Problem:
Jim is a CFO of a mid-sized construction company. One of his key tasks is to ensure that the company has sufficient cash to pay its daily and hourly workers who are hired whenever need arises. The company operates all 365 days a year and Jim estimates that on any day his payroll is Normally distributed with mean $25,000 and standard deviation $7,000. Jim manages his cash reserves using the order-up-to model: each morning he places an order for cash with the bank and the armored vehicle arrives 2 days later with the money. It is company's policy to pay all workers on the same day, but in rare cases when the company runs out of cash it pays workers as soon as possible while increasing their paycheck by 1% for each day of delay. For each dollar carried the company incurs 15% cost annually, which includes cost of capital and insurance.
Required:
Question 1) What is the profit-maximizing order-up-to level for cash?
Question 2) Suppose Jim is interested in ensuring that the company immediately satisfies all employee salary requirements with a 95% probability. What is the corresponding order-up-to level?
Question 3) To reduce lines and move payroll closer to workers, Jim considers opening another payroll office. Exactly half of the workers will receive payments at one office and the other half will receive payments at the other office. Jim plans to divide evenly the total safety stock that it keeps now, putting 50% of it in each of the two payroll offices. Compared to the current single payroll office system, will the cycle service level (that is, the probability of not stocking out in a cycle) be higher or lower? Why?
Solve the given numerical problem and illustrate step by step calculation.