Matching Supply with Demand An Introduction to Operations Management 4Th Edition By Gerard Cachon - Test Bank

Matching Supply with Demand An Introduction to Operations Management 4Th Edition By Gerard Cachon – Test Bank

 

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Matching Supply with Demand: An Introduction to Operations Management, 4e (Cachon)

Chapter 5  Batching and Other Flow Interruptions: Setup Times

                     and the Economic Order Quantity Model

 

[The following information applies to questions 1-2.]

 

The Yum and Yee food truck near the business school serves customers during the lunch hour by taking orders and making fresh batches of stir-fry. Customers have only one choice during the lunch hour since the objective is to maximize the number of customers served. Assume that each customer places just one lunch order, and all lunch orders are the same size—one unit of stir-fry.

The stir-fry cooking works in this manner. First, a batch of orders is cooked in a wok by one person. The cooking depends upon the number of orders in the batch. The time to cook just one order is 3 minutes. For each additional order in the batch, it takes 0.5 minutes more to cook. Thus, cooking two orders in a batch takes 3.5 minutes, cooking three orders takes 4 minutes, and so on.

 

The other process is bagging and accepting payments (done by a separate person), which takes 0.80 minutes per order.

 

1) If Yum and Yee operates with batch sizes of 8 units, what is their process capacity (in orders per minute)?

 

Answer:  1.23 units per minute

Explanation:  The capacity for cooking setup time is 2.5 min. and processing time per order is 0.5min. The food truck produces 8 units with 2.5min + 0.5min * 8 = 6.5 min. The capacity is 8/6.5 min = 1.23 units/min.

 

The capacity for bagging and accepting payments: 1min/0.8min = 1.25units/min.

The process capacity is the capacity of cooking(bottleneck) = 1.23unit/min.

Difficulty: 3 Hard

Topic:  The Impact of Setups on Capacity

AACSB:  Analytical Thinking

Blooms:  Analyze

 

 

2) Calculate the batch size (in orders) that will maximize the overall flow rate (assume there is ample demand)? Do NOT round the batch size (i.e., assume for this calculation that a non-integer batch size is possible).

 

Answer:  8.33 units per batch

Explanation:  Optimal order size should equalize the capacity of the cooking step and the bagging step. That is, suppose the batch size is denoted by x, then we have (2.5 + 0.5 * x) /x = 0.8 min. Solve for x; x = 8.33 units/batch.

 

Or use the formula:

Capacity = 1/0.8 min = 1.25 orders/min

Batch size = Capacity * setup time /(1- capacity * processing time)

= 1.25 * 2.5 / (1- 1.25 * 0.5) = 8.33 units/batch.

Difficulty: 3 Hard

Topic:  Interaction between Batching and Inventory

AACSB:  Analytical Thinking

Blooms:  Analyze

 

3) Recall the salt production process. At a facility on the island of Vanuatu, they have 7 salt pans, each covering 6 acres. The pans are flooded with sea water, and evaporation leaves the pan dry, covered with sea salt. From the time the pan is flooded, it takes 10 weeks on average for a salt pan to be ready for harvesting. Harvesting the salt involves using bulldozers to scoop up the salt, which is then carted off to a terminal to be loaded on a ship. A single bulldozer requires 3 days to harvest each acre of salt, and this facility has 2 of them. There is ample capacity of trucks to transport salt from the pans to the terminal. Harvesting can occur any day during the week, and clearly, the pan cannot be flooded during harvesting. Each acre yields 1000 cubic meters (m3) of salt. After the salt is harvested from a pan, it is flooded with sea water to begin the process again. Assume (i) there is ample demand for salt, and (ii) ship capacity and the loading process is sufficiently fast so that they do not constrain the process. How much salt can this facility produce per day on average (in m3)?

 

Answer:  532 m3

Explanation:  Every 6 acres require 10 weeks for evaporation. With one bulldozer, 18 days are required for harvesting, but they have 2, so the harvesting of the pan can be done in 9 days. So, 6 acres can be produced in 10 × 7 + 9 = 79 days. Six acres yield 1,000 m3, and 6,000 / 79 = 75.9 m3 is produced per pan per day. There are 7 pans, so the total production is 7 × 75.9 = 532 m3

Difficulty: 3 Hard

Topic:  Interaction between Batching and Inventory

AACSB:  Knowledge Application

Blooms:  Apply

 

 

[The following information applies to questions 4-6.]

