447733

CHAPTER 14 INVENTORY MANAGEMENT

QUESTIONS FOR WRITING AND DISCUSSION

1. Ordering costs are the costs of placing and receiving an order. Examples include clerical costs, documents, insurance, and unloading.

2. Setup costs are the costs of preparing equipment and facilities so that they can be used for producing a product or component. Examples include wages of idled production workers, lost income, and the costs of test runs.

3. Carrying costs are the costs of carrying in-ventory. Examples include insurance, taxes, handling costs, and the opportunity cost of capital tied up in inventory.

4. Stockout costs are the costs of insufficient inventory (e.g., lost sales and interrupted production).

5. As ordering costs decrease, fewer and larg-er orders must be placed. This, in turn, in-creases the units in inventory and, thus, in-creases carrying costs.

6. Reasons for carrying inventory include the following: (a) to balance setup and carrying costs; (b) to satisfy customer demand; (c) to avoid shutting down manufacturing facilities; (d) to take advantage of discounts; and (e) to hedge against future price increases.

7. The economic order quantity is the amount that should be ordered so as to minimize the sum of ordering and carrying costs.

8. Reorder point = 3 × 12 = 36 units; Safety stock = 3(15 – 12) = 9 units

9. Safety stock is simply the difference be-tween maximum demand and average de-mand, multiplied by the lead time. By reor-dering whenever the inventory level hits the safety stock point, a company is ensured of always having sufficient inventory on hand to meet demand.

10. JIT minimizes carrying costs by driving in-ventories to insignificant levels. Ordering costs are minimized by entering into long-term contracts with suppliers (or driving se-tup times to zero).

11. JIT manufacturing is a demand-pull ap-proach to manufacturing. It differs from tradi-tional manufacturing by significantly reduc-ing reliance on inventories, forming manufacturing cells, using interdisciplinary labor, decentralizing services, and adopting a philosophy of total quality management.

12. Manufacturing cells are collections of ma-chines and labor dedicated to the production of a single product or subassembly. Each cell is capable of performing a variety of op-erations. This differs from the departmental organization where a collection of the same machines is used to perform the same oper-ation on multiple products.

13. By forming manufacturing cells that are dedicated to a single product, all costs as-sociated with the cell are traceable to the product. Machinery and services that for-merly belonged to several products now be-long only to a single product. For example, depreciation, material handling, and main-tenance become direct product costs.

14. JIT hedges against future price increases and obtains lower input prices (better usually than quantity discounts) by the use of long-term contractual relationships with suppliers. Suppliers are willing to give these breaks so that they can reduce the uncertainty in the demand for their products.

15. EDI, or electronic data interchange, allows suppliers to have access to a buyer’s data-base. Information on the buyer’s database is used to determine when supplies should be delivered. When supplies arrive, their receipt is noted electronically, and payment is in-itiated. No paperwork is involved. Conti-nuous replenishment is where suppliers are given responsibility to replenish the buyer’s inventory stock. EDI facilitates this by pro-viding information (electronically) needed by the supplier to make replenishment deci-sions.

16. Shutdowns in a JIT environment are avoided by practicing total preventive maintenance

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and total quality control and by developing close relationships with suppliers to ensure on-time delivery of materials. Internally, a Kanban system is used to ensure the timely flow of materials and components.

17. The Kanban system is used to ensure that parts or materials are available when needed (just in time). The flow of materials is controlled through the use of markers or cards that signal production of the neces-sary quantities at the necessary time.

18. Constraints represent limited resources or demand. Internal constraints are limiting fac-tors found within the firm. External con-straints are limiting factors imposed on the firm from external sources.

19. Loose constraints are those where the prod-uct mix chosen does not consume all the available resources. A binding constraint is one where the product mix uses all the li-mited resource.

20. Following are three measures of organiza-tional performance used by the theory of constraints: throughput—the rate at which an organization generates money; invento-ry—the money an organization spends in turning materials into throughput; and oper-ating expenses—the money the organiza-

tion spends in turning inventories into throughput. The objective is to maximize throughput and minimize inventory and op-erating expenses.

21. Lower inventories mean that a company must pay attention to higher quality—it can-not afford to have production go down be-cause of defective parts or products. It also means that improvements can reach the customer sooner. Lower inventories mean less space, less overtime, less equipment—in short, lower costs of production and, thus, lower prices are possible. Lower inventories also mean (usually) shorter lead times and better ability then to respond to customer requests.

22. Following are the five steps that TOC uses to improve organizational performance: (1) identify constraints, (2) exploit binding con-straints, (3) subordinate everything else to decisions made in Step 2, (4) elevate bind-ing constraints, and (5) repeat process.

