SCMA 331 Final Chapter 12
In the production order quantity (POQ) model, inventory does not arrive in a single moment but flows in at a steady rate, resulting in a larger production/order quantity than in an otherwise identical EOQ problem.
True
One function of inventory is to take advantage of quantity discounts.
True
At the economic order quantity, holding costs are equal to product costs.
False
Cycle counting is an inventory control technique exclusively used for cyclical items.
False
In the quantity discount model, the cost of acquiring goods (product cost) is not a factor in determining lot size.
False
In the simple EOQ model, if annual demand were to increase, the EOQ would increase proportionately.
False
In the simple EOQ model, if the carrying cost were to double, the EOQ would also double.
False
Insurance and taxes on inventory are part of the costs known as setup or ordering costs.
False
Which item to order and with which supplier the order should be placed are the two fundamental issues in inventory management.
False
Work-in-process inventory is devoted to maintenance, repair, and operating materials.
False
Safety stock in inventory systems depends only on the average demand during the lead time.
False
Describe the difference between a fixed-quantity and a fixed-period inventory system?
In a fixed-quantity inventory system, when the quantity on hand reaches the reorder point, an order is placed for the specified quantity. In a fixed-period inventory system, an order is placed at the end of the review period. The quantity ordered is that needed to bring inventory up to a specified level.
________ is extra stock that is carried to serve as a buffer.
Safety stock
________ is the complement of the probability of a stockout.
Service level
Define service level.
The service level is the probability that demand will not be greater than supply during lead time; it is the complement of the probability of a stockout.
If setup costs are reduced by substantial reductions in setup time, the production order quantity is also reduced.
True
In ABC analysis, "A" items are the most tightly controlled.
True
Retail inventory that is unaccounted for between receipt and time of sale is known as shrinkage.
True
Service level is the complement of the probability of a stockout.
True
The fixed-period inventory model can have a stockout during the review period as well as during the lead time, which is why fixed-period systems require more safety stock than fixed-quantity systems.
True
The reorder point is the inventory level at which action is taken to replenish the stocked item.
True
Identify the typical components that constitute inventory holding or carrying costs.
Typical components of inventory holding or carrying costs include housing costs, material handling costs, labor cost from extra handling, investment costs, pilferage, scrap, and obsolescence.
Identify three techniques to control service inventories.
(1) good personnel selection, training, and discipline; (2) tight control of incoming shipments; and (3) effective control of all goods leaving the facility
Holding costs are $35 per unit per year, the ordering cost is $120 per order, and sales are relatively constant at 300 per month. (a) What is the optimal order quantity? (b) What are the annual holding and setup costs?
(a) Order size is Q* = = 157.12 or 157. (b) Annual inventory costs are ($120) + ($35) + $2749.49 + $2749.60 = $5,499.09
A specific product has demand during lead time of 100 units, with a standard deviation during lead time of 25 units. What safety stock (approximately) provides a 95% service level? A) 41 B) 55 C) 133 D) 140 E) 165
A
In the basic EOQ model, if the cost of placing an order doubles, and all other values remain constant, the EOQ will: A) increase by about 41%. B) increase by 100%. C) increase by 200%. D) increase, but more data is needed to say by how much. E) either increase or decrease.
A
Which of the following items is mostly likely managed using a single-period order model? A) Christmas trees B) canned food at the grocery store C) automobiles at a dealership D) metal for a manufacturing process E) gas sold to a gas station
A
If daily demand is constant at 10 units per day, and lead time averages 12 days with a standard deviation of 3 days, 95 percent service requires how much safety stock? A) 28 units B) 30 units C) 49 units D) 59 units E) 114 units
C
If daily demand is normally distributed with a mean of 15 and standard deviation of 5, and lead time is constant at 4 days, a 90 percent service level will require how much safety stock? A) 7 units B) 10 units C) 13 units D) 16 units E) 26 units
C
In a safety stock problem where both demand and lead time are variable, demand averages 150 units per day with a daily standard deviation of 16, and lead time averages 5 days with a standard deviation of 1 day. What is the standard deviation of demand during lead time? A) 15 units B) 100 units C) 154 units D) 500 units E) 13,125 units
C
The assumptions of the production order quantity model are met in a situation where annual demand is 3650 units, setup cost is $50, holding cost is $12 per unit per year, the daily demand rate is 10 and the daily production rate is 100. What is the production order quantity for this problem? A) 139 B) 174 C) 184 D) 365 E) 548
C
A disadvantage of the fixed-period inventory system is that: A) it involves higher ordering costs than the fixed quantity inventory system. B) additional inventory records are required. C) the average inventory level is decreased. D) since there is no count of inventory during the review period, a stockout is possible. E) orders usually are for larger quantities.
D
If demand is not uniform and constant, then stockout risks can be controlled by: A) increasing the EOQ. B) spreading annual demand over more frequent, but smaller, orders. C) raising the selling price to reduce demand. D) adding safety stock. E) reducing the reorder point.
D
What is the primary purpose of the basic economic order quantity model shown below? Q* = √ (2DS/H) A) to calculate the reorder point, so that replenishments take place at the proper time B) to minimize the sum of carrying cost and holding cost C) to maximize the customer service level D) to minimize the sum of setup cost and holding cost E) to calculate the optimum safety stock
D
Which of the following is NOT one of the four main types of inventory? A) raw material inventory B) work-in-process inventory C) maintenance/repair/operating supply inventory D) safety stock inventory E) finished-goods inventory
D
The soft goods department of a large department store sells 175 units per month of a certain large bath towel. The unit cost of a towel to the store is $2.50 and the cost of placing an order has been estimated to be $12.00. The store uses an inventory carrying charge of I = 27% per year. Determine (a) the optimal order quantity, (b) the order frequency, and (c) the annual holding and setup cost. If, through automation of the purchasing process, the ordering cost can be cut to $4.00, what will be (d) the new economic order quantity, (e) the order frequency, and (f) annual holding and setup costs? Explain these results.
Annual demand is 175 × 12 = 2100. (a) Q* = = 273.25; (b) N = = 7.69 (c) TC = ($12) + (.27)($2.50) = $92.22 + $92.22 = $184.44 At S=$4: (d) Q* = = 157.76; (e) N = = 13.31 (f) TC = ($4) + (.27)($2.5) = $53.24 + $53.24 = $106.48 The lower order cost encourages smaller, more frequent orders, and it lowers total costs.
An advantage of the fixed-period inventory system is that: A) safety stock will be lower than it would be under a fixed-quantity inventory system. B) there is no physical count of inventory items when an item is withdrawn. C) no inventory records are required. D) orders usually are for smaller order quantities. E) the average inventory level is reduced.
