Estructura de costes

The premise of this chapter is that in general smaller lot sizes (process, transfer, and buffer stock) lead to better manufacturing performance and greater customer satisfaction. Yet, as explained, there are valid reasons for using large lot sizes and carrying large buffer stocks. Thus, if a company sets out to significantly reduce lot sizes and buffer stocks, it will not be able to do it all at once. Nor should it try. In lean production, reduction of lot sizes and buffer stocks is part of the continuous improvement process. It is, like PDCA, a process. The idea is to reduce lot sizes and buffers a little bit at a time and see what happens. As soon as the reduction begins to cause a problem, the next step is to find the source of the problem, prescribe a solution, and implement it. When the source of the problem has been eliminated, the lot sizes and buffers can again be reduced until new obstacles arise, and so on.

Some problem sources can be eliminated right away. For example, a machine that is unreliable might require only periodic, scheduled recalibration; in that case, the source of uncertainty can be removed as can all the buffers surrounding the machine. Other problem sources will be much more difficult to resolve, for example, a supplier that is habitually late, not willing to change, and for which there is no alternative supplier. Even with difficult problems, however, the principle is the same: keep trying no matter how long it takes; eventually a way to eliminate the source of the problem will appear (a different, more reliable supplier will be located, or else the production of the item will be moved in house). Like continuous improvement, reduction of lot sizes and buffer stocks should proceed methodically and perpetually.

Summary

Lot sizing affects manufacturing competitive advantage because it influences the cost, quality, lead time, and flexibility of production. Traditionally, U.S. managers have favored larger lot sizes, primarily because of the large expense associated with setting up production, placing orders, and making deliveries. Large size lots are also the result of using large setup expenses in EOQ-based models, which give the economic optimum, but only in terms of dollar costs. The drawback of large lot sizes is that even when they minimize dollar costs, they lead to greater nondollar costs associated with increased production lead times, hidden defects, and reduced scheduling flexibility.

Lean production acknowledges the problems and wastes connected with using large lot sizes. Small lot-size production is achieved by giving more purchasing responsibility to frontline workers, by reorganizing the facility layout to reduce material transfer distances and cost, by relocating materials to the point of use, and by working with suppliers to find ways to increase the frequency of deliveries, reduce the need for incoming inspection, and reduce the costs of handling, purchasing, and transportation. Even when process lot sizes must be somewhat large, using small-size transfer batches can increase speed and flexibility.

To the extent that large lot sizes and buffer stocks are maintained to absorb process variability and allow continued production in the face of problems, lot-size and buffer-stock reduction is a method of continuous improvement. It is a way to reveal the sources of variability and problems, and to force their removal.

The minimal lot size of a process batch depends not just on costs, but also on demand, production capacity, and setup times. Sometimes these factors in combination mandate larger lot sizes, particularly at bottleneck or almost-bottleneck operations. However, for a given demand and production rate, the major determinant of process lot size is the setup time. Changeovers and equipment setups that are long and inefficient are the major barrier to small lot-size production. Like many other wastes on the factory floor, however, setups are inefficient and time-consuming not because they have to be, but because seldom does anyone look carefully for ways to improve them. The next chapter describes a methodology for analyzing setups and the procedures for reducing setup time.

Notes

1. There are many costs besides dollar costs associated with lot sizing. These costs ultimately affect the quality of output and functioning of the organization (and so the bottom line), but they are difficult or impossible to quantify. These nondollar costs are discussed later.

2. That is, fixed cost has been confused with fixed procedures. Indeed, setup and ordering are fixed-cost activities (S remains constant regardless of the size of the lot); however, they are not fixed procedures in the sense that the steps involved in setup or ordering cannot be changed. They can be changed.

3. See J. Evans, D. Anderson, D. Sweeney, and T. Williams, Applied Production and Operations Management, 3rd ed. (St. Paul, MN: West Publishing, 1990), Chapter 13.