 

Sarah’s Organic Soap Company makes four kinds of organic liquid soap: regular, lavender, citrus, and tea tree. The demand for the four scents are 150, 120, 75, and 50 kg per hour respectively. Sarah’s production process can produce any soap at the rate of 450 kg per hour, but 1.5 hours are needed to switch between scents. During those switchover times, the process doesn’t produce any soap. Sarah wants to choose a production schedule that (i) cycles repeatedly through the four scents, (ii) meets the required demand and (iii) minimizes the amount of inventory held.

 

4) How many kg of regular soap should Sarah produce before switching over to another scent?

 

Answer:  7,363.636 kg

Explanation:  The total setup time is 1.5 * 4 = 6 hours. The total demand for all four scents per hour is 150 + 120 + 75 + 50 = 395 kg/hour. The process capacity equals the demand, which is 395 kg/hr. The processing time = 1/450 hr. The batch size = capacity * setup time / (1- capacity * processing time) = 395 * 6 / (1- 395/450) = 19,390.91 kg.

 

In each batch, 150/395 * 19,390.91 = 7,363.636 kg of regular soap should be produced.

Difficulty: 3 Hard

Topic:  Setup Times and Product Variety

AACSB:  Knowledge Application

Blooms:  Apply

 

5) Sarah needs to purchase organic palm oil to make her soaps. She needs 1,000 kg of palm oil per day on average. The supplier charges a $60 delivery fee per order (which is independent of the order size) and $4.75 per kg. Sarah’s annual holding cost is 25%. Assume 52 weeks per year and 5 days per week. If Sarah wants to minimize inventory holding and ordering costs, how much palm oil should she purchase with each order (in kg)?

 

Answer:  5,125.786 kg

Explanation:  Use EOQ formula, Q = sqrt (2 * fixed cost * flow rate/holding cost)

= sqrt (2 * $60 * 1,000/ ($4.75 * 0.25/(52 * 5))) = 5,125.786 kg.

Difficulty: 3 Hard

Topic:  Balancing Setup Costs with Inventory Costs: The EOQ Model

AACSB:  Analytical Thinking

Blooms:  Analyze

 

 

6) Sarah’s supplier is willing to sell her palm oil at a 5% discount if she purchases 10,000 kg at a time. If she were to purchase 10,000 kg per order, what would be her average inventory holding and delivery fees per day (in $)? (Note: Do not include her purchasing costs per day, which would be 1,000 × 4.75 × 95%.)

 

Answer:  Inventory cost per day: $21.6947; Delivery fees per day: $6

Explanation:  Delivery cost per day will be $60/(10,000kg/1,000kg/day) = $6/day.

The average inventory level is 10,000/2 = 5,000kg. Inventory cost per day will be $4.75 * (1-5%) * (25%/52/5) * 5,000kg = $21.6947. The sum of the two is $27.6947.

Difficulty: 3 Hard

Topic:  Balancing Setup Costs with Inventory Costs: The EOQ Model

AACSB:  Analytical Thinking

Blooms:  Analyze

 

[The following information applies to questions 7-9.]

 

Joe needs to purchase malt for his micro-brew production. His supplier charges $35 per delivery (no matter how much is delivered) and $1.20 per gallon. Joe’s annual holding cost per unit is 35% of the dollar value of the unit. Joe uses 5,000 gallons of malt per week.

 

7) How many gallons should Joe order from his supplier with each order?

 

Answer:  6,583 gallons

Explanation:  Suppose Joe orders x gallons per order. The fixed portion of the delivery cost is $35 * 5,000 * 52/x per year. The average annual inventory holding cost is x/2 * 1.2 * 35%. Then, the total weekly cost is $35 * 5,000 * 52/x + x/2 * 1.2 * 35%. The cost is minimized at x = sqrt (35 * 5,000 * 52/ (0.6 * 35%)) = 6,583 gallons.

Difficulty: 3 Hard

Topic:  Balancing Setup Costs with Inventory Costs: The EOQ Model

AACSB:  Analytical Thinking

Blooms:  Analyze

 

8) Suppose Joe were to order 3,800 gallons each time he orders. How many orders per year would he place on average?

