Supplement D  Special Inventory Models

Supplement

D / Special Inventory Models

TRUE/FALSE

  1. The economic production lot size represents the maximum quantity of on-hand inventory for a manufacturer.

Answer: False

Reference: Noninstantaneous Replenishment

Difficulty: Moderate

Keywords: ELS, economic, product, lot, size, inventory

  1. 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.

Answer: True

Reference: Noninstantaneous Replenishment

Difficulty: Moderate

Keywords: ELS, economic, product, lot, size

  1. When facing quantity discounts, the EOQ found with the lowest price level is the lowest total cost plan.

Answer: False

Reference: Quantity Discounts

Difficulty: Moderate

Keywords: EOQ, quantity, discount

  1. The one-period inventory model is commonly known as the newsboy problem.

Answer: True

Reference: One-Period Decisions

Difficulty: Moderate

Keywords: newsboy, one-period, period

MULTIPLE CHOICE

  1. 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?
  2. The average cycle inventory is fewer than 225 units.
  3. The average cycle inventory is greater than 300 units.
  4. The rate of buildup in cycle inventory during the production cycle is fewer than 100 units per day.
  5. The rate of buildup in cycle inventory during the production cycle is greater than or equal to 400 units per day.

Answer: c

Reference: Noninstantaneous Replenishment

Difficulty: Moderate

Keywords: noninstantaneous, replenishment, buildup

Scenario D.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.

  1. Use the information in Scenario D.1. What is the economic production lot size (ELS)?
  2. Fewer than or equal to 400 units
  3. Greater than 400 units but fewer than or equal to 480 units
  4. Greater than 480 units but fewer than or equal to 500 units
  5. Greater than 500 units

Answer: d

Reference: Noninstantaneous Replenishment

Difficulty: Moderate

Keywords: ELS, noninstantaneous, replenishment, economic, production, lot

  1. Use the information in Scenario D.1. How many production runs per year are needed if Jerry chooses to produce at his economic production lot size (ELS)?
  2. Fewer than or equal to 10 runs
  3. Greater than 10 runs but fewer than or equal to 20 runs
  4. Greater than 20 runs but fewer than or equal to 30 runs
  5. Greater than 30 runs

Answer: c

Reference: Noninstantaneous Replenishment

Difficulty: Moderate

Keywords: ELS, noninstantaneous, replenishment, economic, production, run

  1. Use the information in Scenario D.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)?
  2. Fewer than or equal to 8 days
  3. Greater than 8 days but fewer than or equal to 10 days
  4. Greater than 10 days but fewer than or equal to 12 days
  5. Greater than 12 days

Answer: d

Reference: Noninstantaneous Replenishment

Difficulty: Moderate

Keywords: ELS, noninstantaneous, replenishment, economic, production, TBO, cycle

  1. Use the information in Scenario D.1. What is the maximum inventory if Jerry chooses to produce at the economic production lot size (ELS)?
  2. Fewer than or equal to 300 units
  3. Greater than 300 units but fewer than or equal to 320 units
  4. Greater than 320 units but fewer than or equal to 340 units
  5. Greater than 340 units

Answer: b

Reference: Noninstantaneous Replenishment

Difficulty: Moderate

Keywords: ELS, noninstantaneous, replenishment, economic, production, maximum, inventory

  1. Use the information in Scenario D.1. If Jerry chooses to produce the batch size suggested by the economic production lot size (ELS) model, what is the annual cost?
  2. Less than or equal to $900
  3. Greater than $900 but less than or equal to $950
  4. Greater than $950 but less than or equal to $1000
  5. Greater than $1000

Answer: b

Reference: Noninstantaneous Replenishment

Difficulty: Moderate

Keywords: ELS, noninstantaneous, replenishment, economic, production, total, cost

  1. 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 5000 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?
  2. Warren’s can comfortably add a fifth flavor without increasing the number of days they operate.
  3. Warren’s cannot add the fifth flavor because the holding cost would increase.
  4. Warren’s can add the fifth flavor only if there is zero setup time between flavors.
  5. Warren’s cannot add the fifth flavor because demand would exceed capacity.

Answer: c

Reference: Noninstantaneous Replenishment

Difficulty: Difficult

Keywords: ELS, noninstantaneous, replenishment, economic, production, total, cost

  1. In a noninstantaneous replenishment model, as the daily demand approaches the daily production rate:
  2. the number of production runs per year decreases.
  3. the length in days of a production run increases.
  4. the economic lot size increases.
  5. the time between production runs decreases.