23. The drum is the binding constraint that sets the production rate in the factory. The rope simply means that the release of materials to the first process is tied to the rate of the drummer constraint. The buffer is an amount of inventory placed in front of the drummer process to protect throughput.

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EXERCISES

14–1

1. Annual ordering cost = PD/Q = $600 × 30,000/6,000 = $3,000 2. Annual carrying cost = CQ/2 = $4 × 6,000/2 = $12,000 3. Cost of current inventory policy = Ordering cost + Carrying cost = $3,000 + $12,000 = $15,000

14–2

1. EOQ = 2PD/C = 800,000)/440(2 ×× = 16,000,000 = 4,000 2. Number of orders = D/Q = 800,000/4,000 = 200 3. Ordering cost = P × Number of orders = $40 × 200 = $8,000

4. Carrying cost = CQ/2 = $4 × 4,000/2 = $8,000

5. Total cost = $8,000 + $8,000 = $16,000 6. Ordering cost = P × Number of orders = $40 × (800,000/8,000) = $4,000 Carrying cost = CQ/2 = $4 × (8,000/2) = $16,000 Inventory cost savings at EOQ = ($ 4,000 + $16,000) − $16,000 = $4,000

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14–3

1. EOQ = 2PD/C = 6,250)/5100(2 ×× = 250,000 = 500 2. Carrying cost = CQ/2 = $5 × 500/2 = $1,250

Setup cost = PD/Q = $100 × 6,250/500 = $1,250

14–4

1. Reorder point = Average rate of usage × Lead time = 8,000 × 3 = 24,000 pounds 2. Maximum usage 12,000 Average usage 8,000 Difference 4,000 Lead time × 3 Safety stock 12,000

Reorder point = (Average rate of usage × Lead time) + Safety stock = (8,000 × 3) + 12,000 = 36,000 pounds

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14–5

1. Maximum daily usage 2,350 Average daily usage 2,000 Difference 350 Lead time × 4 Safety stock 1,400

Reorder point = (Average rate of usage × Lead time) + Safety stock = (2,000 × 4) + 1,400 = 9,400 units 2. Maximum setup time in days 5 Average setup time in days 4 Difference in days 1 Average daily usage × 2,000 Safety stock 2,000

Reorder point = (Rate of usage × average lead time) + Safety stock = (2,000 × 4) + 2,000 = 10,000 units

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14–6

1. EOQ = 2PD/C = 324,000)/24,000(2 ×× = 0001,296,000, = 36,000 (batch size for lawn mower engines) 2. Setup cost = PD/Q = $4,000 × 324,000/36,000 = $36,000

Carrying cost = CQ/2 = $2 × 36,000/2 = $36,000

Total cost = $72,000 ($36,000 + $36,000) 3. ROP = Average daily sales × Lead time

ROP = 1,296 × 11 = 14,256 lawn mower engines 4. EOQ = 2PD/C = 750,000)/37,200(2 ×× = 0003,600,000, = 60,000 (batch size for jet ski engines)

Setup cost = $7,200 × 750,000/60,000 = $90,000

Carrying cost = $3 × 60,000/2 = $90,000

Total cost = $180,000 ($90,000 + $90,000)

ROP = 1,500 × 12 = 18,000 jet ski engines

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14–6 Concluded

5. Lawn mowers require 9 batches per year (324,000/36,000). Jet ski engines re-quire 12.5 batches per year (750,000/60,000). The lead time for the lawn mower engines is 11 days and that of the jet ski engines is 12 days. Thus, the total work days needed to produce the annual demand is 249 [(11 × 9) + (12 × 12.5)]. Since there are 250 work days available each year, it is possible to meet the annual demand. Given the initial inventory levels of each product, the daily and annual demand, and the lead times, Shields must build a sche-dule that coordinates production, inventory usage, and sales. This is a push system because production and inventory use anticipated demand rather than current demand.

14–7

1. Cost for 2-day setup = $4,000 Cost for 0.5 day setup = 0.25 × $4,000 = $1,000 Cost of 0.05 day setup = 0.10 × $1,000 = $100 EOQ = 1,000)/2324,000(2 ×× = 0324,000,00 = 18,000 lawn mower engines EOQ = 100)/2324,000(2 ×× = 32,400,000 ≈ 5,692 lawn mower engines 2. The batch size decreases as the setup time and cost decrease. If the setup

time is 0.05 day (about 1 hour), then the firm can produce 4,000 × 0.95 = 3,800 units per day, sufficient to meet the combined daily demand for the two en-gines. This implies the ability to produce on demand and eliminates the need to carry finished goods inventory, a JIT objective.

