The following question has been answered before, they just do not answer the har
ID: 350003 • Letter: T
Question
The following question has been answered before, they just do not answer the hardest part, part C. This is the fulll question (answer can be found on Chegg).
Hartley Incorporated buys plastic resin by the ton and then packages and distributes it in smaller amounts to industrial users. The resin typically costs $50 per ton, and Hartley uses 80,000 tons each year. Placing an order for more resin costs $500 in allocated labor cost for purchasing personnel. Holding costs for the resin are estimated at 1 percent of the product value each month. Hartley operates 365 days a year. a. How much resin should Hartley order each time? b. What will be the average inventory and annual holding cost?
c. Suppose that instead of having each replenishment order delivered all in one shipment, Hartley asks its resin supplier to deliver each order in equally sized shipment, one shipment per day, with each shipment big enough to cover two days' worth of demand. How will this affect Hartley's order quantity, average inventory, and annual holding costs? (hint: Realize in this second scenario that Hartley's inventory level will never reach Q.)
The problem with question C is the hint. When Hartley orders a shipment every day for 2 days of demand, doesn't Q increase infinitely (orders > demand every day)?
Explanation / Answer
Annual demand, D = 80000 tons
Order cost, S = 500
Holding cost, H = 50*1%*12 = 6 per ton per year
a) Quantity of resin HArtley should order each time, EOQ = SQRT(2DS/H) = SQRT(2*80000*500/6) = 3651.5 tons
b) Average inventory = Q/2 = 3651.5/2 = 1825.75 tons
Annual holding cost = (Q/2)*H = 1825.75*6 = $ 10954.5
c) In this case, it is equivalent to Economic Production Quantity model
Delivery rate (shipment per day) = 2 * demand rate , or p = 2d , so d/p = 1/2
EPQ = SQRT(2DS/(H*(1-d/p))) = SQRT(2*80000*500/(6*(1-1/2))) = 5164 tons
Hartley's order quantity = 5164 tons
Average inventory = (Q/2)*(1-d/p) = (5164/2)*(1-1/2) = 1291 tons
Annual holding cost = 1291*6 = $ 7746
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