Operations Management: Processes and Supply Chains, 12e (Krajewski)
Supplement C Special Inventory Models
1) The economic production lot size represents the maximum quantity of on-hand inventory for a
manufacturer.
2) For analysis using the economic production lot size (ELS) model to be useful, the producer must be
able to produce the item faster than it is consumed.
3) Consider a noninstantaneous replenishment situation in which the production rate is 100 units per day,
the demand rate is four units per day, and the economic production lot size is 500 units. Which of the
following statements is true?
A) The average cycle inventory is fewer than 225 units.
B) The average cycle inventory is greater than 300 units.
C) The rate of buildup in cycle inventory during the production cycle is fewer than 100 units per day.
D) The rate of buildup in cycle inventory during the production cycle is greater than or equal to 400 units
per day.
Scenario C.1
Jerry Allison is in charge of production for a small producer of plumbing supplies. The cricket model has
an estimated annual demand of 12,000 units and can be produced at a production rate of 90 units per day.
The company produces (and sells) the cricket 300 days per year. Setup cost to produce this model
averages $22 and the item has a holding cost of $3 per unit per year.
4) Use the information in Scenario C.1. What is the economic production lot size (ELS)?
A) fewer than or equal to 400 units
B) greater than 400 units but fewer than or equal to 480 units
C) greater than 480 units but fewer than or equal to 500 units
D) greater than 500 units
5) Use the information in Scenario C.1. How many production runs per year are needed if Jerry chooses
to produce at his economic production lot size (ELS)?
A) fewer than or equal to 10 runs
B) greater than 10 runs but fewer than or equal to 20 runs
C) greater than 20 runs but fewer than or equal to 30 runs
D) greater than 30 runs
6) Use the information in Scenario C.1. If Jerry chooses to produce batches dictated by the economic
production lot size (ELS) model, how many days elapse between the start of consecutive production runs
(what is the time between runs or TBO)?
A) fewer than or equal to 8 days
B) greater than 8 days but fewer than or equal to 10 days
C) greater than 10 days but fewer than or equal to 12 days
D) greater than 12 days
7) Use the information in Scenario C.1. What is the maximum inventory if Jerry chooses to produce at the
economic production lot size (ELS)?
A) fewer than or equal to 300 units
B) greater than 300 units but fewer than or equal to 320 units
C) greater than 320 units but fewer than or equal to 340 units
D) greater than 340 units
8) Use the information in Scenario C.1. If Jerry chooses to produce the batch size suggested by the
economic production lot size (ELS) model, what is the annual cost?
A) less than or equal to $900
B) greater than $900 but less than or equal to $950
C) greater than $950 but less than or equal to $1,000
D) greater than $1,000
9) Consider a manufacturer that uses the economic production lot size (ELS) model. What must be the
relationship be between production rate and demand rate for the producer to spend double the time in
the production and demand portion of the inventory cycle than they spend in only the demand portion of
the inventory cycle?
A) p = 1.5d
B) p = d
C) 2p = d
D) p = 2d
10) Consider a manufacturer that uses the economic production lot size (ELS) model. What must be the
relationship be between production rate and demand rate for the producer to spend exactly the same
time in the production and demand portion of the inventory cycle as they spend in only the demand
portion of the inventory cycle?
A) p = d
B) p = 0.5d
C) p = 2d
D) p = 1.5d
11) The time between orders is given by the formula ELS/D. What is the significance of its inverse, D/ELS?
A) the number of orders per year
B) the time between consuming an order
C) the ratio of demand only to production and demand cycles
D) the ratio of the maximum inventory to the production quantity
12) Consider a manufacturer that uses the economic production lot size (ELS) model. What must the
relationship be between production rate and demand rate for the producer to realize a maximum
inventory that is exactly two-thirds of their lot size?
A) p = 2d
B) p = 0.5d
C) p = 0.33d
D) p = 3d
13) Warren’s Ice Cream makes 4 different flavors of ice cream using their secret process and top-secret
recipes. Each of their flavors is equally popular and experiences a demand of 5,000 gallons/year. Warren’s
process is capable of producing 100 gallons/day once they incur the $25 setup cost. The ice cream holding
cost is 10% of the $5 per gallon price. Warren’s plant runs 250 days a year and stays busy doing so, but
management feels they can add another flavor to their product line and increase their revenue. Which of
the following statements is appropriate for this scenario?
