Lecture 15 capacity design2
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  • 1. Unit 2 Management of Conversion System Chapter 5: Capacity DesignLesson 15:- Economies and Diseconomies of scale and Learning curveLearning ObjectivesAfter reading this lesson you will be able to understand Economies of scale Diseconomies of scale Learning curve and its usesDear students, the concepts of economies of scale and diseconomies of scaleare of vital significance, as we shall presently realize.What is Economies of scale?The concept that increasing its output rate can reduce the average unit costof a good or service is called economies of scale.There are four principal reasons to go for economies of scale Fixed costs are spread over more units – In the short term, certain costs do not vary with changes in the output rate. When the output rate – and, therefore, the facility’s utilization rate- increases, the average unit cost drops because fixed costs are spread over more units. As increments of capacity often are rather large, a firm initially might have to buy more capacity than it needs. However,
  • 2. demand increases in subsequent years can then be absorbed withoutadditional fixed costs. Construction costs are reduced –Certain activities and expenses remain same in building small and largefacilities alike. Doubling the size of the facility usually does not doubleconstruction costs. Industries such as breweries and oil refineries benefitfrom strong economies of scale because of this phenomenon. Costs of purchased material are cut –Higher volumes can reduce the costs of purchased materials and services.It gives the purchaser a better bargaining position and the opportunity totake advantage of quantity discounts. Process advantages are found –High volume production provides many opportunities for cost reduction.At a higher output rate, the process shifts toward a line process, withresources dedicated to individual products. Firms may be in a position tojustify the dedicating resources to individual products. For example,higher volume allow a paper manufacturer to achieve greater efficiencythan manufacturers producing a wide variety of products in smallvolumes, because the mill can set up its machines for one long run of acertain grade of paper and not have to make as many adjustments fordifferent grades.Let us now focus our attention on the other issue i.e. the diseconomies ofscale.
  • 3. What is Diseconomies of scale?The average cost per unit increases as the facility’s size increases. Thereason is that excessive size can bring complexity, loss of focus, andinefficiencies that raise the average unit cost of a product or service. Theremay be too many layers of employees and bureaucracy, and managementloses touch with employees and customers. The organization is less agileand losses the flexibility needed to respond to changing demand. Many largecompanies become so involved in analysis and planning that they innovateless and avoid risks. The result is that small companies outperform corporategiants in numerous industries. Figure 5.3 illustrates the transition fromeconomies of scale to diseconomies of scale. The 500-bed hospital showseconomies of scale because the average unit cost at its best operating level isless than that of the 250-bed hospital. However, further expansion to a 750-bed hospital leads to higher average unit costs and diseconomies of scale.One reason the 500-bed hospital enjoys greater economies of scale than the250 –bed hospital is that the cost of building and equipping it is less thantwice the cost for the smaller hospital. The 750-bed facility would enjoysimilar savings. Its higher average unit costs can b explained only bydiseconomies of scale, which outweigh the savings realized in constructioncosts.
  • 4. Figure 5.3 Economies and Diseconomies of scaleLet us now take an example of estimating requirementsExample 5.2*A copy center in an office building prepares bound reports for two clients.The center makes multiple copies (the lot size) of each report. Theprocessing time to run, collate, and bind each copy depends on, among otherfactors, the number of pages. The center operates 250 days per year, with aneight hours shift. Management believes that a capacity cushion of 15% isbest. It currently has 3 copy machines. Based on the following table ofinformation, determine how many machines are needed at the copy center. Item Client X Client YAnnual demand forecast (copies) 2000 6000Standard processing time (hour/copy) 0.5 0.7Average lot size (copies per report) 20 30Standard setup time (hours) 0.25 0.40Solution. [Dp + (D/Q)s]Product1 + [Dp + (D/Q)s]Product2 + ...M= N[1 - C/100] [2000 * 0.5 + (2000 / 20) * 0.25]clientX + [6000 * 0.7 + (6000 / 30) * 0.40]clientY = (250days / year )(1shift / day )(8hours / shift )(1 − 15 / 100) 5305 = 1700