B
) Suppose that papers for a newspaper stand cost $0.40 and sell for $0.80. They currently have no salvage value. If the stand owner is able to find an outlet that would provide a salvage value of $0.10, what would be the increase in service level? A) .5 B) 0 C) .07 D) 1 E) unable to determine given only the above information
C
Demand for dishwasher water pumps is 8 per day. The standard deviation of demand is 3 per day, and the order lead time is four days. The service level is 95%. What should the reorder point be? A) about 18 B) about 24 C) about 32 D) about 38 E) more than 40
E
If the standard deviation of demand is six per week, demand is 50 per week, and the desired service level is 95%, approximately what is the statistical safety stock? A) 8 units B) 10 units C) 16 units D) 64 units E) Cannot be determined without lead time data.
E
Service level is: A) the probability of stocking out. B) the probability of not stocking out. C) something that should be minimized in retail. D) calculated as the cost of a shortage divided by (the cost of shortage + the cost of overage) for single-period models. E) B and D
E
What is the difference between P and Q inventory systems? A) order size B) order spacing C) maximum service level D) lead time length E) A and B
E
The EOQ model is best suited for items whose demand is dependent on other products.
False
Average daily demand for a product is normally distributed with a mean of 20 units and a standard deviation of 3 units. Lead time is fixed at 25 days. What reorder point provides for a service level of 95 percent?
ROP = DL + Z × σd × = 20(25) + 1.65 × 3 × = 500 + 24.75 = 524.75
Consider a local club selling Christmas trees. If demand is normal with a mean of 200 and a standard deviation of 50, how many trees should the club stock if service level must be greater than 95%?
The Z-value for a 95% service level is 1.65; thus, ideal inventory is 200 + 50(1.65) = 282.5 = 283.
One advantage of cycle counting is that it maintains accurate inventory records.
True
Demand for gallons of milk (a perishable item) is normally distributed with a weekly mean of 50 and standard deviation of 15. How many additional gallons of milk must be stocked to increase the service level from 50% to 80%?
Z for 50% is 0, Z for 80% is .84. Thus, the increase in milk stock would be 15(.84) - 15(0) = 12.6 = 13 gallons extra.
A(n) ________ system triggers inventory ordering on a uniform time frequency.
fixed-period (P) system
What happens to the cost of safety stock when the service level increases?
Because Z increases, the amount of safety stock increases; therefore, the investment in (cost of) safety stock increases.
________ is a continuing reconciliation of inventory with inventory records.
Cycle counting
What is cycle counting?
Cycle counting is a continuing audit to reconcile inventory with inventory records.
Which of the following should be higher in P systems than Q systems? A) lead time B) demand C) order size D) order spacing E) safety stock
E
What is a fixed-period system?
It is a system in which inventory orders are made at regular time intervals.
How sensitive is the EOQ to variations in demand or costs?
The EOQ is relatively insensitive to small changes in demand or setup or carrying costs because the cost curve is relatively shallow (flat) around the EOQ. This means that variations in setup costs, holding costs, or demand make relatively modest differences in total cost.
A major challenge in inventory management is to maintain a balance between inventory investment and customer service.
True
Daily demand for a product is normally distributed with a mean of 150 units and a standard deviation of 15 units. The firm currently uses a reorder point system, and it seeks a 75% service level during the lead time of 6 days. a. What safety stock is appropriate for the firm? b. What is the reorder point?
a. SS = 0.67 × 15 × = 24.6 units b. ROP = 150(6) + 24.6 = 924.6 units
In a quantity discount problem, if the savings in annual product cost is smaller than the increase in the sum of annual setup cost and annual holding cost, the discount should be ________.
rejected or refused
A(n) ________ model gives satisfactory answers even with substantial variations in its parameters.
robust
Clement Bait and Tackle has been buying a chemical water conditioner for its bait (to help keep its baitfish alive) in an optimal fashion using EOQ analysis. The supplier has now offered Clement a discount of $0.50 off all units if the firm will make its purchases monthly or $1.00 off if the firm will make its purchases quarterly. Current data for the problem are: D = 720 units per year; S = $6.00, I = 20% per year; P = $25. (a) What is the EOQ at the current behavior? (b) What is the annual total cost, including product cost, of continuing their current behavior? (c) What are the annual total costs, if they accept either of the proposed discounts? (d) At the cheapest of the total costs, are carrying costs equal to ordering costs? Explain.
(a) Q* = = 41.57 or 42 units at a time. (b) TC = 720($25) + ($6) + (.2)($25) = $18,000 + $103.92 = $103.93 + $18,207.85 (c) Placing orders on a monthly basis implies twelve orders per year where Q = 720 / 12 = 60. Placing orders on a quarterly basis implies four orders per year where Q = 720/4 = 180. The following table shows the total costs. Range 1 Range 2 Range 3 Quantity 1-59 60-179 ≥180 Unit Price, P $25 $24.5 $24 Q* (Square root formula) 41.57 41.99 42.43 Order Quantity 41.57 60 180 Setup cost 103.92 72 24 Holding cost 103.93 147 432 Product cost 18,000.00 17,640 17,280 Total cost, Tc $18,207.85 $17,859 $17,736 (d) They are not. Accepting the discount requires an order quantity that is not EOQ. With the more favorable discount, setup costs are $24 while holding costs are $432. The trade-off is worth it due to the $720 in annual product cost savings.
The inventory management costs for a certain product are S=$8 to order, and H=$1 to hold for a year. Annual demand is 2400 units. Consider the following ordering plans: (a) order all 2400 at one time, (b) order 600 once each quarter, and (c) order 200 once each month. Calculate the annual holding and setup costs associated with each plan. (d) Is there another plan, cheaper than any of these? Calculate this order quantity along with its total annual holding and setup costs.
(a) TC2400 = 1($8) + ($1) = $1208.00 (b) TC600 = 4($8) + ($1) = $332.00 (c) TC200 = 12($8) + ($1) = $196.00 (d) Q* = = 196 is the cheapest solution. TC196 = (2400/196)($8) + ($1) = $97.96 + $98.00 = $195.96
________ is a method for dividing on-hand inventory into three classifications based on annual dollar volume.
ABC analysis
Describe ABC inventory analysis in one sentence. Identify three policies that may be based upon the results of an ABC analysis.
ABC inventory analysis is a method for dividing on-hand inventory into three classifications based on annual dollar volume. Some policies include: (1) purchasing resources expended on supplier development should be much higher for individual A items than for C items; (2) A items should have tighter physical inventory control; and (3) forecasting A items may warrant more care than forecasting other items.
