Operations, Social Initiatives and Process Optimization Short Notes for XAT: Concepts, Formulas, Worked Examples & Practice

Operations, Social Initiatives and Process Optimization short notes for XAT: 2 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

NGO Operations: Final Decision Checklist

Final Decision Checklist

Pinpoint the Objective

Maximize meals, minimize cost, maximize nutrition, or minimize time.

List Hard Constraints

Identify absolute physical, financial, and temporal limits.

Find the Bottleneck

System capacity equals the capacity of the slowest step.

Audit the Resources

Check if donations are complementary and volunteers are allocated by skill.

Beware the 'Free' Trap

Assign hidden costs to all donated or free resources before deciding.

The Scheduling Checklist

Map Dependencies: What must happen before what?

Identify Parallelism: What can happen at the exact same time?

Find the Critical Path: The longest sequence dictates the minimum time.

Check Resource Limits: Are there physical constraints like stoves or chefs?

Recalculate if Needed: If constraints force tasks to be sequential, update total time.

Operations, Social Initiatives and Process Optimization: Solved Questions with Step-by-Step Explanations (2 Problems)

Question 1 · Decision Making (DM) MCQ

In a kitchen scheduling network with multiple paths from start to finish, the critical path is best defined as:

A.
The path with the shortest total duration
B.
The path that uses the fewest resources
C.
The longest sequence of dependent tasks, which determines the minimum completion time
D.
The path with the most parallel activities

Correct Answer:

Step-by-Step Solution

Key idea: this is a definition-recall question about the critical path, recognizable because it directly asks for the definition of 'critical path' in a scheduling network.

Step 1: Recall that in a network of tasks, there are multiple paths from start to finish.

Step 2: The critical path is the longest path (sequence of dependent tasks) through the network.

Step 3: It determines the minimum possible completion time because all other (shorter) paths can finish within this duration.

Step 4: It is not about shortest duration (A), fewest resources (B), or most parallel activities (D).

Answer: The longest sequence of dependent tasks, which determines the minimum completion time.

Question 2 · Decision Making (DM) MCQ

An NGO kitchen has 1 prep station and 1 stove. They receive a donation of exactly 14 kg of potatoes, which must be fully used to make Aloo Curry (AC) or Aloo Tikki (AT).

AC requires 2 kg potatoes, 20 mins prep, 30 mins cook.
AT requires 1 kg potatoes, 30 mins prep, 10 mins cook.

The kitchen must make at least as many AC as AT.

Preparation for a dish must be completely finished before its cooking can begin. There is no time lost in transferring a dish. The stove can only cook one dish at a time, but the prep station can prep the next dish while the stove is cooking.

What is the maximum number of meals they can finish cooking within 220 minutes?

A.
6
B.
7
C.
8
D.
9

Correct Answer:

Step-by-Step Solution

Key idea: This is a bounding and scheduling synthesis question. We must maximize the number of meals subject to a strict ingredient constraint, a ratio constraint, and a makespan constraint where prep and cook overlap.

Step 1: Define variables and constraints.

Let $x$ be AC, $y$ be AT.

Potatoes: $2 x + y = 14$ .

Ratio: $x \geq y$ .

Meals = $x + y$ . Since $y = 14 - 2 x$ , Meals = $14 - x$ . To maximize meals, we must minimize $x$ .

From $x \geq 14 - 2 x ⟹ 3 x \geq 14 ⟹ x \geq 5$ .

So the theoretical minimum for $x$ is 5, giving $y = 4$ and Meals = 9.

Step 2: Check if $x = 5, y = 4$ fits in 220 minutes.

Total prep time = $5 (20) + 4 (30) = 220$ mins.

Total cook time = $5 (30) + 4 (10) = 190$ mins.

Since Prep > Cook, the prep station is the bottleneck. The stove will be idle at the end.

To minimize total time, the stove must start as early as possible. We should prep the item with the shortest cook time first? No, we want the stove to start immediately. The first item takes 30 mins to prep (AT). So the stove starts at 30 mins.

The stove works continuously for 190 mins. Total time = $30 + 190 = 220$ mins.

This fits exactly within the 220-minute limit!

Step 3: Verify other combinations just in case.

If $x = 6, y = 2$ : Meals = 8. Prep = 180, Cook = 200. Cook is bottleneck. Time = Cook + first prep = $200 + 20 = 220$ . Also fits, but gives fewer meals.

Since we want the MAXIMUM meals, 9 is the answer.

Answer: 9

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Operations, Social Initiatives and Process Optimization Short Notes for XAT: Concepts, Formulas, Worked Examples & Practice

Operations, Social Initiatives and Process Optimization short notes for XAT: 2 study cards covering concepts, formulas, shortcuts and exam traps, plus solved

A question from this chapter

Question 1

In a kitchen scheduling network with multiple paths from start to finish, the critical path is best defined as:

Question 2

An NGO kitchen has 1 prep station and 1 stove. They receive a donation of exactly 14 kg of potatoes, which must be fully used to make Aloo Curry (AC) or Aloo Tikki (AT). AC requires 2 kg potatoes, 20 mins prep, 30 mins cook. AT requires 1 kg potatoes, 30 mins prep, 10 mins cook. The kitchen must make at least as many AC as AT. Preparation for a dish must be completely finished before its cooking can begin. There is no time lost in transferring a dish. The stove can only cook one dish at a time, but the prep station can prep the next dish while the stove is cooking. What is the maximum number of meals they can finish cooking within 220 minutes?

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