  • 5. = 3.12Note - If demand continues at the current level or grows, it may beworthwhile to consider the proposal to acquire a fourth machinePOM in practice 5.3* – Production capacity analysis at ChampioninternationalChampion International Corporation is one of the largest forest productscompanies in the world, employing over 41,000 people in the United States,Canada, and Brazil. Champion manages over 3 million acres of timberlandsin the United States. Its objective is to maximize the return of the timberbase by converting trees into three basic product groups: (1) buildingmaterials, such as lumber and plywood; (2) white paper products, includingprinting and writing grades of white paper; (3) brown paper products, suchas linerboard and corrugated containers. Given the highly competitivemarkets within the forest products industry, survival dictates that Championmust maintain its position as a low-cost producer of quality products. Thisrequires an ambitious capital program to improve the timber base and tobuild additional modern, cost-effective timber conversion facilities. An integral pulp and paper mill is a facility in which wood chips andchemicals are processed in order to produce paper products o dried pulp. Tobegin with, wood chips are cooked and bleached in the pulp mill; theresulting pulp is piped directly into storage tanks as shown in Figure 5.5.From the storage tanks the pulp is sent to either the paper mill or a dryer. Inthe paper mill, the pulp is routed to one or more paper machines whichproduce the finished paper products. Alternatively, the pulp is sent to adryer, and the dried pulp is then sold to other paper mills, which do not have
  • 6. the capability of producing their own pulp. The total system, referred to asan integrated pulp and paper mill, is a large facility costing several hundredmillion dollars. One of Champion’s major pulp and paper facilities is presentlycomprised of a pulp mill, three paper machines, and a dryer. As the facilitydeveloped, it was found that the pulp mill could produce more pulp than thecombination of paper machines and the dryer could use. A study wasundertaken to determine whether it would be worthwhile to invest inimprovements to increase the capacity of the dryer. One of the first questionsto be answered in the study was how much additional pulp could beproduced and dried, given each possible capacity increase on the dryer. A simple approach to this question is to look at average flows. Forexample, the pulp mill has a capacity of 940 tons per day (TPD), the threepaper machines together average 650 TPD of pulp use, and the dryer canhandle 200 TPD. Based on average flows for each ton of increased dryercapacity, we can produce one more ton of pulp in the pulp mill. Note,however, that this is true only until the capacity of the dryer reaches 290TPD, after which further improvements to the dryer will have no benefit. The above analysis is inadequate because it ignores the day-to-daydeviations from the average. That is, all of the equipment in the mill issubject to downtime and to variations in efficiency. For example, supposethat on one day, the pulp mill is inoperable for more than the average lengthof time; on the same day, the paper machines are experiencing less than theusual downtime. In this case there will be very little pulp available for thedryer, regardless of its capacity. This lack of pulp will not “average out” ondays when the opposite conditions occur, since there will be far more pulp
  • 7. available than the pulp dryer can handle. Consequently, the pulp storagetanks will become full, and the pulp mill will have to shut down. Based upon the above analysis, we can conclude that in order not tooreduce the production on the paper machines; the ratio of additional pulpproduction to the increase in dryer capacity will be less than 1. Since thebenefits of any investment in the dryer are directly proportional to this ratio,a simulation was undertaken in order to estimate this ratio as precisely aspossible. The simulation model that was developed had the followingcomponents:Pulp Mill –The pulp mill was assumed to have an average production rate of 1044TPDwhen it is operating, with an average of 10 percent downtime. The actualdowntime used in the model in each time period simulated was drawnrandomly from a sample of actual downtimes experienced by the pulp millover several months. Thus one day the pulp mill might be down 2 percent ofthe time, the next day 20 percent and so on.Paper Machine –The rate of pulp flow to the paper machines in a time period is a function ofthe particular type of paper being mad and the amount of downtime on thepaper machines. In the simulation, the rate of pulp flow was input to themodel based on a typical schedule of types of paper to be made. Thedowntime for each machine was drawn from a sample of actual downtimes.Pulp Dryer –
  • 8. In each run of the model, downtime on the dryer was drawn from a sampleof actual downtimes. The capacity of the dryer was set at different levels indifferent runs.Storage Tanks –The connecting link between the pulp mill, the paper machines, and thedryer is the pulp storage tanks. In the model all pulp produced by the pulpmill is added to the inventory in these tanks. All pulp drawn by the dryer andpaper machines is subtracted from this inventory. If the storage tanks areempty, the model must shutdown the paper machines. If the tanks are full,the pulp mill must be shut down. The actual rate at which the dryer isoperated at any moment must be set by the model (as it is in the reality) totry to keep the storage tanks from becoming “too empty” or “too full”. A computer program was developed to simulate the above process.The simulation program was run at various levels of dryer capacity. Thesimulation results showed that for every TPD of additional pulp capacity,approximately 0.8 TPD of additional pulp could actually be dried withoutreducing the production on the paper machines. This number was then usedby management in comparing the costs and benefits of the capital investmentnecessary to increase the pulp dryer capacity. Note that if the “averagebasis” analysis had been used, the benefits of the project would have beenoverstated by 25 percent.
