The annual demand for an item is 10,000 units. The cost to process an order is $75 and the annual inventory holding cost is 20% of item cost. What is the optimal order quantity, given the following price breaks for purchasing the item? What price should the firm pay per unit? What is the total annual cost at the optimal behavior? Quantity Price 1 – 9 $2.95 per unit 10 – 999 $2.50 per unit 1,000 – 4,999 $2.30 per unit 5,000 or more $1.85 per unit

The annual demand for an item is 10,000 units. The cost to process an order is $75 and the annual inventory holding cost is 20% of item cost. What is the optimal order quantity, given the following price breaks for purchasing the item? What price should the firm pay per unit? What is the total annual cost at the optimal behavior? Quantity Price 1 – 9 $2.95 per unit 10 – 999 $2.50 per unit 1,000 – 4,999 $2.30 per unit 5,000 or more $1.85 per unit

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Description: The annual demand for an item is 10,000 units. The cost to process an order is $75 and the annual inventory holding cost is 20% of item cost. What is the optimal order quantity, given the following price breaks for purchasing the item? What price sho

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter3: Introduction To Optimization Modeling

Section3.8: A Multiperiod Production Model

Problem 22P

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The annual demand for an item is 10,000 units. The cost to process an order is $75 and the annual inventory holding cost is 20% of item cost. What is the correct ordering policy (give optimal order quantity), given the following price breaks for purchasing the item? What price should the firm pay per unit? What is the total annual cost at the optimal behavior? Quantity: Price: 1-9 $2.95 per unit 10-999 $2.50 per unit 1,000-4,999 $2.30 per unit 5,000 or more $1.85 per unit
A company is planning for its financing needs and uses the basic fixed-order quantity inventory model. Which of the following is the total cost (TC) of the inventory given an annual demand of 10,000, setup cost of $32, a holding cost per unit per year of $4, an EOQ of 400 units, and a cost per unit of inventory of $150?
Suppose demand is know and constant at 500 units per year (one year has 250 working days). The holding cost is $2 per unit per year and the ordering cost is $20 per order. Also assume that the lead time is 10 days. Compute the optimal order quantity (EOQ) and the optimal annual inventory cost. Draw a picture of the evolution of the inventory level with time. Indicate the ROP on the picture as well as the length of the cycle. Now assume that the lead time is 90 days. Indicate the ROP on the picture.
The demand for a clothing brand is shown in the table below. The cost per order is about $4000. Cost of each unit of clothing = $5. Carrying cost percentage = 25% per item per 5 months. The analysis period = 5 month duration. Month Demand 1 400 2 300 3 200 4 400 5 500 a. Using this data, compute the solutions using the Lot for Lot and Periodic Order Quantity heuristics? Which of these heuristics would perform better and why? b. Assuming that the demand follows a normal distribution with the mean and variance from the data given above, determine the optimal order should be greater or lesser than the single period EOQ model.
ANT Infra orders two kinds of precast items: A and B for use in its projects from two different suppliers. The precasts are needed throughout the entire 52-week year. Precast A are used at a relatively constant rate and are ordered whenever the remaining quantity drops to the reorder level. While, precast B is ordered from a supplier who delivers by every three weeks. Data for both precast items are as follows:Item Precast A Precast BAnnual demand 10,000 5,000Holding cost (% of item cost)20% 20%Order cost $150 $25Lead time 4 weeks 1 weekSafety stock 55 units 5 unitsItem cost $10.00 $2.00 a. Employ Q system for precast A and calculate the EOQ, the reorder point, total inventory cost? b. Employ P system for precast B and estimate the target level inventory and total inventory cost?
A mail-order house uses 16,870 boxes a year. Carrying costs are 60 cents per box a year, and ordering costs are $96. The following price schedule applies. Number of BoxesPrice per Box1,000 to 1,999$1.25 2,000 to 4,9991.20 5,000 to 9,9991.15 10,000 or more1.10 a.Determine the optimal order quantity. (Round your answer to the nearest whole number.) Optimal order quantity5000 boxes b.Determine the number of orders per year. (Round your answer to 2 decimal places.) Number of order per year
Exercise 2: The demand per year (D) for product X is 12,100 units. The costs of placing an order (S) are $4.50. The unit cost (C) of the item is $25.00. The maintenance cost (H) per unit per year is 30% of the item's cost. 1. Use the economic order quantity (EOQ) model to determine: *Optimal quantity to order* The expected number of orders*Optimal time between orders*The total annual cost of maintaining that optimal amountNOTE: Show calculations of how you arrived at each amount 2. Answer, what are the potential benefits of using EOQ analysis for inventory management? How can you help businesses strike a balance between inventory holding costs and ordering costs?
The Olde Town Microbrewery makes Townside beer,which it bottles and sells in its adjoining restaurant and bythe case. It costs $1700 to set up, brew, and bottle a batchof the beer. The annual cost to store the beer in inventory is$1.25 per bottle. The annual demand for the beer is 21,000bottles and the brewery has the capacity to produce 30,000bottles annually.a. Determine the optimal order quantity, total annual inventory cost, the number of production runs per year, andthe maximum inventory level.b. If the microbrewery has only enough storage space tohold a maximum of 2500 bottles of beer in inventory,how will that affect total inventory costs?
A single inventory item is ordered from an outside supplier. The anticipateddemand for this item over the next 12 months is 6, 12, 4, 8, 15, 25, 20, 5, 10, 20, 5,12. Current inventory of this item is 4, and ending inventory should be 8. Assume aholding cost of $1 per period and a setup cost of $40. Determine the order policyfor this item based onb. Least unit cost
A book shop is planning to order calendars for sale starting in October. Only one order is placed. The calendars cost $1.50 and the shop sells them for $3 each. At the end of December, the shop reduces the calendar price to $1 and can sell all the surplus calendars at this price. The October-to-December demand can be approximated by a normal distribution with = 500 calendars and = 120 calendars.1. What inventory model should be used to determine the order quantity to maximize the total expected proÖt? Why?2. What is the optimal service level?3. How many calendars should the shop order so as to maximize the total expected proÖt?
A manager receives a forecast for next year. Demand is projected to be 600 units for the first half of the year and 920 units for the second half. The monthly holding cost is $2 per unit, and it costs an estimated $55 to process an order. a.Assuming that monthly demand will be level during each of the six-month periods covered by the forecast (e.g., 100 per month for each of the first six months), determine an order size that will minimize the sum of ordering and carrying costs for each of the six-month periods. (Round your answers to the nearest whole number.) Period Order Size 1 – 6 months?_____units 7 – 12 months?_____units b.If the vendor is willing to offer a discount of $10 per order for ordering in multiples of 50 units (e.g., 50, 100, 150), would you advise the manager to take advantage of the offer in either period? If so, what order size would you recommend? (Round intermediate calculations to 2 decimal places.) Period Order Size 1 – 6 months?____ units 7 – 12 months?____…
In the production quantity EOQ model, what would be theeffect of the production rate becoming increasingly largeas the demand rate became increasingly small, until theratio d/p was negligible?