Solve the following exercise using dynamic programming: a company distributes an article with a demand of 15,000 articles per year, it is Considering that annual retention costs are $5 per item, it is estimated that the demand is delayed and this causes a cost of $10 per year. Everytime that an order is placed this causes costs of $50. The demand during the time of delivery follows a normal distribution with means of 200 units and a variance of 5 units.
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1. Solve the following exercise using dynamic programming: a company distributes an article with a demand of 15,000 articles per year, it is Considering that annual retention costs are $5 per item, it is estimated that the demand is delayed and this causes a cost of $10 per year. Everytime that an order is placed this causes costs of $50. The demand during the time of delivery follows a
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- In Problem 12 of the previous section, suppose that the demand for cars is normally distributed with mean 100 and standard deviation 15. Use @RISK to determine the best order quantityin this case, the one with the largest mean profit. Using the statistics and/or graphs from @RISK, discuss whether this order quantity would be considered best by the car dealer. (The point is that a decision maker can use more than just mean profit in making a decision.)A newsvendor orders the quantity that maximizes expected profit for two products, X and Y. The critical ratio for both products is .8. The demand forecast for both products is 9000 units and both are normally distributed. Product X has more uncertain demand in the sense that it has the larger standard deviation. Of which of the two products does the newsvendor order morea. Product X because it has less certain demand. b. Product Y because it has more certain demand. c. The order quantities are the same because they have the same critical ratio. d. More information is needed to determine which has the higher order quantity.Joe is selling Christmas trees to pay his college tuition.He purchases trees for $10 each and sells them for $25each. The number of trees he can sell is normally distributedwith a mean of 100 and standard deviation of 30. How manytrees should Joe purchase?
- Rex manufacturing purchases a printed circuit board for use in its automatic, computerized, robotbartender. The manufacturing facility has placed the following monthly demands on purchasedgoods inventory during the past year. Month 1 2 3 4 5 6 7 8 9 10 11 12 Demand 205 193 197 220 202 226 179 197 186 202 179 214 This demand schedule can be assumed to be random, to follow a normal distribution, and to berepresentative of what will occur in the future. Rex estimates that a fixed cost of $300 isincurred each time an order is placed for the boards, and that the inventory holding cost is about20% per year of the value of inventory. Each board has an estimated value of $192 at the pointof storage. The lead time on purchase orders is (1/5) month.Part A: What is the EOQ?Part B: What is the safety stock required to assure the management that the chance of a stock outin a cycle is no more than 1%?Part C: What is the reorder level?Happy Henry’s car dealer sells an imported car called the EX123. Once everythree months, a shipment of the cars is made to Happy Henry’s. Emergencyshipments can be made between these three-month intervals to resupply the carswhen inventory falls short of demand. The emergency shipments require twoweeks, and buyers are willing to wait this long for the cars, but will generally goelsewhere before the next three-month shipment is due.From experience, it appears that the demand for the EX123 over a three-monthinterval is normally distributed with a mean of 60 and a variance of 36. The cost ofholding an EX123 for one year is $500. Emergency shipments cost $250 per carover and above normal shipping costs.a. How many cars should Happy Henry’s be purchasing every three months?b. Repeat the calculations, assuming that excess demands are back-ordered fromone three-month period to the next. Assume a loss-of-goodwill cost of $100 forcustomers having to wait until the next three-month period and a…A book and paper store distributes one specialized monthly magazine. When looking at the sales the last years, they have concluded that the demand for each issue of the magazine will be normally distributed with an expected sale of 250 and a standard deviation of 100. The purchase price for the magazine is $20. and the sales price is $50.The store has an agreement with a second -hand store that buys unsold magazines for $5 each. How many magazines should the store buy of each issue?
- General Motors is trying to determine how frequently they should have tires delivered to their Flint, Michign truck assembly plant. The tires are large and expensive to hold in inventory, and there is also a sgiicant fee each te a tire delivery is made. Which of the following tools would be most useful in making this decision O A/F Ratio Method Newsvendor Model Base Stock Model Economic Order Quantity Model Minimum Cycle Length ModelAboloway Company stocks a part that has a daily demand represented by the empirical distribution (shown in the table below). When restocking this part, the average lead time from the supplier is 3 days with a standard deviation of 0.5 days. The plant manager wants to determine how much safety stock to maintain for this part to ensure that stock-outs will not be incurred in more than 5.5% of the order cycles. Daily demand (d) in units Frequency 5 10 10 35 15 65 20 32 25 8 Total Observations = 150 3a. Find the mean and standard deviation for demand. 3b. Based on the information in problems 3 and 3a, what is the mean and standard deviation of demand during the lead time? 3c. Based on the information in problems 3, 3a, and 3b, how much safety stock should the plant manager maintain to ensure that stock-out will not be incurred in more than 5.5% of the order cycles?Please do not give solution in image format thanku Deltic sells this component for 55 per unit with a 4-month delivery lead time. Assume Deltic covers all transportation and related processing until delivery. TCX’s demand forecast for the upcoming selling season (12 months) is a normal distribution with mean 13500 and standard deviation 3736,4 . TCX sells each unit, after integrating their proprietary software, for 135. Assume that TCX uses a holding cost rate of 25 %, and any leftover units can be sold for 30 on average. Due to the long lead time and high minimum order quantity required, TCX is planning on a single order from Deltic to meet their needs in the next year. How many of these components should TCX order? Calculate the resulting expected annual profits for TCX.
- Daily demand of a chemical at an oil refinery is normally distributed with a mean of 60 litres and a standard deviation of 7. The supplier reliably delivers the chemical by maintaining a constant lead time of 1 week. There are no delivery charges from the supplier. Sales occur throughout the year. An order placement requires one hour of an administrative employee who is paid $20 per hour. Receiving and storing a chemical shipment requires two workers to work for half an hour. Workers are paid $12 per hour each. Chemical’s purchase price is $500 per litre. Annual cost of capital is 5%. Other holding costs are estimated to be $0.5 per litre. Find the order quantity and the reorder point to satisfy a 95% service level during the lead time. (Round answers to 2 decimal places.)Annual demand for number 2 pencils at the campus store is normallydistributed with mean 1,000 and standard deviation 250. The store purchases thepencils for 6 cents each and sells them for 20 cents each. There is a two-monthlead time from the initiation to the receipt of an order. The store accountantestimates that the cost in employee time for performing the necessary paperworkto initiate and receive an order is $20, and recommends a 22 percent annual interest rate for determining holding cost. The cost of a stock-out is the cost of lostprofit plus an additional 20 cents per pencil, which represents the cost of loss ofgoodwill.b. Find the simultaneous optimal values of Q and R.Annual demand for number 2 pencils at the campus store is normallydistributed with mean 1,000 and standard deviation 250. The store purchases thepencils for 6 cents each and sells them for 20 cents each. There is a two-monthlead time from the initiation to the receipt of an order. The store accountantestimates that the cost in employee time for performing the necessary paperworkto initiate and receive an order is $20, and recommends a 22 percent annual interest rate for determining holding cost. The cost of a stock-out is the cost of lostprofit plus an additional 20 cents per pencil, which represents the cost of loss ofgoodwill.d. What is the safety stock for this item at the optimal solution?