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iipm pom assingment
OPERATIONS AND OPTIMIZATION RESEARCH ASSIGNMENT 1 – ISBE B SS 2010 ( To be submitted by 1100 hours on 10 Dec 2010) 1. Shubh Labh Mutual Fund has Rs 500,000 for one of the three investment options in the stock market – a growth fund, government bonds or a blue chip company. Shubh Labh feels that the stock market can assume the states as listed below. The company’s estimate of the associated payoffs is also given in the table.
Type of Investment Growth Fund Government Bonds Blue Chip Company Boom 375000 500000 250000 Stock Market Trend Moderate Moderate Growth Decline 150000 -50000 100000 -150000 100000 0 Collapse -400000 -500000 -300000
Using the minimax regret criterion for decision making , which option should Shubh Labh adopt? 2. A news agency receives its weekly order for a magazine every Monday and cannot reorder during the week. Each copy costs Rs 1.80 and is sold for Rs 3.00. Unsold copies may be returned the following week for a Rs 1.20 rebate. When the agency runs out of copies and cannot supply a customer, it estimates its ‘good will’ loss at Rs 2.40 in future profits, as the customer will take his business else where for a couple of weeks at least. Demand has been remarkably constant between 28 and 40 copies a week, as shown below:
Demand (Copies) Fraction of time 28 0.30 32 0.40 36 0.20 40 0.10
(a) Construct a payoff table and determine the optimal number of copies to stock. (b) Construct an opportunity loss table and find the optimal number of copies to stock. (c) How much would it be worth to know the exact demand each week? What would be the expected profit if this were possible? 3. A car manufacturer uses a special control device in each car that he produces. In order to avoid a faulty device, each device can be tested either before installation at a cost of Rs 2 per device tested or can be installed without testing and the faulty devices replaced after assembly at a cost of Rs 20 per device. The faulty devices cannot be repaired and must be discarded. The devices are purchased from a manufacturer in batches of 10,000. Based on past experience the proportion of defectives and the associated probability are estimated to be:
Proportion of Faulty Devices
Probability
0.08 0.12 0.16
0.20 0.70 0.10
(a) What inspection method should the car manufacturer adopt? (b) What is the expected value of perfect information (EVPI)? 4. A mineral processing company has to decide about the number of spare gear trains that it should order along with a high horse power gear box connected to a grinding unit. Although the life of a gear can be as high as 30 years or more, sudden failures cannot be ruled out. In case of failure it would be expensive and time consuming to get a spare gear train. The cost would be Rs 2,00,000 including the loss of production due to down time of the equipment. If ordered out with the gearbox, a gear train would cost only Rs 10,000 per unit. The following data is based on the past experience of a 100 gear boxes:
Number of spare gear trains required 0 1 2 3 4 Number of gear boxes requiring the spares 93 4 2 1 0
What should be the optimal order size? 5. An electronics manufacturing unit is considering modernisation and expansion of its facilities. It has the option of only modernising its works at a cost of Rs 35 lakhs or modernising and expanding simultaneously at a cost of Rs 60 lakhs. A third option available to the company is to modernise now and go in for expansion after three years. The modernisation after three years will cost Rs 40 lakhs. The company estimates that the demand for the first three years may be low or high with probabilities of 0.3 and 0.7 respectively. It is further estimated that the if the demand during the first 3 years is low, then the probability that demand during the subsequent years that is fourth to tenth year will remain low is 0.9. If the demand is high during the first 3 years, it is likely to remain high for the next 7 years with a probability of 0.85. The estimated payoffs , if the plant is only modernised are Rs 5.5 lakhs annually in case of low demand and Rs 6.0 lakhs annually in case of high demand. If the plant is modernised and expanded then the payoffs will be Rs 3 lakhs annually in case of low demand, and in case of high demand Rs 12 lakhs annually for the first 3 years and Rs 15 lakhs annually thereafter. Construct a decision tree and determine the best strategy for the company. 6. A and B play a game in which each has three coins, a twenty five paise, a fifty paise and one rupee. Each selects a coin without the knowledge of the other’s choice. If the sum of the coins is an odd amount, A wins B’s coins; if the sum is even B wins A’s coins. Find the best strategy for each player and the value of the game. 7. Assume that two firms are competing for market share for a particular product. Each firm is considering what promotional strategy to employ for the coming period. Assume that the following payoff matrix describes the increase in market share for Firm A and decrease in market share for firm B. Determine the optimal strategy for each firm.
No Advt No Advt Medium Advt High Advt 5 10 20
Firm A
Firm B Medium Advt 0 6 15
High Advt -10 2 10
Which firm would be the winner in terms of market share? 8. The management of a corporation is in the process of deciding whether to agree to negotiate with the striking union now or to delay. The decision is difficult because the management does not know the union leadership’s position. The union leaders may be adamant and insist on their original demands, they may be ready to compromise or they may be ready to yield and accept the original management offer. The matrix of payoffs to management as management sees it, is (in Rs 1 million units).