A) Warren’s can comfortably add a fifth flavor without increasing the number of days they operate.
B) Warren’s cannot add the fifth flavor because the holding cost would increase.
C) Warren‘s can add the fifth flavor only if there is zero setup time between flavors.
D) Warren’s cannot add the fifth flavor because demand would exceed capacity.
14) In a noninstantaneous replenishment model, as the daily demand approaches the daily production
rate, the:
A) number of production runs per year decreases.
B) length in days of a production run increases.
C) economic lot size increases.
D) time between production runs decreases.
15) The ________ is the optimal lot size in situations in which replenishment is not instantaneous.
16) A manufacturer produces aluminum cans internally rather than purchasing them and uses the
economic production lot size equation to govern this process. The length of time that the aluminum can
batch runs is given by the equation ________ and the time between the start of one batch of cans to the
next is found by the equation ________.
17) The pile of inventory accumulated in an economic production lot size situation is ________ than the
lot size dictated by the ELS calculation.
18) In an economic production lot size situation, the production rate is always ________ than the demand
rate.
19) In an economic production lot size situation, the producer is producing half the time if the ratio of
production rate to demand rate is ________.
20) Briefly explain why the economic production lot size (ELS) is actually larger than the EOQ when there
are noninstantaneous replenishments.
21) Sketch the economic production lot size (ELS) graph of inventory level as a function of time and label
all elements of the graph.
Answer:
22) A production manager is making a decision on batch size for a product with an annual demand of
25,000 units per year. The setup cost for each batch is $45 and once the setup is complete, the product
may be produced at the rate of 650 units per day. There is a holding cost of $2 per unit per year and the
plant operates on a 250-day production year. How big should the production batch be and how long (in
days) will it take to produce the batch?
23) Walter White must satisfy an annual demand of 50,000 pounds per year. The setup cost for each batch
is $6,500 and once the setup is complete, the product may be produced at the rate of 1800 pounds per day.
There is a holding cost of $15 per unit per year and the plant operates on a 350-day production year. How
big should the production batch be and how long (in days) will it take to produce the batch?
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24) Walter White must satisfy an annual demand of 50,000 pounds per year. The setup cost for each batch
is $6,500 and once the setup is complete, the product may be produced at the rate of 1,800 pounds per
day. There is a holding cost of $15 per unit per year and the plant operates on a 350-day production year.
Determine the relevant parameters and sketch the inventory cycle through two complete cycles, labeling
all lines and vertices.
25) A production manager uses the economic lot size approach to determine the batch size for a product
with an annual demand of 20,000 units per year. The setup cost for each batch is $50 and once the setup is
complete, the product may be produced at the rate of 800 units per day. There is a holding cost of $2 per
unit per year and the plant operates on a 250-day production year. If the machine used to produce this
product is needed for another item and it takes one day to set up regardless of product, how many
production days are available for production of the new item?
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C.2 Quantity Discounts
1) When facing quantity discounts, the EOQ found with the lowest price level is always the lowest total
cost plan.
2) A pencil supplier just introduced quantity discounts. The price schedule follows.
Order Quantity
Price per Unit
000 – 199
$4.00
200 – 399
$3.75
400 and more
$3.50
XYZ store’s annual demand remains at 350 units and ordering cost at $2 per order. If annual holding cost
is 30 percent of the pencils’ per-unit price, what order quantity should XYZ select to minimize all costs?
A) fewer than or equal to 150 units
B) greater than 150 units but fewer than or equal to 199 units
C) greater than 199 units but fewer than or equal to 399 units
D) greater than 399 units
3) Which one of the following statements about quantity discounts is best?
A) The minimum cost point on each price curve is always feasible.
B) A price break is the maximum quantity needed to get a discount.
C) If the EOQ for the lowest price is feasible, this is the best lot size.
D) Either price or quantity is sufficient for the search for the best lot size.