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14–8

1. JIT does not accept setup (or ordering) costs as a given; rather, JIT at-tempts to drive these costs to zero through reducing the time it takes to set up and by developing long-term contracts with suppliers. Carrying costs are minimized by reducing inventories to insignificant levels.

2. JIT reduces lead times, which increases a firm’s ability to meet requested delivery dates. This is accomplished by (1) reduction of setup times, (2) improved quality, and (3) cellular manufacturing.

3. The problems that usually cause shutdowns are (1) machine failure, (2) de-fective material or subassembly, and (3) unavailability of a material or subassembly, or (4) late delivery of parts. JIT attempts to solve each of the four problems by emphasizing total preventive maintenance and total quality control (strives for zero defects) and building the right kind of rela-tionship with suppliers.

4. Unreliable production processes are addressed by total quality man-agement. As fewer and fewer defective units are produced, there is less and less need for inventory to replace nonconforming units.

5. The objective of taking advantage of discounts is to lower the cost of in-ventory. JIT accomplishes the same objective by negotiating long-term contracts with a few chosen suppliers and establishing more extensive supplier involvement.

6. JIT emphasizes long-term contracts that stipulate prices and acceptable quality levels.

2. JIT has the policy of stopping production if a problem is detected so that the

problem can be corrected (of course, the problem may also cause production to stop, independent of a policy or practice of stopping so that the source of the problem can be corrected). Since JIT produces on demand, any interrup-tion of production means that throughput is lost. TOC uses a time buffer lo-cated in front of the binding constraint to protect throughput. The time buffer is designed to keep the constrained resource busy for a specified period of time, a time long enough to overcome most disruptions in production.

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14–9

1. The withdrawal Kanban controls movement of work among the manufacturing processes. It specifies the quantity that a subsequent process should with-draw from the preceding process.

2. The production Kanban also controls movement of work among the manufac-

turing processes. It specifies the quantity that the preceding process should produce.

3. The vendor Kanban controls movement of parts between the processes and

outside suppliers. It is used to notify suppliers to deliver more parts.

14–10

The phrase “implementing JIT” conveys to many the notion that one day a com-pany is conventional and the next day it is JIT with all of the benefits that are typ-ically assigned to JIT. In reality, changing to a JIT environment takes time and pa-tience. It is more of an evolutionary process than a revolutionary process. It takes time to build a “partners-in-profits” relationship with suppliers. Many firms at-tempt to force the JIT practices with suppliers by dictating terms, but this ap-proach really runs counter to the notion of developing close relationships, some-thing that is vital for the JIT purchasing side to work. There must be trust and mutual benefits, not unilateral benefits, for JIT purchasing to become a success. Also, management should be aware of the disequilibrium that workers may expe-rience with JIT. Many workers may view JIT methodology as simply a way of ex-tracting more and more work out of them with no compensating benefits. Others may see JIT as a threat to their job security as the nonvalue-added activities they perform are eliminated or reduced. Furthermore, management should be ready and willing to place some current sales at risk with the hope of ensuring stronger future sales, or with the hope of reducing inventory and operating costs to im-prove overall profitability. How else can you justify lost sales due to production stoppages that are designed to improve quality and efficiency?

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14–11

1. e 2. a 3. d

4. e 5. c

14–12

1. Before JIT unit cost: $262,000/200,000 = $1.31 After JIT unit cost: $238,000/200,000 = $1.19

JIT costing is more accurate because there are more costs that are traceable to each product.

2. Direct materials: Direct Direct labor: Direct Maintenance: Direct Electricity: Direct Depreciation: Direct (on cell equipment) Material handling: Direct Engineering: Driver tracing Setups: Direct Building and grounds: Allocated (driver tracing using square feet for the

building costs may be a reasonable possibility) Supplies: Direct Supervision (plant): Allocated Cell supervision: Direct Department Supervision: Allocated

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14–13

1. Model A Model B Price $20.00 $35.00 Variable cost 15.00 15.00 Contribution margin $ 5.00 $20.00 ÷ Machine hours ÷ 0.5 ÷ 2.5 Contribution margin per machine hour $10.00 $8.00

The company should sell only the model A housing with contribution margin per machine hour of $10. Gallard can produce 80,000 (40,000/0.5) of the model A housings per year. These 80,000 units, multiplied by the $5 contribution margin per unit, would yield a total contribution margin of $400,000.

2. Produce and sell 50,000 of the model A housings, which would use 25,000

machine hours. Then, produce and sell 6,000 of the model B housings, which would use the remaining 15,000 machine hours.