Compare the assumptions of the production order quantity model to those of the basic EOQ model.
All are the same, except for the assumption that receipt of inventory is instantaneous, which holds for the EOQ, but not the POQ.
ABC analysis classifies inventoried items into three groups, usually based on annual units or quantities used.
False
ABC analysis is based upon the principle that: A) all items in inventory must be monitored very closely. B) there are usually a few critical items, and many items that are less critical. C) an item is critical if its usage is high. D) more time should be spent on class "C" items because there are many more of them. E) as with grade distributions in many MBA courses, there should be more medium-level "B" items than either "A" or "C" items.
B
Cycle counting: A) is a process by which inventory records are verified once a year. B) eliminates annual inventory adjustments. C) provides a measure of inventory turnover. D) assumes that all inventory records must be verified with the same frequency. E) assumes that the most frequently used items must be counted more frequently.
B
Which of the following statements regarding Amazon.com is FALSE? A) The company was opened by Jeff Bezos in 1995. B) The company was founded as, and still is, a "virtual" retailer with no inventory. C) The company is now a world-class leader in warehouse automation and management. D) The company uses both United Parcel Service and the U.S. Postal Service as shippers. E) Amazon obtains its competitive advantage through inventory management.
B
A certain type of computer costs $1,000, and the annual holding cost is 25% of the value of the item. Annual demand is 10,000 units, and the order cost is $150 per order. What is the approximate economic order quantity? A) 16 B) 70 C) 110 D) 183 E) 600
C
For a certain item, the cost-minimizing order quantity obtained with the basic EOQ model is 200 units, and the total annual inventory (carrying and setup) cost is $600. What is the inventory carrying cost per unit per year for this item? A) $1.50 B) $2.00 C) $3.00 D) $150.00 E) not enough data to determine
C
The two most basic inventory questions answered by the typical inventory model are: A) timing of orders and cost of orders. B) order quantity and cost of orders. C) timing of orders and order quantity. D) order quantity and service level. E) ordering cost and carrying cost.
C
Which of the following statements regarding control of service inventories is TRUE? A) Service inventory is a fictional concept, because services are intangible. B) Service inventory needs no safety stock, because there's no such thing as a service stockout. C) Effective control of all goods leaving the facility is one applicable technique. D) Service inventory has carrying costs but no setup costs. E) Good personnel selection, training, and discipline are easy.
C
Which of the following is NOT an assumption of the economic order quantity model shown below? Q* = √ (2DS/H) A) Demand is known, constant, and independent. B) Lead time is known and constant. C) Quantity discounts are not possible. D) Production and use can occur simultaneously. E) The only variable costs are setup cost and holding (or carrying) cost.
D
Explain what "decoupling" means in the context of inventory management.
Decoupling means to separate various parts of the production process. Each of the parts can then function at its own best pace.
When quantity discounts are allowed, the cost-minimizing order quantity: A) is always an EOQ quantity. B) minimizes the sum of holding and ordering costs. C) minimizes the unit purchase price. D) may be a quantity below that at which one qualifies for that price. E) minimizes the sum of holding, ordering, and product costs.
E
Which of the following is an element of inventory holding costs? A) housing costs B) material handling costs C) investment costs D) pilferage, scrap, and obsolescence E) All of the above are elements of inventory holding costs.
E
Which of the following statements regarding the reorder point is TRUE? A) The reorder point is that quantity that triggers an action to restock an item. B) There is a reorder point even if lead time and demand during lead time are constant. C) The reorder point is larger than d × L if safety stock is present. D) A shorter lead time implies a smaller reorder point. E) All of the above are true.
E
Several inventory models assume "independent demand." Explain what that term means and why the assumption is important.
Independent demand means that demand for one particular item does not affect, and is not affected by, demand for a different item. When item demands are dependent, such as when wheels are demanded for assembly onto lawnmowers, different models (Chapter 14) may apply.
________ is the time between placement and receipt of an order.
Lead time
In the EOQ model, for a given level of demand, annual holding cost is larger as the order quantity is ________.
larger
In an economic order quantity problem, the total annual cost curve is at its ________ where annual holding costs equal annual setup costs.
minimum
What are the assumptions of the EOQ model?
(1) Demand for an item is known, reasonably constant, and independent of decisions for other items. (2) Lead time—that is, the time between placement and receipt of the order—is known and consistent. (3) Receipt of inventory is instantaneous and complete. (4) Quantity discounts are not possible. (5) The only variable costs are the cost of setting up or placing an order and the cost of holding or storing inventory over time. (6) Stockouts (shortages) can be completely avoided if orders are placed at the right time.
Identify the four types of inventory.
(1) raw material inventory; (2) work-in-process inventory; (3) maintenance/repair/operating supply (MRO) inventory; and (4) finished-goods inventory
Given the following data: D=65,000 units per year, S = $120 per setup, P = $5 per unit, and I = 25% per year, (a) calculate the EOQ, and (b) calculate annual costs of holding and setup following EOQ behavior.
(a) Q* = = 3532.7 units (b) TC = (S) + (H) = ($120) + (.25)($5) = $2207.94 + $2207.94 = $4415.88
Louisiana Specialty Foods can produce its famous meat pies at a rate of 1650 cases of 48 pies each per day. The firm distributes the pies to regional stores and restaurants at a steady rate of 250 cases per day. The cost of setup, cleanup, idle time in transition from other products to pies, etc., is $320. Annual holding costs are $11.50 per case. Assume 250 days per year. (a) Determine the optimum production run (batch size). (b) Determine the number of production runs per year. (c) Determine maximum inventory. (d) Determine total inventory-related (setup and carrying) costs per year (rounded to the nearest dollar).
(a) Q*p = = = 2024.7 or 2025 cases. (b) There will be 62,500 / 2024.7 = 30.87 runs per year. (c) The maximum inventory level is Q = 2024.7 = 1717.9 units. (d) Total inventory management costs are TC = ($320) + ($11.50) = $9878 + $9878 + $19,756.
Holstein Computing manufactures an inexpensive audio card (Audio Max) for assembly into several models of its microcomputers. The annual demand for this part is 100,000 units. The annual inventory carrying cost is $5 per unit and the cost of preparing an order and making production setup for the order is $750. The company operates 250 days per year. The machine used to manufacture this part has a production rate of 2000 units per day. (a) Calculate the optimum lot size. (b) How many lots are produced in a year? (c) What is the average inventory for Audio Max? (d) What is the annual holding and setup cost for Audio Max
(a) Q*p = = = 6123.7 or 6124 units. (b) There are approximately N = = = 16.33 cycles per year. (c) The maximum inventory is Q = 6123.7 = 4899 units; average inventory is 4899 / 2 = 2449.5 units. (d) Annual inventory management costs are 16.33($750) + 2449.5($5) = $12,247.50 + $12,247.50 = $24,495.
