Description
Operations Research
Dec 2026 Examination
Q1 A mid-sized Indian retail chain, RetailMart, has experienced frequent stockouts of popular products and excess inventory of slow-moving items across its 80 stores nationwide. These inefficiencies have led to both customer dissatisfaction and increased warehousing costs. The management recently hired a team of operations research (OR) specialists who implemented a linear programming model to optimize inventory allocation, taking into account regional demand patterns, storage costs, and supplier lead times. However, integrating this new model required significant changes to existing processes and staff retraining. Apply the operations research problem-solving process to illustrate how RetailMart can systematically address its inventory management challenges. In your answer, detail the key steps from problem formulation, model development, implementation, to establishing control, and discuss how each stage ensures improved stock availability, cost reduction, and stakeholder adoption within the organization. (10 Marks)
Ans 1.
Introduction
RetailMart’s stockouts and excess inventory look like two separate problems. They actually share one root cause. Demand is scattered unevenly across 80 stores, and the old allocation process never adjusted for that reality. Operations research offers a structured way to fix this, not through guesswork but through a defined, repeatable process. That process runs from clearly framing the problem, through building and testing a model, to rolling it out and keeping it under control afterward. Each stage protects against a different kind of failure, from solving the wrong problem to losing staff buy-in during rollout. Walking through these stages for RetailMart shows exactly
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Q2 (A) A logistics provider is optimizing deliveries from 4 plants (A, B, C, D: with supplies 140, 210, 170, 180 units respectively) to 5 retail centers (P, Q, R, S, T: with demands 120, 160, 110, 140, 170 units, respectively). The per unit transport costs (in Rs.) are given below. Check if the problem is unbalanced and after introducing an appropriate dummy (if needed) then use the Least Cost Method (LCM), construct an initial basic feasible solution, and compute the minimum total transportation cost. (5 Marks)
Ans 2(A).
Introduction
Four plants must supply five retail centers at the lowest possible cost. Total supply and total demand both equal 700 units, so the problem is balanced. No dummy row or column is needed here. The Least Cost Method builds an initial feasible solution directly from the lowest-cost cells
Q2 (B) An Indian technology company is launching an ambitious multi-phased product development project. The project uses both CPM (Critical Path Method) and PERT (Project Evaluation and Review Technique) for scheduling its R&D, production, and market launch activities. Senior leadership is concerned about resource bottlenecks and project delays due to uncertain task durations and limited human resources. As the project progresses, some activities on the critical path face delays due to unforeseen technical roadblocks, while non-critical activities finish ahead of schedule. The project manager must choose the most appropriate network analysis method to navigate this uncertainty and justify resource reallocation to meet deadlines. Evaluate the effectiveness of CPM and PERT in managing projects with unpredictable activity durations and limited resources, as in the scenario described. Critically assess which method would be most suitable for minimizing delays and justify strategies for improving resource allocation to ensure project success. (5 Marks)
Ans 2(B).
Introduction
This product launch is running on two scheduling tools at once. CPM assumes certainty. PERT assumes uncertainty. The real project is neither fully predictable nor fully random, which is exactly the problem.
Concept and Application
CPM’s Assumptions and Where It Fits Here
CPM assumes activity durations are known with reasonable certainty, which suits well-defined
