Operations Research · Unit 8
Decision Theory and Inventory Management
Exam-focused notes for Decision Theory and Inventory Management (Operations Research, ORS255): what the TU syllabus asks and how it has actually been tested, with 8 solved past questions from this unit.
What this unit covers
- Decision making under uncertainty
- Payoff tables and probability distributions
- Expected Monetary Value (EMV) criteria
- Marginal analysis approach
- Optimal stock determination
- Demand probability distributions
- Cost-benefit analysis in decisions
Marginal analysis approach
Question
A small cafe sells freshly made vegetable sandwiches each day. Unsold sandwiches cannot be stored overnight and thus become worthless at the end of the day. Following is the distribution of the daily demand for sandwiches observed over 100 days.
| Daily demand | 220 | 230 | 240 | 250 | 260 |
|---|---|---|---|---|---|
| No. of days | 5 | 20 | 30 | 35 | 10 |
(a) Find the optimal quantity that will maximize the expected profit.
(b) Find the expected profit with perfect information (EPPI).
(c) Find the expected value of perfect information (EVPI).
[10]
Daily Demand 220 230 240 250 260 ------------------ No. of Days 5 20 30 35 10 Probability 0.05 0.20 0.30 0.35 0.10 Total days = 100, so probability = frequency/100. Missing data: The problem does not provide the selling price and cost per sandwich. These ar...
Full solved answer →Cloud Storage Pricing and Demand Analysis
A cloud services provider buys data storage at Rs. 20 per GB and sells it to clients at Rs. 25 per GB. Any unsold storage capacity is wasted. The daily demand for storage has the following probability distribution. If each day's demand is independent of the previous day, using the marginal analysis approach calculate the required measures.
| Demand (GB) | 46 | 48 | 50 | 52 | 54 | 56 | 58 | 60 | 62 | 64 |
|---|---|---|---|---|---|---|---|---|---|---|
| Probability | 0.01 | 0.03 | 0.06 | 0.10 | 0.20 | 0.25 | 0.15 | 0.10 | 0.05 | 0.05 |
(a) Calculate the maximum expected profit.
(b) Find the expected profit with perfect information (EPPI).
(c) Compute the expected value of perfect information (EVPI).
(d) What will be the maximum amount the cloud provider would be willing to pay for perfect and reliable information?
[10]
- Cost price (CP): Rs. 20 per GB - Selling price (SP): Rs. 25 per GB - Marginal Profit (MP) per GB sold = $25 - 20 = 5$ - Marginal Loss (ML) per GB unsold = $20$ (cost wasted) Demand distribution: Demand 46 48 50 52 54 56 58 60 62 64 -----------------------...
Full solved answer →Write short notes on: (a) Marginal analysis approach in decision making. Write short notes on: (b) Modified distribution (MODI) method. [2.5+2.5]
Definition: Marginal analysis is a decision-making technique that examines the additional (incremental) benefits and costs resulting from a small change in an activity or decision variable. Key Principles: 1. Marginal Concept: Focuses on the change in total...
Full solved answer →Milk Ordering Problem - Marginal Analysis
- Purchase (cost) price: Rs. 20 per litre - Selling price: Rs. 25 per litre - Marginal Profit (per litre sold): $MP = 25 - 20 = 5$ - Marginal Loss (per litre unsold, thrown away): $ML = 20$ - Demand distribution: Demand 46 48 50 52 54 56 58 60 62 64 -------...
Full solved answer →Write short notes on: a) Marginal Analysis Approach in decision making. Write short notes on: b) Arithmetic Method in game theory. [2.5+2.5]
Definition: Marginal analysis is a decision-making technique that examines the incremental changes in costs and benefits resulting from a specific decision or action, rather than analyzing total values. Key Concepts: - Marginal Cost (MC): The additional cos...
Full solved answer →Optimal Number of Magazines Using Marginal Analysis
A newspaper boy estimates the probability of the demand for a new magazine is as follows: A copy of the magazine cost of Rs. 8 can be sold for Rs. 10. Based on this information, find optimal number of the newspaper that would maximize the profit by using marginal analysis approach.
| Demand | 11 | 12 | 13 | 14 | 15 |
|---|---|---|---|---|---|
| Probability | 0.10 | 0.15 | 0.30 | 0.25 | 0.20 |
[5]
- Cost per magazine (C) = Rs. 8 - Selling price per magazine (S) = Rs. 10 - Marginal Profit (MP) = Selling price - Cost = $10 - 8 = $ Rs. 2 (profit per unit if sold) - Marginal Loss (ML) = Cost per unit unsold = Rs. 8 (loss per unit if not sold) Demand dist...
Full solved answer →Expected Monetary Value
Milk Salesman Decision Problem
A milk salesman estimates the probability of the demand for a litre of milk as follows: He purchases a litre of milk @ Rs. 60 and sells it @ Rs. 70. Assuming that the unsold milk has no scrap value, find:
(a) Find optimum quantity that would obtain Max. EMV. (b) Find the minimum value of EOL. (c) What is the value of expected profit with perfect information (EPPI)?
| Demand | 11 | 12 | 13 | 14 | 15 |
|---|---|---|---|---|---|
| Probability | 0.10 | 0.15 | 0.30 | 0.25 | 0.20 |
[10]
- Purchase cost = Rs. 60 per litre - Selling price = Rs. 70 per litre - Profit per litre sold = $70 - 60 = $ Rs. 10 - Loss per litre unsold (no scrap) = Rs. 60 - Demand distribution: Demand 11 12 13 14 15 -------------------------------------- Prob 0.10 0.1...
Full solved answer →Milk Salesman Decision Problem
A milk salesman estimates the probability of the demand for a litre of milk as follows: He purchases a litre of milk @ Rs. 60 and sells it @ Rs. 70. Prepare payoff table and find optimum stock by using EMV criteria assuming the unsold milk has no scrap value.
| Demand | 11 | 12 | 13 | 14 | 15 |
|---|---|---|---|---|---|
| Probability | 0.10 | 0.15 | 0.30 | 0.25 | 0.20 |
[5]
- Purchase cost: Rs. 60 per litre - Selling price: Rs. 70 per litre - Profit per litre sold = $70 - 60 = 10$ - Loss per litre unsold (no scrap) = Rs. 60 - Demand and probabilities: Demand 11 12 13 14 15 ------------------ Prob 0.10 0.15 0.30 0.25 0.20 - If ...
Full solved answer →Make Unit 8 stick
Practice ORS255 with flashcards & quizzes