Description

Operations Analytics

Dec 2026 Examination

 

Q1 A manufacturing company uses prescriptive analytics to optimize its production schedule for two products, P and Q, each requiring three resources: labor (in hours), raw material (in kg), and machine time (in hours). The company has the following constraints and profit details for an upcoming week:

Resource	Max Availability	Usage per unit of P	Usage per unit of Q
Labor (hours)	300	3	5
Raw Material (kg)	500	8	6
Machine Time (hours)	360	4	2

 

Each unit of P yields a profit of Rs.450 and each unit of Q yields Rs.650. To satisfy market criteria, the total quantity of P must be at least 30% and no more than 70% of the total output (P+Q). Additionally, due to a promotional campaign, every unit of Q after the first 40 sold receives only Rs.500 profit, while the rest retain full profit. Formulate the prescriptive analytic model and compute the optimal number of units for P and Q to maximize total profit, applying all constraints, and state the maximum achievable profit. Clearly show each step and justify all your variable definitions and constraints. (10 Marks)

Ans 1.

Introduction

Deciding how much of each product to make under limited labor, raw material, and machine time is a classic prescriptive analytics problem, but this case adds two real-world twists that make it genuinely interesting. The mix of products must satisfy a market share band rather than being freely chosen, and the profit earned on one product drops after a certain volume is crossed, due to a promotional pricing tier. Formulating this correctly as a linear optimization model, with every constraint and variable clearly justified, turns a vague weekly scheduling question into a defensible production plan with a provably maximum profit.

Concept and Application

Defining the Decision Variables

The two decisions the company controls are how many units of product P and how many units of

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Q2 (A) For the given details, calculate the estimate sales for Year 5 using Holt’s Linear Trend

Method:

Smoothing constant for level: α=0.5

Smoothing constant for trend: β=0.4

Initial level: l1= 100

Initial trend: b1= 20

The Actual sales are: Year 1 : 100 units Year 2: 120 units Year 3: 117 units Year 4: 135 units

Ans 2(A).

Introduction

Sales data showing a clear upward movement needs a forecasting method that tracks both the current level and the pace at which it changes. Holt’s Linear Trend Method does this, updating a level and trend estimate together each period.

Concept and Application

The Level and Trend Update Each Period

 

Q2 (B) A national fashion retailer, similar to Zara, utilizes daily sales data and trend tracking to inform production and replenishment strategies across its stores. Recently, the company faced both overstocking in coastal cities and stockouts in colder regions during a prolonged winter. Its inventory classification currently uses a standard ABC analysis but does not integrate FSN (Fast, Slow, Non-moving) or XYZ (demand variability) methods. Senior management is debating whether to expand classification techniques and refine inventory allocation regionally. Critically evaluate the retailer’s current use of ABC classification versus the adoption of multi-dimensional classification (such as combining ABC, FSN, and XYZ) for inventory optimization. Assess the impact on regional allocation and justify the most effective strategy for balancing stock levels and service quality across diverse locations. (5 Marks)

Ans 2(B).

Introduction

Relying on a single classification lens to manage inventory across very different regions and climates was always going to create blind spots somewhere. Standard ABC analysis tells this fashion retailer which products matter most by value, but it says nothing about how fast a product actually moves or how unpredictable its demand is from one region to another, and the