Answer: d

Reference: Noninstantaneous Replenishment

Difficulty: Moderate

Keywords: ELS, noninstantaneous, replenishment, economic, production, total, cost

  1. A pencil supplier just introduced quantity discounts. The price schedule follows.

Order Quantity / Price per Unit
000–199 / $4.00
200–399 / $3.00
400 and more / $2.00

XYZ store’s annual demand remains at 500 units and ordering cost at $10 per order. If annual holding cost is 10 percent of the pencils’ per-unit price, what order quantity should XYZ select to minimize all costs?

  1. Fewer than or equal to 150 units
  2. Greater than 150 units but fewer than or equal to 199 units
  3. Greater than 199 units but fewer than or equal to 399 units
  4. Greater than 399 units

Answer: d

Reference: Quantity Discounts

Difficulty: Moderate

Keywords: quantity, discount, order

  1. Which one of the following statements about quantity discounts is best?
  2. The minimum cost point on each price curve is always feasible.
  3. A price break is the maximum quantity needed to get a discount.
  4. If the EOQ for the lowest price is feasible, this is the best lot size.
  5. Either price or quantity is sufficient for the search for the best lot size.

Answer: c

Reference: Quantity Discounts

Difficulty: Moderate

Keywords: quantity, discount, feasible

  1. As an inventory manager, you must decide on the order quantity for an item. Its annual demand is 300 units. Ordering cost is $20 each time an order is placed, and the holding cost is 30 percent of the per-unit price. Your supplier provided the following price schedule.

Price per Unit / Order Quantity
$6.00 / 000–149
$5.00 / 150–199
$4.00 / 200 and more

What ordering-quantity policy do you recommend?

  1. Fewer than or equal to 50 units
  2. Greater than 50 units but fewer than or equal to 149
  3. Greater than 149 units but fewer than or equal to 199 units
  4. More than 199 units

Answer: d

Reference: Quantity Discount

Difficulty: Moderate

Keywords: quantity, discount, order

  1. Use the information in Scenario D.2. What is the payoff with an order quantity (Q) of 40 units if the demand (D) is 30 units?
  2. Less than or equal to $2,000
  3. Greater than $2,000 but less than or equal to $4,000
  4. Greater than $4,000 but less than or equal to $6,000
  5. Greater than $6,000

Answer: c

Reference: One-Period Decisions

Difficulty: Moderate

Keywords: one-period, period, order, quantity, payoff

  1. Use the information in Scenario D.2.. What is the best order quantity?
  2. Fewer than or equal to 20 units
  3. Greater than 20 units but fewer than or equal to 40 units
  4. Greater than 40 units but fewer than or equal to 50 units
  5. Greater than 50 units

Answer: b

Reference: One-Period Decisions

Difficulty: Moderate

Keywords: one-period, period, order, quantity

  1. Use the information in Scenario D.3. What is the payoff when 40 units are ordered but a demand of 50 materializes?
  2. $150
  3. $300
  4. $450
  5. $600

Answer: d

Reference: One-Period Decisions

Difficulty: Moderate

Keywords: one-period, period, payoff, quantity

  1. Use the information in Scenario D.3. What is the payoff when 40 units are ordered but a demand of 30 materializes?
  2. $0
  3. $100
  4. $350
  5. $450

Answer: c

Reference: One-Period Decisions

Difficulty: Moderate

Keywords: payoff, one-period, period, quantity

  1. Use the information in Scenario D.3. What is the order quantity with the highest expected payoff?
  2. 20 units
  3. 30 units
  4. 40 units
  5. 50 units

Answer: b

Reference: One-Period Decisions

Difficulty: Moderate

Keywords: one-period, order, quantity, payoff

  1. A world traveler prepares to leave the comforts of home for a back to nature visit to Gilligan’s Island, where all transactions are conducted in coconuts and the banking system is completely undeveloped. The traveler can buy cocoanuts for $2 each before the journey. If he fails to bring enough cocoanuts with him and runs out, he must get some cocoanuts flown in at a cost of $5 each. If he finishes his vacation and has leftover cocoanuts he can cash them in when he returns home, but will receive only $1.50 per cocoanut. What is his loss per unit if he overstocks on cocoanuts prior to leaving home?
  2. $0.50
  3. $1
  4. $3.50
  5. $4.50

Answer: a

Reference: One-Period Decisions

Difficulty: Easy

Keywords: one-period, order, quantity, payoff

  1. Which of these statements about the one-period model is best?
  2. Purchasing a quantity with the highest expected payoff will result in a positive payoff regardless of demand during the period.
  3. The loss per unit cannot exceed the profit per unit.
  4. If demand exceeds the purchased quantity then the payoff exceeds the expected payoff.
  5. The expected payoff is always less than the actual payoff.