The new office supply discounter, Paper Clips, Etc. (PCE), sells a certain type of ergonomically correct office chair that costs $300. The annual holding cost rate is 40% of the item cost, annual demand is 900 units, and the ordering cost is $20 per order. The lead time is 4 days. Because demand is variable (standard deviation of daily demand is 2.4 chairs), PCE has decided to establish a customer service level of 90%. The store is open 300 days per year. a. What is the optimal order quantity? b. What is the safety stock? c. What is the reorder point?
(a) The optimal order quantity is Q* = = 17.32 or 17 chairs. (b) Safety Stock is SS = 1.28 ∙ 2.4 ∙ = 6.14 or 6 chairs. (c) ROP = lead time demand + safety stock = (3 chairs/day × 4 days) + 6.14 = 18 chairs.
A newspaper boy is trying to perfect his business in order to maximize the money he can save for a new car. Daily paper sales are normally distributed, with a mean of 100 and standard deviation of 10. He sells papers for $0.50 and pays $0.30 for them. Unsold papers are trashed with no salvage value. How many papers should he order each day and what % of the time will he experience a stockout? Are there any drawbacks to the order size proposed and how could the boy address such issues?
: Service level = Cs/(Cs + Co) = .2/(.2+.3) = .4 Z value for this service level is -.25 (read the value for .6 on the one-sided table and reverse its sign (since .6 - .5 = .1 and we want .5 - .1 = .4). Thus he should stock 100 + (-.25)(10) = 97.5 = 98 papers If service level is 40% he will experience stockout 1-Service level % of the time = 100% - 40% = 60% of the time will be a stockout The main drawback is the high % of the time that there will be a stockout. Customers could become unhappy and demand could plummet. Thus the boy must be careful to balance his optimum order size with one that will keep customers satisfied. Increasing the salvage value would go a long way to increasing the ideal service level.
Demand for a product is approximately normal, averaging 5 units per day with a standard deviation of 1 unit per day. Lead time for this product is approximately normal, averaging 10 days with a standard deviation of 3 days. What reorder point provides a service level of 90 percent?
: This problem requires formula (12-17), since both demand and lead time are variable. The value of z that corresponds to 90 percent service is 1.28 σDLT = = = 15.33 ROP = 5(10) + 1.28(15.33) = 50 + 19.62 = 69.62
A local club is selling Christmas trees and deciding how many to stock for the month of December. If demand is normally distributed with a mean of 100 and standard deviation of 20, trees have no salvage value at the end of the month, trees cost $20, and trees sell for $50 what is the service level? A) .60 B) .20 C) .84 D) .40 E) unable to determine given the above information
A
Q is to ________ systems as P is to ________ systems. A) fixed quantity, fixed period B) variable demand, constant demand C) variable lead time, variable demand D) variable quantity, variable period E) quality, price
A
The fixed-period inventory system requires more safety stock than a fixed-quantity system because: A) a stockout can occur during the review period as well as during the lead time. B) this model is used for products that have large standard deviations of demand. C) this model is used for products that require very high service levels. D) replenishment is not instantaneous. E) setup costs and holding costs are large.
A
The main trait of a single-period model is that: A) inventory has limited value after a certain period of time. B) it has the largest EOQ sizes. C) the order quantity should usually equal the expected value of demand. D) supply is limited. E) the cost of a shortage cannot be determined accurately.
A
Which of the following is a requirement of Q systems? A) perpetual inventory system B) constant order spacing C) variable lead time D) constant demand E) all of the above
A
What is a reorder point?
A reorder point is the inventory level (point) at which action is taken (an order placed) to replenish the stocked item.
A product whose EOQ is 40 units experiences a decrease in ordering cost from $90 per order to $10 per order. The revised EOQ is: A) three times as large. B) one-third as large. C) nine times as large. D) one-ninth as large. E) cannot be determined
B
A product whose EOQ is 400 units experiences a 50% increase in demand. The new EOQ is: A) unchanged. B) increased by less than 50%. C) increased by 50%. D) increased by more than 50%. E) cannot be determined
B
A production order quantity problem has a daily demand rate = 10 and a daily production rate = 50. The production order quantity for this problem is approximately 612 units. What is the average inventory for this problem? A) 61 B) 245 C) 300 D) 306 E) 490
B
A bakery wants to determine how many trays of doughnuts it should prepare each day. Demand is normal with a mean of 5 trays and standard deviation of 1 tray. If the owner wants a service level of at least 95%, how many trays should he prepare (rounded to the nearest whole tray)? Assume doughnuts have no salvage value after the day is complete. A) 5 B) 4 C) 6 D) 7 E) unable to determine with the above information
D
The proper quantity of safety stock is typically determined by: A) using a single-period model. B) carrying sufficient safety stock so as to eliminate all stockouts. C) multiplying the EOQ by the desired service level. D) setting the level of safety stock so that a given stockout risk is not exceeded. E) minimizing total costs.
D
The purpose of safety stock is to: A) replace failed units with good ones. B) eliminate the possibility of a stockout. C) eliminate the likelihood of a stockout due to erroneous inventory tally. D) control the likelihood of a stockout due to variable demand and/or lead time. E) protect the firm from a sudden decrease in demand.
D
Huckaby Motor Services, Inc. rebuilds small electrical items such as motors, alternators, and transformers, all using a certain type of copper wire. The firm's demand for this wire is approximately normal, averaging 20 spools per week, with a standard deviation of 6 spools per week. Cost per spool is $24; ordering costs are $25 per order; inventory handling cost is $4.00 per spool per year. Acquisition lead time is four weeks. The company works 50, 5-day weeks per year. a. What is the optimal size of an order, if minimization of inventory system cost is the objective? b. What are the safety stock and reorder point if the desired service level is 90%?
Demand is 20 × 50 = 1000 spools per year a. Q* = = 111.8 Huckaby should order 112 spools at one time. b. SS = 1.28 × 6 × = 15.36 or about 15 spools. The ROP is thus 20(4) + 15 = 95 spools.
ABC analysis is based on the presumption that carefully controlling all items is necessary to produce important inventory savings.
False
According to the global company profile, Amazon.com's advantage in inventory management comes from its almost fanatical use of economic order quantity and safety stock calculations.