Total contribution margin = ($5 × 50,000) + ($20 × 6,000) = $370,000

14–14

1. Gear X Gear Y Contribution margin $ 25.00 $10.00 ÷ Machine hours ÷ 2.0 ÷ 0.5 Contribution margin per machine hour $12.50 $20.00

2. The company should sell only Gear Y with contribution margin per machine hour of $20. Jorgenson can produce 20,000 (10,000/0.5) units of Gear Y per year. These 20,000 units, multiplied by the $10 contribution margin per unit, would yield a total contribution margin of $200,000.

3. Produce and sell 15,000 of the model A housings, which would use 7,500 ma-

chine hours. Then, produce and sell 1,250 units of Gear X, which would use the remaining 2,500 machine hours.

Total contribution margin = ($25 × 1,250) + ($10 × 15,000) = $181,250

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14–15

1. Type I Type II Type III Price $40.00 $60.00 $75.00 Variable cost 25.00 38.00 60.00 Contribution margin $15.00 $22.00 $15.00 ÷ Machine hours ÷ 0.50 ÷ 0.80 ÷ 1.50 Contribution margin per machine hour $30.00 $27.50 $10.00

The company should sell only the Type I rod with contribution margin per machine hour of $30. Perkins can produce 60,000 (30,000/0.5) Type I rods per year. These 60,000 units, multiplied by the $15 contribution margin per unit, would yield a total contribution margin of $900,000.

2. Produce and sell 20,000 Type I rods, which would use 10,000 machine hours.

Then, produce and sell 20,000 Type II rods, which would use 16,000 machine hours. Finally, produce and sell 2,666 Type III rods, which would use the re-maining 4,000 machine hours.

Total contribution margin = ($15 × 20,000) + ($22 × 20,000) + ($15 × 2,666) = $779,990

14–16

1. The production rate is 600 regular bows per day and 200 deluxe bows per day. The rate is set by the molding process. It is the drummer process since it is the only one with a buffer inventory in front of it.

2. Goicoechea has 0.5 day of buffer inventory (400 bows/800 bows per day). This

time buffer is determined by how long it takes the plant to correct problems that create production interruptions.

3. A is the rope, B is the time buffer, and C is the drummer constraint. The rope

ties the production rate of the drummer constraint to the release of raw mate-rials to the first process. The time buffer is used to protect throughput. Suffi-cient inventory is needed to keep the bottleneck operating if the first process goes down. The drummer sets the production rate.

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PROBLEMS

14–17

1. Ordering cost = PD/Q = $40 × 14,000/400 = $1,400

Carrying cost = CQ/2 = $1.75* × 400/2 = $350

*10 percent of purchase price or 0.10 × $17.50

Total cost = $1,400 + $350 = $1,750 2. EOQ = 2PD/C = 75100014402 ./),( ×× = 000640, = 800

Ordering cost = PD/Q = $40 × 14,000/800 = $700

Carrying cost = CQ/2 = $1.75 × 800/2 = $700

Total cost = $700 + $700 = $1,400

Savings = $1,750 – $1,400 = $350

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14–17 Concluded

3. Rate of usage = 7 × 50 = 350 days = 14,000/350 = 40 blocks per day

Reorder point = Average rate of usage × Lead time = 40 × 5 = 200

This coincides with the current reorder policy. 4. The order quantity would have to be 600 instead of 800 (the EOQ). If so, the

following inventory costs would be incurred:

Ordering cost = $40 × 14,000/600 = $933

Carrying cost = $1.75 × 600/2 = $525

Total cost = $933 + $525 = $1,458

This restriction would mean an additional cost of only $58 ($1,458 – $1,400) over the cost of using the EOQ.

5. The most cheese that should be kept on hand given the 10-day constraint is

400 blocks (40 × 10). Reorder would occur when inventory dropped to 200 units.

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14–18

1. EOQ = 2PD/C = 50.5/)571,101002( ×× = 400,384 = 620

Reorder point = Average rate of usage × Lead time = 30 × 4 = 120

Ordering cost = PD/Q = $100 × 10,571/620 = $1,705

Carrying cost = CQ/2 = $5.50 × 620/2 = $1,705

Total cost = $1,705 + $1,705 = $3,410 2. Maximum usage 35 Average usage 30 Difference 5 Lead time × 4 Safety stock 20

Ordering cost = PD/Q = $100 × 10,571/620 = $1,705

Carrying cost = CQ/2 = $5.50 × [(20 + 620)/2] = $1,760

Total cost = $1,705 + $1,760 = $3,465

New reorder point = (Average usage × Lead time) + Safety stock = (30 × 4) + 20 = 140

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14–19

1. EOQ = 2PD/C = 30003600062 /),,( ×× = 000000144 ,, = 12,000 (batch size)

Geneva’s response was correct given its current production environment. The setup time is two working days. The production rate possible is 750 units per day after setup. Thus, the time required to produce the additional 9,000 units would be 14 working days [2 + (9,000/750)].