 

Answer:  68.42 orders per year

Explanation:  5,000 * 52 /3800 = 68.42

Difficulty: 3 Hard

Topic:  Balancing Setup Costs with Inventory Costs: The EOQ Model

AACSB:  Knowledge Application

Blooms:  Apply

 

 

9) If Joe places an order for 15,000 gallons, then he will receive a 4% discount off the regular price of $1.20. If Joe were to do this with each order, what would be his average weekly total cost (in $)? Note: Include the cost to purchase the units, the delivery charges, and inventory holding costs.

 

Answer:  $5,830 is the average weekly total cost

Explanation:  With a 4% discount, the malt is 1.2 * (1 – 0.04) = $1.152 per gallon. The weekly purchase cost is $1.152 * 5,000 = $5,760. Weekly delivery charges equal 5,000/15,000 * $35 = $11.67. The weekly inventory holding cost is 15,000/2 * $1.152 * (35%/52) = $58.15. The total cost is $5,760 + $11.67 + $58.15 = $5,830.

Difficulty: 3 Hard

Topic:  Balancing Setup Costs with Inventory Costs: The EOQ Model

AACSB:  Analytical Thinking

Blooms:  Analyze

 

10) It is costly to hold inventory (e.g., storage costs, obsolescence costs, etc.) but inventory can also be useful in a process because… (choose the best answer)

1. A) Adding inventory to a process will shorten the average time a unit spends in a process.
2. B) Adding inventory to a process can increase the capacity of the process.
3. C) Adding inventory to a process is likely to increase quality.
4. D) None of the above.
5. E) All of the above.

 

Answer:  B

Explanation:  Adding inventory (or adding buffer) reduces the chance that the process is starving for items to work on, thus improves the processes capacity. The average time that a unit spends in a process is the sum of processing time at each step and the time spent waiting for servers to be available. Adding inventory will not affect the processing time nor the waiting time, as waiting time is determined by the processing time of each step. Thus, A is not correct. Inventory does not influence quality either.

Difficulty: 3 Hard

Topic:  Choosing a Batch Size in the Presence of Setup Times

AACSB:  Reflective Thinking

Blooms:  Analyze

 

 

11) Which of the following most directly expresses the motivation behind the expression “Do not block the bottleneck!”?

1. A) If the bottleneck has nothing to work on, the overall capacity of the process will be lower than it could be.
2. B) If the bottleneck is prevented from working (e.g., it has nowhere to put its output,) the overall capacity will be reduced.
3. C) Blocking the bottleneck will increase the coefficient of variations of the arrival process, which decreases capacity.
4. D) Blocking the bottleneck increases inventory turns, which increases the annual holding costs.
5. E) It is not good to block the bottleneck because there are economies of scale in inventory management.

 

Answer:  B

Explanation:  To prevent a reduction in capacity, processing at the bottleneck must remain constant. If work at the bottleneck location is blocked, then overall production is affected.

Difficulty: 3 Hard

Topic:  Choosing a Batch Size in the Presence of Setup Times

AACSB:  Reflective Thinking

Blooms:  Analyze

 

12) Which of the following most directly expresses the motivation behind the expression “Buffer or Suffer”?

1. A) Adding product variety to a process with setup times is likely to increase the average amount of inventory needed.
2. B) To increase capacity, it is important to reduce setup times in a process.
3. C) If you want to increase the capacity of a process, add capacity first to the bottleneck.
4. D) If there is variability in the arrival process, or during activity times, make sure there is sufficient inventory between stages, otherwise capacity will be reduced.
5. E) When there are setup costs, producing in large enough batches is important to avoid reducing capacity.

 

Answer:  D

Explanation:  The addition of extra inventory, or buffer, helps prevent a loss in production time during periods of inactivity. Production capacity is maximized when there is a safety stock of supplies between production stages.

Difficulty: 3 Hard

Topic:  Interaction between Batching and Inventory

AACSB:  Reflective Thinking

Blooms:  Analyze

 

 

13) Henry Ford famously proclaimed, “You can have any color you want, as long as it is black.” Which of the following best reflects his motivation for this position?

1. A) He believed that customers didn’t like other colors, so why go through the hassle of making different color cars.
2. B) With more than one color, the process would have switch over time, and that could reduce the overall utilization of the process.
3. C) He wanted to establish “black” cars as part of his company’s brand image at that time.
4. D) Assembling non-black cars takes longer than black cars.
5. E) He understood that increasing inventory in a process could lead to a longer flow time through the process.

 

Answer:  B

Explanation:  With more than one color, the process would have to switch from one color to another, which would incur idle time on switchovers and utilization would decrease.