False
Consider a local club selling Christmas trees. If trees cost $15 and sell for $60 with no salvage value, what is the ideal service level? If salvage value is increased to $5, what is the change in service level?
Original service level = Cs/(Cs + Co) = 45/(45 + 15) = .75 or 75% New service level = Cs/(Cs + Co) = 45/(45 + 10) = .82, or an increase of .07 or 7%
Your company has compiled the following data on the small set of products that comprise the specialty repair parts division. Perform ABC analysis on the data. Which products do you suggest the firm keep the tightest control over? Explain. SKU Annual Demand Unit Cost R11 250 $250 S22 75 $90 T33 20 $60 U44 150 $150 V55 100 $75
R11 and U44 represent over 80% of the firm's volume in this area. R11 is classified A, U44 is classified B, and all others are C. The tightest controls go to R11, then U44 because of their high percentage of sales volume.
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. (a) What is the optimal order quantity, given the following price breaks for purchasing the item? (b) What price should the firm pay per unit? (c) 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
Range 1 and Range 2 are irrelevant, because the EOQ is larger than the upper end of each range. Data for the other two ranges follow. Range 3 Range 4 Q* (Square root formula) 1805.788 2013.468 Order Quantity 1805.788 5000 Holding cost $415.33 $925.00 Setup cost $415.33 $150.00 Unit costs $23,000.00 $18,500.00 Total cost, Tc $23,830.66 $19,575.00 (a) Order 5000 units at a time. (b) The price is $1.85 per unit. (c) Total annual purchasing, holding, and setup costs = $19,575.00.
Demand for ice cream at the Ouachita Dairy can be approximated by a normal distribution with a mean of 47 gallons per day and a standard deviation of 8 gallons per day. The new management desires a service level of 95%. Lead time is four days; the dairy is open seven days a week. What reorder point would be consistent with the desired service level?
SS = 1.65 × 8 × = 26.4 gallons; and ROP = 47(4) + 26.4 = 214.4 gallons.
Milk is stocked at the grocery store each week. At the end of the week unsold milk is reduced in price by 70% and always sells for this lower price instantly. If weekly demand for milk is normally distributed with a mean of 200 gallons and standard deviation of 25 gallons, find the price for which a fresh gallon of milk sells. Assume a service level of 95% and that the store purchases milk for $2 per gallon.
Service level = Cs/(Cs + Co). If the selling price per gallon is X the salvage price is .3X. Thus, Cs = X-2 and Co = 2 - .3X. Solving .95 = X - 2/(X - 2 + 2 - .3X) gives X = $5.97, so the milk sells for $5.97 per gallon.
Daily demand for a product is normally distributed with a mean of 200 units and a standard deviation of 20 units. The firm currently uses a reorder point system, with a lead time of 4 days. a. What safety stock provides a 50% service level? b. What safety stock provides a 90% service level? c. What safety stock provides a 99% service level?
Standard deviation during lead time is 20 ∙ = 40 units. Z is 0 for 50% service level, 1.28 for 90%, and 2.33 for 99%. The resulting safety stocks are: a. 0, b. 51.2, and c. 93.2.
An organization has had a policy of ordering 70 units at a time. Their annual demand is 340 units, and the item has an annual carrying cost of $2. The assumptions of the EOQ are thought to apply. For what value of ordering cost would this order size be optimal?
Start with the economic order quantity model, and solve for S. 70 = becomes S = = $14.41
A product has a reorder point of 110 units, and is ordered four times a year on average. The following table shows the historical distribution of demand values observed during lead time. Demand Probability 100 .3 110 .4 120 .2 130 .1 Managers have noted that stockouts occur 30 percent of the time with this policy, and they question whether a change in inventory policy, to include some safety stock, might be an improvement. The managers realize that any safety stock would increase the service level, but they are worried about the increased costs of carrying the safety stock. Currently, stockouts are valued at $20 per unit per occurrence, while inventory carrying costs are $10 per unit per year. What is your advice? Do higher levels of safety stock add to total costs, or not? What level of safety stock is best?
The cheapest inventory policy has 10 units of safety stock. The managers should not be concerned about carrying cost only, but should consider that, while carrying costs rise, stockout costs fall.
A product has a reorder point of 260 units, and is ordered ten times a year on average. The following table shows the historical distribution of demand values observed during lead time. Demand Probability 240 .1 250 .2 260 .4 270 .2 280 .1 Currently, stockouts are valued at $5 per unit per occurrence, while inventory carrying costs are $2 per unit per year. Should the firm add safety stock? If so, how much safety stock should be added?
The current policy is not the cheapest inventory policy for this product. The cheapest inventory policy has a reorder point of 280, so the firm should add 20 units of safety stock.
The Winfield Distributing Company has maintained an 80% service level policy for inventory of string trimmers. Mean demand during lead time is 170 trimmers, and the standard deviation during lead time is 60 trimmers. The annual cost of carrying one trimmer in inventory is $6. The area sales people have recently told Winfield's management that they could expect a $400 improvement in profit (based on current figures of cost per trimmer) if the service level were increased to 99%. Is it worthwhile for Winfield to make this change?
This is solved with a cost comparison: total costs status quo compared to total costs at higher service, as amended by the increased profit. First calculate the safety stock. SS = 0.84 ∙ 60 = 50.4 trimmers at $6 each, this safety stock policy costs about $302.40. At a service level of 99%, the safety stock rises to 2.33 ∙ 60 = 139.8, which will cost $838.80. The added cost is $536.40, which is more than the added profit, so Winfield should not increase its service level.
Average daily demand for a product is normally distributed with a mean of 5 units and a standard deviation of 1 unit. Lead time is fixed at four days. (a) What is the reorder point if there is no safety stock? (b) What is the reorder point if the service level is 80 percent? (c) How much more safety stock is required if the service level is raised from 80 percent to 90 percent?
This problem requires formula 12-15, since demand is variable but lead time is constant. (a) With no safety stock, the reorder point is D × L = 5 × 4 = 20 units (b) For an 80 percent service level, Z is 0.84. The reorder point is ROP = DL + Z x σd × = 5 × 4 + 0.84 x 1 × = 20 + 1.7 = 21.7. (c) At 90 percent service, z=1.28. Safety stock is 1.28 × 1 × = 2.6 , an increase of 2.6 - 1.7 = 0.9 units.
