# Business, optimization?

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Business, optimization?

Business, optimization?

The manager of a car wash received a revised price list from the vendor who supplies soap, and a promise of a shorter lead time for deliveries. Formerly the lead time was 8 days, but now the vendor promises a reduction of 25 percent in that time. Annual usage of soap is 5930 gallons. The car wash is open 360 days a year. Assume that daily usage is normal, and that it has a standard deviation of 5 gallons per day. The ordering cost is $40 and annual carrying cost is $4 a gallon. The revised price list (cost per gallon) is shown in the following table: Order Size Unit Price 1–399 400–599 1.7 600++ 1.62 The store manager is considering to provide a service level of 0.75.How much is the Quantity from EOQ? (Keep two decimal places) How much is the total annual inventory related costs (holding, ordering, and purchase costs), if the car wash order the quantity from EOQ model? How much is the total annual inventory related costs (holding, ordering, and purchase costs), if the bakery orders just enough to get the soap at the price of $1.7? How much is the total annual inventory related costs (holding, ordering, and purchase costs), if the car wash orders just enough to get the soap at the price of $1.62? What is the car wash’s optimal order quantity, given this quantity discount information? How often (in days) should the car wash order? How long (in days) is the lead time? What is the Z value for the desired service level? How much safety stock is needed to provide the desired service level? What is the ROP for the desired service level? 2) A small copy center uses approximately 28 boxes of copy paper a week. Experience suggests that usage can be well approximated by a normal distribution with a standard deviation of 9 box per week. 2 weeks are required to fill an order for letterhead stationery. Ordering cost is $4, and annual holding cost is $0.84 per box. The manager’s desired service level is 0.8. Assume a year is 52 weeks.How much is the annual demand rate? How much is the optimal order quantity? (keep two decimal places) How many times a year the copy center place a new order of papers? (keep two decimal places) How many weeks does each order of paper last? Compute the total annual cost of ordering and carrying boxes of papers: What is the Z value for the desired service level? How much safety stock is needed to provide the desired service level? What is the ROP for the desired service level? 3) Demand for walnut fudge ice cream at the Sweet Cream Dairy can be approximated by a normal distribution with a mean of 110 gallons per week and a standard deviation of 15 gallons per week. The new manager desires a service level of 85 percent. Lead time is 3 days, and the dairy is open seven days a week (Hint: work in terms of weeks).What is the Z value for the desired service level? How many (fraction of) “weeks” is the lead time? If we use a continuous inventory system, what safety stock level would be consistent with the desired service level? If we use a continuous inventory system, what ROP would be consistent with the desired service level? 4) The Dine Corporation is both a producer and a user of brass couplings. The firm operates 220 days a year and uses the couplings at a steady rate of 24200 per year. Couplings can be produced at a rate of 210 per day. Annual storage cost is $3 per coupling, and machine setup cost is $79 per run.What is the “daily” demand rate? How many units the company should produce in each production run? How many brass couplings are in the inventory when the firm stops the production in a given production run? How many production runs per year will there be? How often the firm starts the production? (in days) How many days in a cycle the firm is producing the products? How many days in a cycle the firm doe not produce any product? How much is the total annual inventory related costs? 5) Joe’s Slop House is a little hole in the wall restaurant that serves slow-cooked barbecue beef sandwiches. The beef for the sandwiches cooks overnight, so each evening Joe decides how much beef to cook for the next day. The beef costs $3 a pound and Joe sells each sandwich (filled with 1 pound of beef) for $4.5. At the end of the day, any leftover beef is given to the neighborhood church for their soup kitchen. The tax deduction for this is worth $0.5 a pound. Daily demand for the beef can be approximated by a normal distribution with a mean of 230 pounds and a standard deviation of 40 pounds.Cost of Shortage (Cs): Cost of Excess (Ce): What is the optimal service level? What is the corresponding z value? How many pounds of beef should Joe cook for the next day? 6) Demand for walnut fudge ice cream at the Sweet Cream Dairy can be approximated by a normal distribution with a mean of 21 gallons per week and a standard deviation of 3.5 gallons per week. The new manager desires a service level of 90 percent. Lead time is 3 days, and the dairy is open seven days a week. (Hint: Work in terms of weeks.)For this problem, we consider both continuous inventory system and periodic inventory system.If we use periodic inventory system, the time from delivery of an order until next review is 10 days (Note: this is reported in days).What is the corresponding z-value for the desired service level? (keep three decimal places) How long is the lead time (in fractions of a week)? How much is the average demand during a week? How much is the standard deviation of the demand during the week? If we use continuous inventory system, what safety stock is consistent with the desired service level? If we use continuous inventory system, what ROP is consistent with the desired service level? If we use periodic inventory system, what safety stock is consistent with the desired service level? If we use periodic inventory system, what is the quantity to order when the supply at hand is 8 gallons?

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