Difficulty: 3 Hard

Topic:  Interaction between Batching and Inventory

AACSB:  Reflective Thinking

Blooms:  Analyze

 

14) A high-volume paper manufacturer borrows $1M to purchase a new printing machine. The annual debt payment is $150,000. The machine can make different types of paper, but the machine must be shut down for one day each time it switches production to a different kind of paper. The manufacturer spends about 24 days per year due to produce changeovers. Dividing the annual debt payment over those 24 days yields $6,250 per day. Should this cost, $6,250, be used as an input to the EOQ model to determine optimal batch sizes for each type of paper? Choose the best answer/explanation.

1. A) Yes, $6,250 is incurred per day independent of the subsequent production volume, so it is the setup cost in the EOQ model.
2. B) Yes, $6,250 is incurred per day independent of the subsequent production volume, so it is the holding cost in the EOQ model.
3. C) No, the square root of $6,250 should be input into the EOQ model as the setup cost.
4. D) No, $150,000 should be input into the EOQ model as the holding cost because it is the opportunity cost of capital.
5. E) None of the above

 

Answer:  E

Explanation:  The annual debt payment is a sunk cost and should not be used in the calculations of the batch sizes.

Difficulty: 3 Hard

Topic:  The Impacts of Setup on Capacity

AACSB:  Reflective Thinking

Blooms:  Analyze

 

 

[The following information applies to questions 15-18.]

 

Kick Scooters

 

Metal frames for kick scooters are manufactured in two steps: stamping and assembly. Each frame is made up of three pieces: one unit of part A and two units of part B.

 

The parts are fabricated by a single stamping machine that requires a setup time of 90 minutes switching between the two part types. Once the machine is set up, the activity time for parts, regardless of type, is 30 seconds each piece. Currently, the stamping machine rotates its production between one batch of 120 part A’s and 240 part B’s. Completed parts move only when the entire batch is produced.

 

During assembly, parts are assembled manually to form the finished products. The three parts and a number of small purchased components are required for each unit of final product. Each product requires 30 minutes of labor time to assemble. There are 12 workers in assembly. There is sufficient demand to sell every scooter the system can make.

 

15) At the current batch sizes, the bottleneck of the system is

1. A) stamping
2. B) assembly
3. C) they both have the same capacity
4. D) cannot be determined

 

Answer:  A

Explanation:  The capacity at stamping is 120/(90 + 120 * 0.5 + 9 + 240 * 0.5) * 60 = 20 units per hour. The capacity at assembly is 1/30 * 12 * 60 = 24 units per hour. Therefore, stamping is the bottleneck.

Difficulty: 3 Hard

Topic:  Choosing a Batch Size in the Presence of Setup Times

AACSB:  Analytical Thinking

Blooms:  Analyze

 

 

 

16) At the current batch sizes, what is the process capacity in units per hour? Choose the answer below that is closest to the correct answer. A unit refers to a complete scooter frame (i.e. one part A and two parts B).

1. A) 1 unit/hour
2. B) 5 units/hour
3. C) 10 units/hour
4. D) 20 units/hour
5. E) 30 units/hour
6. F) 40 units/hour

 

Answer:  D

Explanation:  Since stamping is the bottleneck, its capacity is also the process capacity.

Difficulty: 3 Hard

Topic:  Choosing a Batch Size in the Presence of Setup Times

AACSB:  Knowledge Application

Blooms:  Analyze

17) One way to increase process capacity is to

1. A) increase the batch size at the stamping step
2. B) decrease the batch size at the stamping step
3. C) add more workers at assembly
4. D) none of the above

 

Answer:  A

Explanation:  At a batch-producing step, increasing the batch size increases the capacity at the step.

Difficulty: 3 Hard

Topic:  Choosing a Batch Size in the Presence of Setup Times

AACSB:  Reflective Thinking

Blooms:  Analyze

 

18) Which batch size for the stamping machine would minimize inventory without decreasing the current flow rate? Choose the answer below that is closest to the correct answer.

1. A) 60 sets
2. B) 120 sets
3. C) 180 sets
4. D) 240 sets
5. E) 300 sets

 

Answer:  C

Explanation:  At a batch size of 180, the capacity at stamping is 180/(90 +180 * 0.5 + 90 + 360 * 0.5) * 60 = 24 units per hour.

Difficulty: 3 Hard

Topic:  Choosing a Batch Size in the Presence of Setup Times

AACSB:  Knowledge Application

Blooms:  Apply