2. To have met the order’s requirements, Geneva could have produced 3,750

units within the 7-work-day window [(7 – 2)750] and would have needed 8,250 units in stock—5,250 more than available. Solving delivery problems like the one described would likely require much more inventory than is currently car-ried. If the maximum demand is predictable, then safety stock could be used. The demand can be as much as 9,000 units per year above the expected de-mand. If it is common for all of this extra demand to occur from one or a few large orders, then protecting against lost sales could demand a sizable in-crease in inventory, an approach that could be quite costly. Perhaps some safety stock with expediting and overtime would be more practical. Or, per-haps Geneva should explore alternative inventory management approaches such as those associated with JIT or TOC.

3. EOQ = 2PD/C = 300036942 /),( ×× = 0002562 ,, ≈ 1,502 (batch size)

The new lead time = (1.5 hours) + [(1,502/2,000) × 8 hours] ≈ 7.5 hours, or about one work day

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14–19 Concluded

At a production rate of 2,000 units per day, Geneva could have satisfied the customer’s time requirements in less than seven days, even without any fi-nished goods inventory. This illustrates very forcefully that inventory may not be the solution to meeting customer needs or dealing with demand uncertain-ty. Perhaps paying attention to setup, moving, and waiting activities offers more benefits. JIT tends to produce smaller batches and shorter cycle times than conventional manufacturing environments. As the EOQ batch size com-putation revealed, by focusing on improving the way production is done, the batch size could be reduced to about 12.5 percent of what it was before the improvements.

4. EOQ = 2PD/C = 300036102 /),( ×× = 000240, ≈ 490 (batch size)

This further reduction in setup time and cost reduces the batch size even more. As the setup time is reduced to even lower levels and the cost is re-duced, the batch size becomes even smaller.

If the cost is $0.864, the batch size is 144:

EOQ = 2PD/C = 30003686402 /),.( ×× = 73620, = 144 (batch size)

Furthermore, with the ability to produce 2,000 units per day or 250 units per hour, the day’s demand (36,000/250 = 144) can be produced in less than an hour. This provides the ability to produce on demand. The key to this out-come was the decrease in setup time and the reduction of wait and move time—all nonvalue-added activities. This illustrates what is meant by refer-ring to inventory management as an ancillary benefit of JIT.

449900

14–20

1. a. The expected demand for the RJ47 battery during the lead time is calcu-lated as the sum of the demand during the lead time times the demand probability for all demand points:

Expected demand = (100 × 0.03) + (200 × 0.05) + (300 × 0.20) + (400 × 0.40) + (500 × 0.25) + (600 × 0.07) = 400

b. The reorder point to minimize stockouts would be the maximum demand during lead time, or 600 units.

2. The probability of a stockout at a special reorder point is the sum of the prob-

abilities for demand greater than the reorder point of 400 units:

Probability of 500 units 0.25 Probability of 600 units 0.07 Total 0.32

14–21

1. KEVCO can expect the following effects:

Planning:

• Production planning will change from a centralized batch function process to a more decentralized activity. In some cases, production teams will be responsible for the entire production process of a product.

• The method and timing of how the company prepares its production sche-dules (including capacity requirements) will change to parallel the demand pull approach as opposed to the push approach.

• The Purchasing Department will need production to have high-quality, reli-able, and flexible suppliers who can quickly deliver orders of varying sizes as needed.

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14–21 Concluded

Operations:

• Setup time changes will reduce lead times significantly. • A Kanban system will need to be implemented. A triggering device such as

a Kanban card is necessary so that the department or cell knows when to begin production.

• Greater employee participation will result from cell production team ar-rangements.

2. At least five benefits:

• Less rework and fewer defective units because of cell-level accountability and control and product solving at the cell level.

• A lower cash investment in inventory and plant space. Handling, storage, insurance, breakage, and obsolescence will all be lower.

• More satisfied customers should result because of shorter lead times and higher quality.

• Improved labor productivity as a result of rearranging the production process and the creation of manufacturing cell teams.

• A reduction of the number of suppliers leading to improved relationships and communication.

• More accurate product costing because of the increase in direct tracing of activities and their costs.

3. Behavioral effects:

• Higher team morale and motivation, since each cell team is responsible for all cell production and will, therefore, have more control over its work and an increased sense of ownership.

