Questions .
Weekly demand for a product at a retailer is normally distributed with a mean of 900 boxes and a standard deviation of 200 boxes. Current purchase quantity is 2,000 units. Demand is independent from one week to the next. The replenishment lead-time is 3 weeks, with a standard deviation of 1.2 weeks.
What safety stock level is necessary to achieve a 97.50% cycle service level?
Note: Round sigma to 3 decimals. Round safety stock to an integer value.
Using the z table, z =
Safety Stock....
Problem 1: Risk and Expected Utility lI'Llonsider aperson with a current wealth \""0 = 101}, EH31] who faces the prospect of p = .25 chance of losing; 211.000 through car theft during the next year. Suppose that his utility function is UHF} = an where W is the person's wealth at the end of the year. This person can buy an antitheFt device that costs $1.95!} and reduces the probability of the to p' = {1.15. {a} 1Will this person buy the antithcft device? Show mathematically why this is the case. Now suppose there is an insurance company that sells full insurance coverage. The premium is determined as the actuarially fair premium plus $200 of admin- istrative charges. The company cannot monitor whether or not the individual installed a device. so the probability of theft used by the insurance company to determine the premium is p = .25. {b} What premium does the insurer charge? Does the consumer buy insurance? Does the consumer buy the device? Show how you de- termine this. Assume now that the insurance company can monitor whether or not the in- dividual installed an anti-theft device and charge a premium based on whether consumer uses the device or not. If a consumer doesn't use the device+ the pre- mium is the actuarial fair price {for p = .25} plus $21110 to cover administrative costs. If a Consumer does use the device1 the premium will he the actuarially fair premium [for p' = .15] plus $2M] of administrative charges and an additional $1ll to cover the monitoring masts [the cost of verifying that the consumer is using the device]. Assume that the insurer does not cover the cost cl buying the device and does not cover theft of the device itself (Le. the insurer only covers the less of El]. (c) How mud: does insurance cost with and without the device installed? What will the individual do? Will the individual install an antithett device? Will he buy insurance? What type of insurance will the person hay: with or without anti-theft device? QUESTION 4 A new start-up firm, I-Start, wants to hire 50 workers. There are two types of workers that would have the required skills: H and L. A worker of type H would generate a monthly revenue of $ R, for the firm and a type L worker would generate a monthly revenue of $ R | for the firm. All workers are currently employed at a monthly salary of $ S . We assume throughout that R, 0 per audited worker. Note that no new workers are hired after the m-month probationary period. (d) Write an expression (in terms of the parameters) that gives I-Start's expected total profits over the entire n-month period under Option 2. [Hint: you need to consider two cases.] From now on assume that Ry =6,000, R, =4,000, S, =4,800, q, =25%, n =36, c = 5,500 and d = 3,000. Thus the only remaining parameters are m, p and &. (e) Assume for this question that & = 0. Rewrite the expressions of part (d) for the values given above and explain the significance of the inequality 2,500m + 40,500p-1,125mp