4. G. Woolsey, A requiem for the EOQ: an editorial, Production and Inventory Management Journal 29, no. 3 (1988): 68–72.

5. M. Umble and M. Srikanth, Synchronous Manufacturing (Cincinnati, OH: South-Western Publishing, 1990), 113–114.

6. Assuming the batches are independent, the standard deviation of the times for a group of batches is the squared root of the sum of the variances of the times for each of the batches.

7. Assumptions: the small batches are processed independently of each other, and the ratio of the average time to standard deviation, t/σ, is the same for every small batch as it is for the large batch (i.e., average time for a small batch t_S is one-fourth the large batch t_L, and standard deviation for a small batch σ_S is also one-fourth the large batch σ_L). See W. Hopp and M. Spearman, Factory Physics (Chicago: Irwin, 1996), 258–260.

8. R. A. Inman, The impact of lot-size reduction on quality, Production and Inventory Management Journal 35, no. 1 (1994): 5–7.

9. The example assumes any savings in lead times have not been filled by other jobs. A principle in lean production is to never schedule for full capacity. Some excess capacity is always available to allow for disruptions, problem-solving activities or, as in this case, special requirements.

10. N. Grunden, The Pittsburgh Way to Efficient Healthcare: Improving Patient Care Using Toyota Based Methods (New York: Healthcare Performance/Productivity Press, 2008).

11. The subject of bottleneck scheduling includes considerations much beyond production lot sizing and is a topic of synchronous manufacturing and the theory of constraints. See E. Goldratt and J. Cox, The Goal, rev. ed. (Croton-on-Hudson, NY: North River Press, 1987); E. Goldratt and R. Fox, The Race (Croton-on-Hudson, NY: North River Press, 1986); Umble and Srikanth, Synchronous Manufacturing.

12. Since most of the setup time in this example is external time, the full 40-hour workweek can be used to determine maximum number of setups.

Questions

1. What factors are included in order and setup costs? What about holding and carrying costs? Give examples. Why is it difficult to attach a precise dollar value to these costs?

2. How does the batch size affect the average inventory? 3. Explain the tradeoff between setup cost and carrying cost.

4. Comment on the following statement: The EOQ and EMQ models are not appropriate for determining the batch size of items processed through a sequence of multiple operations, but they might be appropriate for determining the batch size of items fully produced at one operation or procured from a supplier.

5. What factors and costs do the EOQ and EMQ models ignore? 6. How does the process batch size affect quality?

7. Discuss the effects of reducing the size of process batches. 8. Discuss the effects of reducing the size of transfer batches.

9. In general, at a bottleneck operation should the process batch size be large or small? Explain. (Assume a setup between each batch, and that larger process batches can be formed by combining multiple job orders for identical or similar items.) Should the transfer batches at a bottleneck be large or small? Explain.

10. If the setup times between products at a bottleneck operation are negligible, should job orders for identical or similar items be combined to increase the process batch size or should the jobs be processed separately? Explain.

11. Suppose an operation has excess capacity (i.e., it is not a bottleneck); however the setup time between batches is not insignificant. Should process batches be large or small? What determines the size of a process batch?

12. Discuss the reasons for carrying buffer stock. Give examples illustrating why buffer stock is carried between stages of a production process, and why it is carried for incoming materials.

13. Discuss how the following costs can be reduced: a. Order placement and processing

b. Material handling c. Shipping and delivery

PROBLEMS

1. A product has the following weekly demands:

Assume no initial inventory Carrying cost = $2.00/unit/week Setup cost = $130

Lead time = 1 week

Using the table, determine the lot sizes and calculate the total cost using: a. Lot-for-lot

b. Two-week period order quantity (assume “inventory” is the amount remaining after the first week of every 2-week order period).

2. A manufacturer buys cardboard boxes from a supplier. The annual demand is 36,000 boxes and is uniformly distributed. The boxes cost $4 each. The estimated order cost is $6, and the carrying cost rate is 30% per year.

a. What are the EOQ, and the annual order and carrying cost?

b. How many times a year are orders placed, and what is the average time, in weeks, between orders?

c. Using the answer from (b), if you round the average time between orders to the nearest week, what should the order quantity be? Would you recommend using this order quantity and time interval?