• Higher individual satisfaction, development, and motivation, as manage-ment will encourage participation, training, and input on how to improve the product and production process.

• A possible resistance to change by those employees who may feel inse-cure or threatened by the change.

• A sense of partnership with management in achieving the goals and objec-tives of the organization resulting in goal congruence.

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14–22

1. The entire Kanban cycle begins with the need to produce a final product—a product demanded by a customer. The demand for a product to be assembled is known from the production schedule. Assume that a final product is needed. The withdrawal Kanban controls movement of work between the as-sembly process and the manufacturing processes. It specifies the quantity that a subsequent process should withdraw from the preceding process. The assembly process uses withdrawal Kanbans to notify the first process that more subassemblies are needed. This is done by having an assembly worker remove the withdrawal Kanban from the container in the withdrawal store and place it on the withdrawal post. This W-Kanban signals that the assembly process is using one unit of Subassembly A and that a replacement for it is needed. The replacement activity is initiated by a carrier who removes the production Kanban from the container of subassemblies in the SB stores area and places this P-Kanban on the production post. The container in the SB stores area is then moved to the withdrawal stores area with the W-Kanban attached (taken from the withdrawal post). The production Kanban tells the workers in the Subassembly A cell to begin producing another unit. The pro-duction Kanban is removed and goes with the unit produced (which goes to the SB stores area). This Kanban system ensures that the second process withdraws subassemblies from the first process in the necessary quantity at the necessary time. The Kanban system also controls the first process by al-lowing it to produce only the quantities withdrawn by the second process. In this way, inventories are kept at a minimum, and the components arrive just in time to be used.

2. The second process uses a vendor Kanban to signal the supplier that another

order is needed. The process is similar to the internal flow described in Re-quirement 1. However, for the process to work with suppliers, the suppliers must be willing to make frequent and small deliveries. It also means that the supply activity works best if the supplier is located in close proximity to the buyer. The subassemblies must be delivered just in time for use. This calls for a close working relationship with the supplier. The inventory function on the materials side is largely assumed by the supplier. To bear this cost, there must be some compensating benefits for the supplier. Long-term contracts and the reduction of demand uncertainty are significant benefits for the sup-plier. EDI can facilitate the entire arrangement. If the supplier has access to the buyer’s on-line database, then the supplier can use the buyer’s produc-tion schedule to determine its own production and delivery schedule, making it easier to deliver parts just in time. In effect, the supplier and buyer almost operate as one company.

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14–23

1. ImmuneBoost: CM per machine hour = ($4.00 – $2.40)/1.60 = $1.00

MentaGrowth: CM per machine hour = ($4.80 – $3.60)/0.80 = $1.50

Since MentaGrowth provides the greatest contribution per machine hour, the company should produce 800,000 bottles of MentaGrowth (640,000/0.8) and zero bottles of ImmuneBoost. The total contribution margin is 800,000 × $1.20 (unit contribution margin) = $960,000

2. First, the company should produce 480,000 bottles of MentaGrowth. This

uses up 384,000 machine hours (480,000 × 0.8). The remaining hours can then be used to produce 160,000 bottles of ImmuneBoost (256,000/1.6). Thus, the optimal mix is 160,000 bottles of ImmuneBoost and 480,000 bottles of Menta-Growth. The maximum total contribution margin is $832,000 [($1.60 × 160,000) + ($1.20 × 480,000)].

14–24

1. Dept. A Dept. B Dept. C Total Component 12-L (1,000 units) Test hoursa 2,000 3,000 3,000 8,000 Machine hoursb 1,000 1,000 2,000 4,000 Component 14-M (800 units) Test hoursc 800 1,600 — 2,400 Machine hoursd 800 800 — 1,600 Component 40-S (2,000 units) Test hourse 4,000 4,000 4,000 12,000 Machine hoursf 4,000 4,000 2,000 10,000 Total test hours 6,800 8,600 7,000 22,400 Total machine hours 5,800 5,800 4,000 15,600

a2 × 1,000; 3 × 1,000; 3 × 1,000 d1 × 800; 1 × 800 b1 × 1,000; 1 × 1,000; 2 × 1,000 e2 × 2,000; 2 × 2,000; 2 × 2,000 c1 × 800; 2 × 800 f2 × 2,000; 2 × 2,000; 1 × 2,000

The demand can be met in all departments except for Department C. Produc-tion requires 7,000 test hours in Department C, but only 5,500 hours are avail-able.