  • 9. *Adapted from Applied production and Operations Management (J. R.Evans at al) West Publishing CompanyWell friends, Labour planning is another area of great significance. Let’s seehow.Labour planningSuppose that a company is interested in determining the number of qualitycontrol inspectors to have for a final inspection of a product. If eachinspector can work at a rate of p minutes per unit at an efficiency e (takinginto account fatigue, personal time, and so forth), let us see the number ofinspectors required in order to meet a required output rate R. In service organizations, labour planning represents one of the mostimportant aspects of capacity planning. Examples include nurse staffing inhospitals, operator staffing at a telephone switchboard, and the number ofgrocery clerks at check-out counters. To illustrate this approach in service organizations, suppose that asocial worker performs two major activities. Activity 1 requires 4 hours,while activity 2 requires 1.5 hours. Each person is available 40 hours perweek and an allowance for personal time and non-routine activities is 20percent. Thus the efficiency factor will be 1 - .20 = .80. The estimatedworkload is 40 cases per week of type 1 and 60 cases per week of type 2.We letp1 = time for activity 1 = 4 hours
  • 10. p2 = time for activity 2 = 1.5 hoursR1 = 40 cases per week of type 1R2 = 60 cases per week of type 2T = 40 hours per weekThen the minimum staff required for this agency is calculated as p1R1 + p 2 R 2 N= Te 4(40) + 1.5(60) = = 7.8125 40(.8)Thus eight workers will be needed to meet the forecasted demand. Ingeneral, k ∑ piRiN= i =1 , where k is the number of different activities performed. TeThe Learning curveDear students, all of us have a fair idea of what The Learning curve is allabout. As you do often (more), you tend to get better at it. Now, Stop thatwide grin. Just don’t get any funny ideas.Allow me to explain.If you have ever learned to type or play a musical instrument, you know thatthe longer and more often you work at it, the better you become. The same istrue in production and assembly operations. Improvement in productivityand quality of work as a job is repeated is called the learning effect. Thiswas recognized in the 1920s at Wright-Patterson Air Force Base in theassembly of aircraft. Studies have shown that the number of labour-hoursrequired to produce the fourth plane was about 80 percent of the amount oftime spent on the second; the eighth plane took only 80 percent as much as
  • 11. the fourth; the sixteenth plane 80 percent of the time of the eighth, and so on.In other words, as production doubles from N units to 2N units, the time perunit of the 2Nth unit is 80 percent of the time of the Nth unit. This is calledan 80 percent learning curve. Such a curve exhibits a steep initial declineand the levels off as workers become more proficient in their tasks. Thelabour content (in person-hours per unit) required to make a product,expressed as a function of the cumulative number of units made, is called alearning curve. Defense industries such as aircraft and electronics which introducemany new and complex products, use learning curves to assist managers inestimating labour requirements and capacity, in determining costs andbudget requirements, and in planning and scheduling production. Eightypercent curves are generally accepted as a standard, although the ratio ofmachine work to manual assembly affects the percentage to use. Obviously,no learning takes place if all assembly is done by machine. As a rule ofthumb, if the ratio of manual to machine work is 3 to 1, then 80 percent is agood value; if the ratio is 1 to 3, then 90 percent is often used. An even splitof manual and machine work gives an 85 percent curve. More generally, theamount of time required to make the Nth unit of the product will be TN = T1 . NaWhere TN = time to make the Nth unit (in person-hours) T1 = time to make the first unit a = (ln x)/(ln 2) x = learning rate (expressed as a decimal)This calls for a practical example.
  • 12. The following example illustrates the use of a learning curve in determininglabour requirements. Sherly Joseph produces handmade Christmas ornaments. She usuallyhires several students part-time in order to meet her productionrequirements. Sherly sells primarily to local department stores who need hermerchandise by December 1. Their orders are not placed until September, soSherly has essentially 8 weeks to make all the items. Since all manual labouris used, Sherly estimates that a 75 percent learning curve can be used as herpart-time employees are trained. She has observed in the past that it takes anaverage of about 60 minutes for a student to make the first ornament. Eachstudent works 10 hours per week. Sherly would like to know how manystudents will be required to meet any level of forecasted demand. A 75 percent learning curve has the following characteristics: Unit Time Required 1 60 2 45 (60 x .75) 4 33.75 (45 x .75) 8 25.31 (33.75 x .75) 16 18.98 (25.31 x .75) 32 14.23 (18.98 x .75) 64 10.68 (14.23 x .75) These points are plotted in Figure 5.6. Table 5.1 lists the approximately cumulative minutes required to produce a given number of units at a 75 percent rate of learning.
  • 13. Table 5.1 Cumulative Time for 75 percent learning curve Number of Cumulative units Time 1 60 2 105 4 179 8 293 16 463 32 850Figure 5.6 A 75 percent learning curveSherly knows from past years that even the most experienced worker willrequire about 15 minutes for each unit. So we can assume that the curvelevels off around 32 units. Thus the first 32 units require approximately 850minutes, or about 14 hours. Let us assume that the employees work at 80
  • 14. percent efficiency, after fatigue factors, getting supplies, and personal timeare taken into account. Therefore, each student can work effectively 10 x 8 x.80 = 64 hours over the 8 – week period. Because the first 32 units take 14hours, the 50 hours remain. At a rate of 4 per hour, each can produce anadditional 4 x 50, or 200, units, for a total of 232. Without using the learning curve, if a rate of 4 per hour is assumed forthe entire 64 hours, then we would have calculated that 256 units would beproduced, and we would have overestimated production by 11 percent,which could be a significant factor. The learning curve can be a useful toolin planning labour requirements and scheduling production when newoperations begin, since it usually takes some time until a steady-state level ofoutput is produced.Points to ponder