Adamant -2 5 Union Compromise 1 -2 Yield 2 -3
Management
Negotiate Delay
(a) (b) (c)
Solve the management’s problem. What should be the Union’s strategy? Discuss the implications of the conclusion to adopt a random strategy.
doc_485035623.doc
iipm pom assingment
OPERATIONS AND OPTIMIZATION RESEARCH ASSIGNMENT 1 – ISBE B SS 2010 ( To be submitted by 1100 hours on 10 Dec 2010) 1. Shubh Labh Mutual Fund has Rs 500,000 for one of the three investment options in the stock market – a growth fund, government bonds or a blue chip company. Shubh Labh feels that the stock market can assume the states as listed below. The company’s estimate of the associated payoffs is also given in the table.
Type of Investment Growth Fund Government Bonds Blue Chip Company Boom 375000 500000 250000 Stock Market Trend Moderate Moderate Growth Decline 150000 -50000 100000 -150000 100000 0 Collapse -400000 -500000 -300000
Using the minimax regret criterion for decision making , which option should Shubh Labh adopt? 2. A news agency receives its weekly order for a magazine every Monday and cannot reorder during the week. Each copy costs Rs 1.80 and is sold for Rs 3.00. Unsold copies may be returned the following week for a Rs 1.20 rebate. When the agency runs out of copies and cannot supply a customer, it estimates its ‘good will’ loss at Rs 2.40 in future profits, as the customer will take his business else where for a couple of weeks at least. Demand has been remarkably constant between 28 and 40 copies a week, as shown below:
Demand (Copies) Fraction of time 28 0.30 32 0.40 36 0.20 40 0.10
(a) Construct a payoff table and determine the optimal number of copies to stock. (b) Construct an opportunity loss table and find the optimal number of copies to stock. (c) How much would it be worth to know the exact demand each week? What would be the expected profit if this were possible? 3. A car manufacturer uses a special control device in each car that he produces. In order to avoid a faulty device, each device can be tested either before installation at a cost of Rs 2 per device tested or can be installed without testing and the faulty devices replaced after assembly at a cost of Rs 20 per device. The faulty devices cannot be repaired and must be discarded. The devices are purchased from a manufacturer in batches of 10,000. Based on past experience the proportion of defectives and the associated probability are estimated to be:
Proportion of Faulty Devices
Probability
0.08 0.12 0.16
0.20 0.70 0.10
(a) What inspection method should the car manufacturer adopt? (b) What is the expected value of perfect information (EVPI)? 4. A mineral processing company has to decide about the number of spare gear trains that it should order along with a high horse power gear box connected to a grinding unit. Although the life of a gear can be as high as 30 years or more, sudden failures cannot be ruled out. In case of failure it would be expensive and time consuming to get a spare gear train. The cost would be Rs 2,00,000 including the loss of production due to down time of the equipment. If ordered out with the gearbox, a gear train would cost only Rs 10,000 per unit. The following data is based on the past experience of a 100 gear boxes:
Number of spare gear trains required 0 1 2 3 4 Number of gear boxes requiring the spares 93 4 2 1 0
What should be the optimal order size? 5. An electronics manufacturing unit is considering modernisation and expansion of its facilities. It has the option of only modernising its works at a cost of Rs 35 lakhs or modernising and expanding simultaneously at a cost of Rs 60 lakhs. A third option available to the company is to modernise now and go in for expansion after three years. The modernisation after three years will cost Rs 40 lakhs. The company estimates that the demand for the first three years may be low or high with probabilities of 0.3 and 0.7 respectively. It is further estimated that the if the demand during the first 3 years is low, then the probability that demand during the subsequent years that is fourth to tenth year will remain low is 0.9. If the demand is high during the first 3 years, it is likely to remain high for the next 7 years with a probability of 0.85. The estimated payoffs , if the plant is only modernised are Rs 5.5 lakhs annually in case of low demand and Rs 6.0 lakhs annually in case of high demand. If the plant is modernised and expanded then the payoffs will be Rs 3 lakhs annually in case of low demand, and in case of high demand Rs 12 lakhs annually for the first 3 years and Rs 15 lakhs annually thereafter. Construct a decision tree and determine the best strategy for the company. 6. A and B play a game in which each has three coins, a twenty five paise, a fifty paise and one rupee. Each selects a coin without the knowledge of the other’s choice. If the sum of the coins is an odd amount, A wins B’s coins; if the sum is even B wins A’s coins. Find the best strategy for each player and the value of the game. 7. Assume that two firms are competing for market share for a particular product. Each firm is considering what promotional strategy to employ for the coming period. Assume that the following payoff matrix describes the increase in market share for Firm A and decrease in market share for firm B. Determine the optimal strategy for each firm.
No Advt No Advt Medium Advt High Advt 5 10 20
Firm A
Firm B Medium Advt 0 6 15
High Advt -10 2 10
Which firm would be the winner in terms of market share? 8. The management of a corporation is in the process of deciding whether to agree to negotiate with the striking union now or to delay. The decision is difficult because the management does not know the union leadership’s position. The union leaders may be adamant and insist on their original demands, they may be ready to compromise or they may be ready to yield and accept the original management offer. The matrix of payoffs to management as management sees it, is (in Rs 1 million units).
Adamant -2 5 Union Compromise 1 -2 Yield 2 -3
Management
Negotiate Delay
(a) (b) (c)
Solve the management’s problem. What should be the Union’s strategy? Discuss the implications of the conclusion to adopt a random strategy.
doc_485035623.doc