Operations Analytics December 2026
Q.1: 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.
Answer:
Introduction:
Prescriptive analytics can be used by the manufacturing company to find out how much of each product to produce in order to ensure that all the available resources are utilized optimally while also ensuring that the profit generated is maximum. In this problem, we have a company that produces two products P and Q. Both the products produced consume labor, raw materials, and machine time. All these resources are available in limited amounts. It is also given that the company wants to maintain a certain product mix where P should form between 30 and 70 percent of the total production. The profit for Q is also different for the first 40 units produced where for the first 40 units the profit per unit is Rs.650 and for every subsequent unit, the profit is only Rs.500. Thus, the problem is not a simple linear programming problem where profit for Q would be constant, rather we have to develop a piecewise function for profit from Q. Thus, the aim is to find out the optimal product mix for the company given these constraints.
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Q.2 (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
Answer:
Introduction:
Holt’s Linear Trend Method is used to forecast future sales under the time series with a changing level plus trend. This technique is appropriate as it considers the most recent actual sales and incorporates their trend. In this problem, the smoothing constants are α = 0.5 for the level and β = 0.4 for the trend, and the initial level and trend are 100 and 20 units, respectively. Using historical sales data from Years 1 to 4, we estimate the level and the trend successively and forecast sales for Year 5.
Q.2 (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.
Answer:
Introduction:
Fashion retail sales management involves dynamic inventory balancing since customer buying trends are highly dependent on the region, season, and current trends. ABC Analysis is an excellent tool to manage inventory based on value, although it fails to account for some products’ high selling frequency and demand predictability. The presented scenario features overstocking in popular coastal regions and stock shortages in cold areas, which is precisely why it is beneficial to adopt a multi-tier approach to inventory management. With the help of the ABC, FSN, and XYZ techniques, the fashion store will manage to reduce overstock, improve regional distribution, ensure availability, and improve customer service.