Demand for a product is relatively constant at five units per day. Lead time for this product is normally distributed with a mean of ten days and a standard deviation of three days. (a) What reorder point provides a 50 percent service level? (b) What reorder point provides a 90 percent service level? (c) If the lead time standard deviation can be reduced from 3 days to 1, what reorder point now provides 90 percent service? How much is safety stock reduced by this change?
This problem requires formula 12-16 since demand is constant but lead time is variable. (a) There is no safety stock; the reorder point is 5 × 10 = 50 units. (b) The value of Z corresponding to 90 percent service is 1.28 ROP = 5(10) + 1.28(5)(3) = 50 + 19.2 = 69.2 units. (c) ROP = 50 + 1.28(5)(1) = 50 + 6.4 = 56.4; safety stock has decreased by 12.8 units.
A firm that makes electronic circuits has been ordering a certain raw material 250 ounces at a time. The firm estimates that carrying cost is I = 30% per year, and that ordering cost is about $20 per order. The current price of the ingredient is $200 per ounce. The assumptions of the basic EOQ model are thought to apply. For what value of annual demand is their action optimal?
This problem reverses the unknown of a standard EOQ problem. 250 = ; solving for D results in D = = 93,750
In cycle counting, the frequency of item counting and stock verification usually varies from item to item depending upon the item's classification.
True
A local artisan uses supplies purchased from an overseas supplier. The owner believes the assumptions of the EOQ model are met reasonably well. Minimization of inventory costs is her objective. Relevant data, from the files of the craft firm, are annual demand (D) =150 units, ordering cost (S) = $42 per order, and holding cost (H) = $4 per unit per year a. How many should she order at one time? b. How many times per year will she replenish her inventory of this material? c. What will be the total annual inventory (holding and setup) costs associated with this material (rounded to the nearest dollar)? d. If she discovered that the carrying cost had been overstated, and was in reality only $1 per unit per year, what is the corrected value of EOQ?
a. Q* = = 56.12. She should order 56 units at a time. b. N = = 2.67 She should place about 2.67 orders per year. c. Setup costs = 2.67($42) = $112. Holding costs = (56.12/2)($4) = $112. Total costs = $112 + $112 = $224. d. At the lower value for H, the EOQ will be doubled to 112.25.
Groundz Coffee Shop uses 4 pounds of a specialty tea weekly; each pound costs $16. Carrying costs are $1 per pound per week because space is very scarce. It costs the firm $8 to prepare an order. Assume the basic EOQ model with no shortages applies. Assume 52 weeks per year, closed on Mondays. a. How many pounds should Groundz order at a time? b. What is total annual cost (excluding item cost) of managing this item on a cost-minimizing basis? c. In pursuing lowest annual total cost, how many orders should Groundz place annually? d. How many days will there be between orders (assume 312 operating days) if Groundz practices EOQ behavior?
a. Q* = = 8. Groundz should order 8 pounds per order. b. TC = ($8) + ($1)(52) = $208 + $208 = $416. The firm will spend $416 annually. c. N = = 26. Groundz should order 26 times per year. d. Days between orders will be 312/26 or approximately every 12 working days.
Thomas' Bike Shop stocks a high volume item that has a normally distributed demand during lead time. The average daily demand is 70 units, the lead time is 4 days, and the standard deviation of demand during lead time is 15. a. How much safety stock provides a 95% service level to Thomas? b. What should the reorder point be?
a. SS = 1.65 × 15 = 24.75 units or 25 units b. ROP = (70)(4) + 25 = 305 units.
Pointe au Chien Containers, Inc., manufactures in batches, and the manufactured items are placed in stock. Specifically, the firm is questioning how best to manage a specific wooden crate for shipping live seafood, which is sold primarily by the mail/phone order marketing division of the firm. The firm has estimated that carrying cost is $4 per unit per year. In addition, annual demand = 60,000 units, and setup cost is $300. The firm currently plans to satisfy all customer demand from stock on hand. Demand is known and constant. The production rate is nearly instantaneous. a. What is the cost minimizing size of the manufacturing batch? b. What is the total annual holding and setup cost of this solution?
a. The cost-minimizing batch size is Q* = = 3000 crates. b. This will cost ($300) + ($4) = $6000 + $6000 = $12,000 per year.
Joe's Camera shop has a favorite model that has annual sales of 145. The cost to place an order to replenish inventory is $25 per order, and annual inventory holding cost per unit is $20. Assume the store is open 350 days per year. a. What is the optimal order size? b. What is the optimal number of orders per year? c. What is the optimal number of days between orders? d. What is the annual holding and setup cost?
a. The optimal order size is Q* = = 19.04, or approximately 19 units. b. The optimal number of orders per year is N = 145 / 19.04 = 7.62 or 8 orders. c. The optimal number of days between orders is 350/7.62 = 45.9 days. d. The annual inventory cost is ($25) + ($20) = $190.39 + $190.40 = $380.79
Consider a product with a daily demand of 400 units, a setup cost per production run of $100, a monthly holding cost per unit of $2.00, and an annual production rate of 292,000 units. The firm operates and experiences demand 365 days per year. Suppose that management mistakenly used the basic EOQ model to calculate the batch size instead of using the POQ model. How much money per year has that mistake cost the company?
d = 400 units D = 400(365) = 146,000 units S = $100 H = $2.00(12) = $24 p = 292,000 / 365 = 800 units The firm actually ordered EOQ = {[2(146,000)100] / 24}1/2 = 1103 units. The firm should have ordered POQ = {[2(146,000)100] / [24(1 - 400/800)]}1/2 = 1560 units. The annual cost of the wrong policy is (146,000/1103)($100) + (1103/2)($24)(1 - 400/800) = $13,237 + $6,618 = $19,855 The annual cost of the correct policy is (146,000/1560)($100) + (1560/2)($24)(1 - 400/800) = $9,359 + $9,360 = $18,719 Thus, the mistake cost $19,855 - $18,719 = $1,136 per year.
When demand is constant and lead time is variable, the safety stock computation requires three inputs: the value of Z, ________, and the standard deviation of lead time.
daily demand
If a safety stock problem includes parameters for average daily demand, standard deviation of demand, and lead time, then ________ is variable and ________ is constant.
demand; lead time
What are the four functions of inventory?
(1) to provide a selection of goods for anticipated customer demand and to separate the firm from fluctuations in that demand; (2) to decouple various parts of the production process; (3) to take advantage of quantity discounts; and (4) to hedge against inflation
In the basic EOQ model, if D = 6000 per year, S = $100, and holding cost = $5 per unit per month, what is the economic order quantity? A) 24 B) 100 C) 141 D) 490 E) 600
C
Most inventory models attempt to minimize: A) the likelihood of a stockout. B) the number of items ordered. C) total inventory-based costs. D) the number of orders placed. E) the safety stock.