Answer: c

Reference: One-Period Decisions

Difficulty: Easy

Keywords: one-period, order, quantity, payoff

FILL In THE BLANK

  1. The ______is the optimal lot size in situations in which replenishment is not instantaneous.

Answer: economic production lot size, ELS

Reference: Noninstantaneous Replenishment

Difficulty: Moderate

Keywords: economic, lot, size, ELS, replenishment

  1. 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 thealuminum can batch runs is ______and the time between the start of one batch of cans to the next is ______.

Answer: ELS/p, ELS/d

Reference: Noninstantaneous Replenishment

Difficulty: Hard

Keywords: economic, lot, size, ELS

  1. A(n) ______is the minimum quantity needed to receive a discount.

Answer: price break

Reference: Quantity Discounts

Difficulty: Moderate

Keywords: price, break, discount, quantity

  1. The need for one-time inventory decisions also can arise in manufacturing plants when ______items are made to a single order and ______are high.

Answer: customized (specials), scrap quantities

Reference: One-Period Decisions

Difficulty: Hard

Keywords: one-period, newsboy, scrap, special

SHORT ANSWERS

  1. Briefly explain why the economic production lot size (ELS) is actually larger than the EOQ when there are noninstantaneous replenishments.

Answer: The cycle inventory is less than Q/2, which reduces the annual holding cost of ordering in cost of Q units. Thus a larger order quantity is justified.

Reference: Noninstantaneous Replenishment

Difficulty: Moderate

Keywords: ELS, noninstantaneous, replenishment

  1. Why are there discontinuities (areas where the curve jumps up or down and is not smooth) in the total cost curve in the quantity discount model?

Answer: The total cost curve has breaks due to the price breaks. Reading the total cost curve from left to right, when purchase quantities reach a price break, an increase in one unit will trigger a per-unit decrease in price, which accounts for the reduction in total cost.

Reference: Quantity Discounts

Difficulty: Moderate

Keywords: quantity, discount, total, cost

  1. When do one-period decisions on inventory arise in practice?

Answer: The one-period inventory models are appropriate when retailers handle seasonal goods that must be sold at a reduced price after the selling season. For manufacturing situations, it can be when customized specials are made and scrap rates are high.

Reference: One-Period Decisions

Difficulty: Moderate

Keywords: one-period, period, newsboy

PROBLEMS

  1. 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?

Answer:

Reference: Noninstantaneous Replenishment

Difficulty: Moderate

Keywords: ELS, noninstantaneous, replenishment, batch

  1. 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?

Answer:

Reference: Noninstantaneous Replenishment

Difficulty: Moderate

Keywords: ELS, noninstantaneous, replenishment, batch, TBO

  1. As an inventory manager, you must decide on the order quantity for an item. Its annual demand is 1,000 units. Ordering costs are $50 each time an order is placed, and the holding cost is 25 percent of the per-unit price. Your supplier provided the following price schedule.

Quantity / Price per Unit
1–199 / $10.00
200–499 / $ 9.80
500 or more / $ 9.60

What ordering-quantity policy do you recommend?

Answer:

Start at lowest cost

,not feasible

Solve for next lowest cost

, feasible,

Compare costs at the feasible 202 and at the lower cost for discount at 500

Therefore, the best order size is 202, with a cost of $10,295.

Reference: Quantity Discounts

Difficulty: Moderate

Keywords: quantity, discount, order

  1. A newsstand is trying to determine how many bundles of newspapers to stock. For each bundle, the newsstand makes $20. However, they lose $5 per bundle if they do not sell. The following discrete probability distribution has been estimated for their daily demand. How many bundles should they stock?

Demand
(bundles) / Probability
4 / .10
5 / .20
6 / .30
7 / .30
8 / .10

Answer:

Profit / $20.00 / (if sold during preferred period)
Loss / $5.00 / (if sold after preferred period)
Demand / 4 / 5 / 6 / 7 / 8
Probability / 0.1 / 0.2 / 0.3 / 0.3 / 0.1
Demand
4 / 5 / 6 / 7 / 8
Quantity / 4 / 80 / 80 / 80 / 80 / 80
5 / 75 / 100 / 100 / 100 / 100
6 / 70 / 95 / 120 / 120 / 120
7 / 65 / 90 / 115 / 140 / 140
8 / 60 / 85 / 110 / 135 / 160
Weighted Payoffs
Order / Expected
Quantity / Payoff
4 / 80 / Greatest Expected Payoff / 115
5 / 97.5
6 / 110 / Associated with Order Quantity / 7
7 / 115
8 / 112.5

Reference: One-Period Decisions

Difficulty: Moderate

Keywords: one-period, probability, discrete, order

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