Explain reverse money flow and forward information flow
   • Give example e.g. manufacturer-retailer with order, delivery, payment
5. 7 Marks
   aExplain the role of Information Technology (IT) and information sharing in improving supply chain performance.
   How to answer

   • Define IT and information sharing in SCM context
   • Explain visibility, coordination, bullwhip reduction
   • Give technologies: ERP, EDI, RFID, SCM software
   • Link to performance metrics: cost, lead time, service level
6. 7 Marks
   bDescribe the effect of variability from multiple suppliers on supply chain performance.
   How to answer

   • Define supplier variability: lead time, quality, quantity
   • Explain impact on safety stock, stockouts, production disruption
   • Explain cost and reliability effects on chain performance
   • Mention mitigation: dual sourcing, contracts, collaboration
7. 7 Marks
   aA company uses 24000 units of a raw material which costs Rs.12.50 per unit. Placing each order costs Rs.22.50 and the carrying cost is 5.4% per year of the average inventory. Find the economic order quantity and the total inventory cost (including the cost of material).
   How to answer

   • State EOQ formula Q* = sqrt(2DS/H)
   • Compute carrying cost H = 5.4% of Rs.12.50 and annual demand
   • Calculate EOQ quantity and number of orders
   • Compute total cost = material + ordering + carrying cost
8. 7 Marks
   bWhat is ABC analysis in inventory control? Describe it in detail with the help of graph.
   How to answer

   • Define ABC classification based on annual consumption value
   • Explain A-B-C categories with % items vs % value
   • Describe Pareto curve graph with cumulative %
   • Explain control policies for each class
9. 7 Marks
   aWhat is Just-In-Time (JIT) manufacturing? Explain its relationship with Lean Manufacturing principles.
   How to answer

   • Define JIT as pull system producing only on demand
   • Explain waste elimination, small lots, kanban, setup reduction
   • Relate to Lean principles: value, flow, pull, perfection
   • Mention benefits and prerequisites
10. 7 Marks
    bCustomers arrive at a box office window, being managed by a single individual, according to a poisson input process with mean rate of 30 per hour. The time required to serve a customer has an exponential distribution with a mean of 90 seconds. Find the average waiting time of a customer. Also determine the average number of customers in the system and average queue length.
    How to answer

    • Identify M/M/1 model with lambda=30/hr, mu=40/hr from 90 sec
    • Apply Wq = lambda/(mu(mu-lambda)) for waiting time
    • Compute Ls = lambda/(mu-lambda) and Lq
    • Convert to minutes and interpret utilization rho
11. 7 Marks
    a

    Solve the following game graphically.

    Player B

    Player A	$B_1$	$B_2$
    $A_1$	1	-3
    $A_2$	3	5
    $A_3$	-1	6
    $A_4$	4	1
    $A_5$	2	2
    $A_6$	-5	0

    How to answer

    • Check for saddle point and dominance to reduce matrix
    • Plot payoff lines for A strategies vs B mix on graph
    • Identify upper/lower envelope and minimax point
    • Solve 2x2 reduced game for optimal mixes and value
12. 7 Marks
    bWhat is optimal strategy? Discuss rectangular games without saddle points.
    How to answer

    • Define optimal strategy and value of game
    • Define saddle point and minimax-maximin criterion
    • Explain solution of rectangular games without saddle point via mixed strategies
    • Mention dominance, graphical and LP methods
13. 7 Marks
    aThe table gives precedence relationships and the duration of various activities.

    1. i)Draw the PERT network
    2. ii)Identify critical path, considering the schedule project duration is 57 days.

    

    How to answer

    • Compute expected time te = (to+4tm+tp)/6 and variance for each activity
    • Construct PERT network from predecessor-successor table
    • Perform forward/backward pass to find earliest/latest times and slack
    • Identify critical path and compare duration with 57 days schedule
14. 7 Marks
    bExplain the rules of network construction and Fulkerson's rule for numbering the events.
    How to answer

    • State basic rules: single start/end, no loops, activity by one arrow
    • Explain dummy activities and precedence representation
    • Explain Fulkerson's numbering steps forward from start
    • Mention check for dangling and crossing errors
15. 14 Marks
    Write short notes on any two:

    1. a)Meta-heuristics in modern engineering optimization.
    2. b)VED analysis.
    3. c)Supply contracts and revenue sharing models in SCM.
    4. d)Special cases in Linear Programming.
    How to answer

    • Select any two topics with definition and key concepts
    • Explain principles, formulas or models with steps
    • Give example or application in OR/SCM
    • Conclude with advantages/limitations