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14–24 Concluded

2. Component 12-L: CM per unit = $203 – $110 = $93 CM per test hour = $93/3 = $31

Test hours needed (Dept. C): 3 × 1,000 = 3,000

Component 14-M: CM per unit = $136 – $86 = $50 Requires no hours in Department C

Component 40-S: CM per unit = $184 – $114 = $70 CM per test hour = $70/2 = $35

Test hours needed (Dept. C): 2 × 2,000 = 4,000

Production should be equal to demand for Component 40-S because it has the highest contribution margin per unit of scarce resource. After meeting demand, any additional labor hours in Department C should be used to pro-duce Component 12-L (5,500 – 4,000 = 1,500; 1,500/3 = 500 units of 12-L).

Contribution to profits: Component 12-L: 500 × $93 = $ 46,500 Component 14-M: 800 × $50 = 40,000 Component 40-S: 2,000 × $70 = 140,000 Total contribution margin $226,500

14–25

1. Molding Grinding Finishing Part A 6,000 12,000 18,000 Part B 20,000 30,000 40,000 Total requirements 26,000 42,000 58,000 Available time 23,040 48,000 67,200 Less: Setup time 5,760 — — Net time available 17,280 48,000 67,200

Note: The time required is computed by multiplying the unit time required by the daily demand. The available time is derived from the workers employed. For example, molding has 48 workers, each supplying 480 minutes per day or 480 × 48 = 23,040 minutes. Assuming two setups, the molding production time is reduced by 48 × 60 × 2 = 5,760 minutes per day (setup occupies one hour and so ties up the 24 workers for one hour).

Molding is the major internal constraint facing Copeland Company.

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14–25 Concluded

2. The contribution margin per unit for A is $100 ($180 – $80) and for B is $120 ($220 – $100). The contribution margin per unit of scarce resource is $10 ($100/10) for A and $6 ($120/20) for B. Thus, A should be produced first. If all 600 units of A are produced, Copeland would need 6,000 molding minutes. Af-ter the setup for A, there are 23,040 – 2,880 = 20,160 minutes available. This would leave 14,160 minutes to setup and produce B (20,160 – 6,000). After set-ting up for B, there are 11,280 minutes left (14,160 – 2,880). Thus, 11,280/20 = 564 units of B can be produced. Producing 600 units of A and 564 units of B will yield a daily contribution margin of $127,680 [($100 × 600) + ($120 × 564)].

3. Ten minutes to set up would tie up the 48 workers for only 10 minutes. Thus,

production time lost is 480 minutes per setup. After setting up and producing all of A required (using 6,000 + 480 =6,480 minutes), this would leave 16,560 minutes to set up and produce Part B (23,040 minutes – 6,480). Setup time for B would use up 480 minutes of molding’s resources, and this leaves 16,080 minutes for producing B (16,560 – 480). Thus, 16,080/20 = 804 units of B could be produced each day. This will increase daily contribution margin by $28,800 [$120 × (804 – 564)].

14–26

1. The constraints are both labor constraints, one for fabrication and one for as-sembly (let X = Units of Sub A and Y = Units of Sub B; hours are used to measure resource usage and availability):

Assembly: (1/2)X + (2/3)Y ≤ 800 (1) Fabrication: (1/3)X + (1/3)Y ≤ 800 (2)

Comparing the assembly constraint with the fabrication constraint, we see that assembly uses more labor time per unit for each subassembly than fabri-cation (1/2 hour of assembly for X vs. 1/3 hour of fabrication for X and 2/3 hour of assembly for Y vs. 1/3 hour of fabrication for Y), so only one binding constraint is possible (assembly labor). Thus, the contribution margin per unit of scarce resource will dictate the outcome. For Sub A, the CM per unit of assembly labor is $40 ($20 × 2) and for Sub B it is $36 ($24 × 1.5). Therefore, only Sub A should be produced. The optimal mix is 1,600 units per day of Sub A and none of Sub B. The daily contribution margin is $32,000 ($20 × 1,600).

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14–26 Concluded

2. The drummer constraint is the assembly constraint. The mix dictates a pro-duction rate of 1,600 units of Part A per day. At this rate, all 800 hours availa-ble of the drummer constraint are used up. The fabrication constraint would use 533.33 hours at this rate, leaving 266.67 hours of excess capacity.

The drummer constraint sets the production rate for the entire factory—in this case, 1,600 units of A per day. The rope concept simply means that the production rate of the fabrication process is controlled by tying the release of materials to the assembly’s rate of production. The daily release of materials to the fabrication process should be enough to produce only 1,600 subas-semblies. The 1.5-day buffer means that there should be a 1.5-day supply of components in front of the drummer process (assembly) so that production can continue if the supply of parts to the assembly process is interrupted. Thus, a 2,400 component inventory is required. This protects throughput in case production or supply is interrupted. The 1.5-day length reflects the time thought necessary to restore most production interruptions.

