Risk and Uncertainty – OT Course Notes

Dear John, I would like to ask you about Example 1, Question c, Chapter 10 - Risk and Uncerntainty in OT Course Notes: John has a factory capacity of 1,200 units per month. Units cost him $6 each to make and his normal selling price is $11 each. However, the demand per month is uncertain and is as follows: Demand Probability 400 0.2 500 0.3 700 0.4 900 0.1 He has been approached by a customer who is prepared to contract to a fixed quantity per month at a price of $9 per unit. The customer is prepared to sign a contract to purchase 300, 500, 700 or 800 units per month. The company can vary production levels during the month up to the maximum capacity, but cannot carry forward any unsold units in inventory. (a) Calculate all possible profits that could result (b) Determine for what quantity John should sign the contract, under each of the following criteria: i) expected value ii) maximin iii) maximax iv) minimax regret (c) What is the most that John would be prepared to pay in order to obtain perfect knowledge as to the level of demand? Answer key: (a) Contract size\Demand 400u 500u 700u 900u 300u 2,900 3,400 4,400 5,400 500u 3,500 4,000 5,000 5,000 700u 4,100 4,600 4,600 4,600 800u 4,400 4,400 4,400 4,400 (b) (i) Expected value if contract size = 300 units = (0.2 ×2,900) + (0.3 × 3,400) + (0.4 × 4,400) + (0.1 × 5,400) = $3,900 500 units = (0.2 × 3,500) + (0.3 × 4,000) + (0.5 × 5,000) = $4,400 700 units = (0.2 × 4,100) + (0.8 × 4,600) = $4,500 900 units = $4,400 Sign contract for 700 units (ii) maximin Worst outcome from: 300 units = $2,900 500 units = $3,500 700 units = $4,100 800 units = $4,400 Sign contract for 800 units (iii) Best outcome from 300 units = $5,400 500 units = $5,000 700 units = $4,600 800 units = $4,400 Sign contract for 300 units (iv) Regret table: Contract size Demand 400u 500u 700u 900u 300u 1,500 1,200 600 0 500u 900 600 0 400 700u 300 0 400 800 800u 0 200 600 1,000 Worst regret for 300 units = $1,500 500 units = $900 700 units = $800 800 units = $1,000 Sign contract for 700 units (c) With perfect knowledge of the level of demand, the payoffs would be as follows: Result of Decision Payoff perf. know. Contract 400 800u 4,400 500 700u 4,600 700 500u 5,000 900 300u 5,400 The expected return with perfect knowledge = (0.2 × 4,400) + (0.3 × 4,600) + (0.4 × 5,000) + (0.1 × 5,400) = $4,800 The expected return without perfect knowledge (from (b)(i) is $4,400 So the most to pay for perfect knowledge = 4,800 – 4,400 = $400 My question is: in Section c, why's EV without perfect information is 4,400 rather than 4,500 (the highest EV of all) ? In addition, I also want to know whether the content "Value of information" is exempted from the syllabus? I hope your reply soon.