3. Suppose for problem 2 the actual demand turns out to be 72,000 boxes instead of 36,000 boxes. If you had used the EOQ from the previous problem, what would the annual order and carrying cost be? What percent larger is this cost than the cost estimated in (a)? What can you conclude about the cost of an incorrect demand estimate?

4. Referring to problem 2, again, suppose the box supplier is located close to the manufacturer’s plant. For any quantity ordered from the manufacturer, the supplier fills it by making daily deliveries of up to 200 boxes per day, for as many days as it takes to fill the order. Both the supplier and the manufacturer use a 5-day workweek.

a. What are the economic order quantity and the annual order and carrying cost? (Hint: Use EMQ.)

b. What is the manufacturer’s annual savings in carrying cost by using this system instead of the one in problem 2?

c. What is the average time, in weeks, between orders?

d. Suppose the manufacturer places orders at 2-week intervals. What should the order quantity be? How many days will it take the supplier to fill the order?

5. A machining area produces part QR for use in an adjacent assembly area. Estimated annual demand for the part is 20,000 units. The value of the part is $50 per unit. The annual carrying and handling cost rate is estimated to be 16%. The plant operates 250 days a year. The assembly area uses one part QR for each product, and it produces 100 products per day. When producing part QR, the machining area can produce 200 units per day. The cost of ordering and setup for part QR is $200.

a. What is the economic order quantity?

b. Suppose the assembly area places an order whenever the on-hand amount of part QR reaches a certain level, the reorder point. If it takes the machining area 2 weeks to begin filling an order, and if the assembly area wants to maintain a minimum, or safety stock of 200 units, at what on-hand quantity should an order be placed (i.e., what is the reorder point)?

c. If part QR were ordered from a supplier for the same costs, and the supplier delivered the entire order all at once, what would the order quantity be?

6. Do the analysis illustrated in Figures 5.3 and 5.4, except assume processing of product Y must precede processing of product X. What effect does this have on the shipping dates?

7. A product moves in sequence through five operations: V, W, X, Y, and Z. The processing time at each operation (min/unit) is 12, 18, 10, 24, and 12. Use a chart like Figure 5.2 to show the flow of the product through the five operations and the inventory accumulation after each operation. Determine the total production lead time and average inventory. Assume the production quantity and process batch size is 100. Use transfer batch sizes of (a) 100, (b) 50, and (c) 25.

8. For problem 7, assume the inventory carrying cost is $5/unit/day, and the material handling cost is $10/transfer. Determine the total carrying and total transfer costs for each of the three transfer batch sizes. Assume carrying cost is based on average inventory.

9. An operation is used to machine 10 kinds of parts. The total weekly requirement for all 10 parts is 900. Each part requires 20 seconds machine time. Assume the machine is to be scheduled for no more than 90% of its total available time. A normal workweek is 40 hours/week, but 4 hours a week are reserved for normal machine preventive and repair maintenance. If the setup for each kind of part is 1 hour:

a. What is the maximum number of setups per week?

b. What is the smallest allowable lot size, assuming all batches are the same size? c. To reduce the lot size in (b) by 50%, what must the setup time be reduced to?

times are shown in the following table. The operation is available 400 min/day, and the setup time between parts production is 10 minutes. If the amount of time each day devoted to setup is to be equally allocated among the three parts, what are the minimum lot sizes of the three parts?

Part Processing Time (sec/unit) Average Daily Volume (units)

GB 10 1,050

QED 7 550

RBW 13 300

11. Four products use the same machine. Processing times, daily production volumes, and setup times for the products are shown below. Assume the machine is run for two shifts, and is available for 800 min/day. The products are to be produced in a sequence that is repeated throughout the day until the required volume is filled. How many times a day can the sequence be repeated, and what is the resulting lot size of each product?