3. The use of local labor efficiency measures would encourage the fabrication

process to produce at a higher rate than the drummer rate (it has excess ca-pacity) and so would run counter to the TOC objectives. In fact, efficient use of labor in fabrication would cause a buildup of about 800 (266.67 × 3) units per day of work in process inventory—a very expensive outcome.

4. Adding a second shift of 50 workers for the assembly process creates an ad-

ditional 400 hours of assembly resource. There would now be 1,200 hours of assembly resource available. The assembly constraint now appears as follows: (1/2)X + (2/3)Y ≤ 1,200. Increasing the assembly resource allows us to in-crease production of Sub A from 1,600 to 2,400 units (1,200/0.5 = 2,400 units). Fabrication can handle the increase [(1/3) × 2,400 = 800 hours—exactly the time available]. The contribution margin without the increase in the labor cost of the second shift is $48,000 ($20 × 2,400). Thus, the daily contribution mar-gin increases by $16,000 ($48,000 – $32,000). Since the cost of adding the second shift of 50 workers is $2,800 (400 × $7), the improvement in profit per-formance is $13,200 ($16,000 – $2,800).

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14–27

1. Potential daily sales:

Small Large Cylinder Cylinder Sales $ 80 $ 110 Materials 40 50 CM per unit $ 40 $ 60 Daily demand × 200 × 100 Daily profit $ 8,000 + $ 6,000 = $14,000 potential Process Resource Demands Resource Supply Cutting Small: 30 × 200 = 6,000 Large: 20 × 100 = 2,000 8,000 9,600 Welding Small: 30 × 200 = 6,000 Large: 60 × 100 = 6,000 12,000 9,600 Polishing Small: 30 × 200 = 6,000 Large: 30 × 100 = 3,000 9,000 12,480 Painting Small: 20 × 200 = 4,000 Large: 30 × 100 = 3,000 7,000 9,600 Zaramar cannot meet daily demand. The welding process requires 12,000 mi-

nutes but has only 9,600 available. All other processes have excess capacity. Thus, welding is the bottleneck.

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14–27 Concluded

2. The contribution margin per unit of welding resource for each product is computed below:

Small: $40/30 = $1.33 Large: $60/60 = $1.00

This suggests that Zaramar should first produce all that it can of the small cy-linder. Thus, 30 × 200 = 6,000 minutes of welding will be dedicated to the small cylinder. The remaining minutes (3,600) will be used to produce all that is possible of the large cylinder: 3,600/60 = 60 units. The optimal mix is small cylinder = 200 units and the large = 60 units, producing a daily contribution of $11,600 [($40 × 200) + ($60 × 60)].

3. The welding process is the drummer. It sets the production rate for the entire

plant. Thus, the plant should produce 200 units of the small cylinder per day and 60 units of the large per day. To ensure that the cutting process does not exceed this rate, the release of materials is tied to the maximum production rate of the welding process (materials for 200 units of the small cylinder and materials for 60 units of the large cylinder would be released). This is the rope. Finally, to protect throughput, a time buffer is set up in front of the weld-ing process. This buffer would consist of 400 cut units for the small cylinder and 120 cut units for the larger cylinder (a two-day buffer).

4. The redesign would increase the polishing time for the small cylinder from

6,000 minutes to 9,200 minutes and, at the same time, decrease the welding time for the small cylinder from 6,000 minutes to 4,000 minutes. This frees up 2,000 minutes of scarce resource in welding and decreases the excess capac-ity of polishing. The extra 2,000 minutes in welding can be used to produce an additional 33 units of the large cylinder (2,000/60). This will increase daily contribution margin by $1,980. It would take 10.1 work days to recover the $20,000 needed for redesign ($20,000/$1,980). This step illustrates one way of elevating constraints—the fourth step in the TOC methodology.

449999

MANAGERIAL DECISION CASE

14–28

1. By discussing the amount by which his company and Piura have reduced costs, Mac may have violated the confidentiality standard. Specifically, Mac should: “Keep information confidential except when disclosure is authorized or legally required.” (II-1) He may also be involved in a conflict of interest, al-though he may not have realized this until the conversation of the evening un-folded. (III-1) Finally, he must “refrain from engaging in any activity that would prejudice carrying out duties ethically.” (III-2)

2. Mac would violate a host of standards: disclosing confidential information, engaging in a conflict of interest, and engaging in conduct that would discre-dit the profession. He would be well advised to refuse the offer and avoid any disclosure of information.

RESEARCH ASSIGNMENT

14–29

Answers will vary.

550000