C
What is MRO an acronym for? What is the function of MRO inventories?
MRO inventories are devoted to maintenance/repair/operating supplies. They exist because the need and timing for maintenance and repair of some equipment are unknown.
Consider two inventory problems with identical demand, holding cost, and setup cost. In one, goods arrive instantly, but in the other goods arrive at a measurable rate. Which of these problems will have the larger optimal order quantity? Why?
The problem with instantaneous delivery is an EOQ problem, and its optimal order quantity is Q*. The problem with noninstantaneous delivery is a POQ problem, with optimal order quantity Q*p. The POQ problem will yield a higher order quantity than the basic model, other things equal, because the effective annual holding cost is lower in the POQ model. This occurs because most of the inventory arrives later (hence is not held from the beginning) compared to the EOQ environment.
A printing company estimates that it will require 1,000 reams of a certain type of paper in a given period. The cost of carrying one unit in inventory for that period is 50 cents. The company buys the paper from a wholesaler in the same town, sending its own truck to pick up the orders at a fixed cost of $20.00 per trip. Treating this cost as the order cost, (a) what is the optimum number of reams to buy at one time? (b) How many times should lots of this size be bought during this period? (c) What is the minimum cost (holding and setup) of maintaining inventory on this item for the period? (d) Of this total cost, how much is carrying cost and how much is ordering cost?
This is an EOQ problem, even though the time period is not a year. All that is required is that the demand value and the carrying cost share the same time reference. This will require approximately 3.5 orders per period. Setup costs and carrying costs are each $70.71, and the annual total is $141.42. (a) EOQ = = 283 ; (b) N = = 3.54 (d) Carrying cost = ($0.50) = $70.71 ; setup cost = ($20) = $70.71 (c) Total cost = $70.71 + $70.71 = $141.42
In the quantity discount model, it is possible to have a cost-minimizing solution where annual ordering costs do not equal annual carrying costs.
True
The demand for automobiles would be considered as independent demand.
True
Identify the typical cost components that constitute ordering costs in inventory systems.
Typical components of ordering costs include cost of supplies, forms, order processing, clerical support, and so forth.
A toy manufacturer makes its own wind-up motors, which are then put into its toys. While the toy manufacturing process is continuous, the motors are intermittent flow. Data on the manufacture of the motors appears below. Annual demand (D) = 50,000 units Daily subassembly production rate = 1,000 Setup cost (S) = $85 per batch Daily subassembly usage rate = 200 Carrying cost = $.20 per unit per year (a) To minimize cost, how large should each batch of subassemblies be? (b) Approximately how many days are required to produce a batch? (c) How long is a complete cycle? (d) What is the average inventory for this problem? (e) What is the total annual inventory cost (holding plus setup) of the optimal behavior in this problem?
(a) Q*p = = 7288.7 or 7289 units. (b) It will take approximately 7289/1000 = 7.3 days to make these units. (c) A complete cycle will last approximately 7289 / 200 = 36.445 days. (d) The maximum inventory level is Q = 7288.7 = 5831 units. Average inventory is 5831 /2 = 2,915 (not one-half of 7283). (e) Total inventory management costs are TC = ($85) + ($0.20) = $583.09 + $583.09 + $1,166.19
The Rushton Trash Company stocks, among many other products, a certain container, each of which occupies four square feet of warehouse space. The warehouse space currently available for storing this product is limited to 600 square feet. Demand for the product is 15,000 units per year. Holding costs are $4 per container per year. Ordering costs are $5 per order. (a) What is the cost-minimizing order quantity decision for Rushton? (b) What is the total inventory-related cost of this decision? (c) What is the total inventory-related cost of managing the inventory of this product, when the limited amount of warehouse space is taken into account? (d) What would the firm be willing to pay for additional warehouse space?
(a) The EOQ is about 194, more than there is room to store. (b) Total cost at Q=194 is (15,000 / 194)($5) + (194 / 2)($4) = $774.60. (c) The warehouse will hold only 150 containers. The annual cost at Q = 150 is 100 × 5 + 75 × 4 = $800. (d) From (b), the EOQ cost is $25.40 less than current cost, which reflects the limited storage space. Rushton would consider paying up to $25.40 for a year's rental of enough space to store 44 additional containers.
A product has a demand of 4000 units per year. Ordering cost is $20, and holding cost is $4 per unit per year. The EOQ model is appropriate. The cost-minimizing solution for this product will cost ________ per year in total annual inventory (holding and setup) costs. A) $400 B) $800 C) $1200 D) Zero; this is a class C item. E) Cannot be determined because the unit price is not known.
B
A product has a demand of 4000 units per year. Ordering cost is $20, and holding cost is $4 per unit per year. The cost-minimizing solution for this product is to order: A) all 4000 units at one time. B) 200 units per order. C) every 20 days. D) 10 times per year. E) none of the above
B
An inventory decision rule states, "When the inventory level goes down to 14 gearboxes, 100 gearboxes will be ordered." Which of the following statements is TRUE? A) One hundred is the reorder point, and 14 is the order quantity. B) Fourteen is the reorder point, and 100 is the order quantity. C) The number 100 is a function of demand during lead time. D) Fourteen is the safety stock, and 100 is the reorder point. E) None of the above is true.
B
Which of the following statements regarding the production order quantity model is TRUE? A) It applies only to items produced in the firm's own production departments. B) It relaxes the assumption that all the order quantity is received at one time. C) It relaxes the assumption that the demand rate is constant. D) It minimizes the total production costs. E) It minimizes inventory.
B
If the actual order quantity is the economic order quantity in a problem that meets the assumptions of the economic order quantity model shown below, the average amount of inventory on hand: Q* = √ (2DS/H) A) is smaller than the holding cost per unit. B) is zero. C) is one-half of the economic order quantity. D) is affected by the amount of product cost. E) goes down if the holding cost per unit goes down.
C
All EXCEPT which of the following statements about ABC analysis are true? A) In ABC analysis, inventory may be categorized by measures other than dollar volume. B) ABC analysis categorizes on-hand inventory into three groups based on annual dollar volume. C) ABC analysis is an application of the Pareto principle. D) ABC analysis suggests that all items require the same high degree of control. E) ABC analysis suggests that there are the critical few and the trivial many inventory items.
D
Among the advantages of cycle counting is that it: A) makes the annual physical inventory more acceptable to management. B) does not require the detailed records necessary when annual physical inventory is used. C) does not require highly trained people. D) allows more rapid identification of errors and consequent remedial action than is possible with annual physical inventory. E) does not need to be performed for less expensive items.
D
Which of the following statements about ABC analysis is FALSE? A) ABC analysis is based on the presumption that controlling the few most important items produces the vast majority of inventory savings. B) In ABC analysis, "A" items should have tighter physical inventory control than "B" or "C" items have. C) In ABC analysis, forecasting methods for "C" items may be less sophisticated than for "A" items. D) ABC analysis is based on the presumption that all items must be tightly controlled to produce important cost savings. E) Criteria other than annual dollar volume, such as high holding cost or delivery problems, can determine item classification in ABC analysis.
D
Which of the following statements about quantity discounts is FALSE? A) The cost-minimizing solution may or may not be where annual holding costs equal annual ordering costs. B) In inventory management, item cost becomes relevant to order quantity decisions when a quantity discount is available. C) If carrying costs are expressed as a percentage of value, EOQ is larger at each lower price in the discount schedule. D) The larger the annual demand, the less attractive a discount schedule will be. E) The smaller the ordering cost, the less attractive a discount schedule will be.
D
Which of the following statements about the basic EOQ model is FALSE? A) If the setup cost were to decrease, the EOQ would fall. B) If annual demand were to double, the number of orders per year would increase. C) If the ordering cost were to increase, the EOQ would rise. D) If annual demand were to double, the EOQ would also double. E) All of the above statements are true.
D
Which of the following would NOT generally be a motive for a firm to hold inventories? A) to decouple various parts of the production process B) to provide a selection of goods for anticipated customer demand and to separate the firm from fluctuations in that demand C) to take advantage of quantity discounts D) to minimize holding costs E) to hedge against inflation
D
Which of these statements about the production order quantity model is FALSE? A) The production order quantity model is appropriate when the assumptions of the basic EOQ model are met, except that receipt is noninstantaneous. B) Because receipt is noninstantaneous, some units are used immediately and not stored in inventory. C) Average inventory is less than one-half of the production order quantity. D) All else equal, the smaller the ratio of demand rate to production rate, the larger is the production order quantity. E) None of the above is false.
D
ABC analysis divides on-hand inventory into three classes, generally based upon which of the following? A) item quality B) unit price C) the number of units on hand D) annual demand E) annual dollar volume
E
Which category of inventory holding costs has a much higher percentage than average for rapid-change industries such as PCs and cell phones? A) housing costs B) material handling costs C) labor cost D) investment costs E) pilferage, scrap, and obsolescence
E
Which of the following is a function of inventory? A) to decouple various parts of the production process B) to provide a selection of goods for anticipated customer demand and to separate the firm from fluctuations in that demand C) to take advantage of quantity discounts D) to hedge against inflation E) All of the above are functions of inventory
E
Which of the following statements about the basic EOQ model is TRUE? A) If the ordering cost were to double, the EOQ would rise. B) If annual demand were to double, the EOQ would increase. C) If the carrying cost were to increase, the EOQ would fall. D) If annual demand were to double, the number of orders per year would increase. E) All of the above statements are true.
E
Central University uses $123,000 of a particular toner cartridge for laser printers in the student computer labs each year. The purchasing director of the university estimates the ordering cost at $45 and thinks that the university can hold this type of inventory at an annual storage cost of 22% of the purchase price. How many months' supply should the purchasing director order at one time to minimize the total annual cost of purchasing and carrying?
First, calculate the EOQ from the data provided. In this problem, the "units" are dollars, and the "price" of each is 1. Q* = = 7093.53 One month's usage is 123000/12 = $10,250. EOQ = 7094. Month's usage = 7094/10250 = 0.69, or about three week's usage. (This is supported by the order frequency of 17 per year).
________ inventory is material that is usually purchased, but has yet to enter the manufacturing process.
Raw material
Lead time for one of Montegut Manufacturing's fastest moving products is 4 days. Demand during this period averages 100 units per day. What would be an appropriate re-order point?
Re-order point = demand during lead time = 100 units/day × 4 days = 400 units.
Define shrinkage. Identify three or more examples of shrinkage.
Shrinkage is retail inventory that is unaccounted for between receipt and sale. Examples will vary, but may include damage and theft as well as sloppy paperwork.
The annual demand, ordering cost, and the annual inventory carrying cost rate for a certain item are D = 600 units, S = $20/order and I = 30% of item price. Price is established by the following quantity discount schedule. What should the order quantity be in order to minimize the total annual cost?
The firm should order 250 units at a time, paying $4.10 per unit. Holding costs are much larger than ordering costs, but this is offset by the unit price reduction. The annual total cost is $2,661.75. The EOQ value for the $4.50 price has an annual cost of $2,880.
Perform an ABC analysis on the following set of products. Item Annual Demand Unit Cost A211 1200 $9 B390 100 $90 C003 4500 $6 D100 400 $150 E707 35 $2000 F660 250 $120 G473 1000 $90 H921 100 $75
The table below details the contribution of each of the eight products. Item G473 is clearly an A item, and items A211, B390, and H921 are all C items. Other classifications are somewhat subjective, but one choice is to label E707 and D100 as A items, and F660 and C003 as B items.
Montegut Manufacturing produces a product for which the annual demand is 10,000 units. Production averages 100 units per day, while demand is 40 units per day. Holding costs are $2.00 per unit per year, and setup cost is $200.00. (a) If the firm wishes to produce this product in economic batches, what size batch should be used? (b) What is the maximum inventory level? (c) How many order cycles are there per year? (d) What are the total annual holding and setup costs?
This is a production order quantity problem. (a) Q*p = = = 1825.7 or 1826 units (b) The maximum inventory level is Q = 1825.7 = 1095.45 or 1095 units (c) There are approximately N = = = 5.48 cycles per year (d) Total annual costs = (5.48)($200) + (1095.45/2)$2 = $2,190.89 or $2,191
In some inventory models, the optimal behavior occurs where ordering costs and carrying costs are equal to one another. Provide an example of a model where this rule does not hold; explain how the model's results are optimal anyway.
This rule will not hold in all instances of the quantity discount model. In order to take advantage of a discount, it may be cheaper to order a quantity that is not an EOQ. The goal in quantity discount models is to minimize the sum of ordering, carrying, and product costs.
Inventory that separates various parts of the production process performs a(n) ________ function.
decoupling
In the production order quantity model, the fraction of inventory that is used immediately and not stored is represented by the ratio of ________.
demand rate to production rate
Amazon's original concept of operating without inventory has given way to a model in which Amazon is a world-class leader in ________.
warehouse automation and management
