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  2. 2. Statistical techniques 1.Time trends and forecasting Time-series methods make forecasts based solely on historical patterns in the data. Time-series methods use time as independent variable to produce demand. In a time series,measurements are taken at successive points or over successive periods. The measurements may be taken every hour, day, week, month, or year, or at any other regular (or irregular) interval. A first step in using time- series approach is to gather historical data. The historical data is representative of the conditions expected in the future. Time-series models are adequate forecasting tools if demand has shown a consistentpatterninthe pastthat isexpectedtorecurin the future.Forexample,new homebuilders in US may see variation in sales from month to month. But analysis of past years of data may reveal that salesof newhomesare increasedgraduallyoverperiodof time.In thiscase trend isincrease in newhome sales.Timeseriesmodelsare characterizedof fourcomponents:trendcomponent,cyclical component,seasonal component,andirregularcomponent.Trendisimportantcharacteristicsof time series models. Although times series may display trend, there might be data points lying above or belowtrendline.Anyrecurringsequence of pointsabove andbelow the trendline thatlastformore than a year is considered to constitute the cyclical component of the time series—that is, these observationsinthe time seriesdeviate fromthe trenddue to fluctuations.The real Gross Domestics Product(GDP) providesgoodexamplesof atime seriesthat displayscyclicalbehavior.The component of the time series that captures the variability in the data due to seasonal fluctuations is called the seasonal component.The seasonal component issimilartothe cyclical componentinthat theyboth referto some regularfluctuationsina time series.Seasonal componentscapture the regularpattern of variabilityinthe time serieswithinone-yearperiods.Seasonal commoditiesare bestexamplesfor seasonal components.Randomvariationsintimesseriesisrepresentedbythe irregularcomponent. The irregularcomponentof the time seriescannotbe predictedinadvance.The randomvariationsin the time seriesare causedbyshort-term, unanticipated andnonrecurringfactorsthataffectthe time series. Smoothingmethods(stable series) are appropriate whena time seriesdisplaysnosignificant effectsof trend,cyclical,orseasonalcomponents.Insuchacase,the goalistosmoothoutthe irregular componentof the time seriesbyusinganaveragingprocess.The movingaveragesmethodisthe most widelyusedsmoothingtechnique.Inthismethod,the forecastis the average of the last“x” number of observations, where “x” is some suitable number. Suppose a forecaster wants to generate three- period moving averages. In the three-period example, the moving averages method would use the average of the most recentthree observationsof data in the time seriesas the forecastfor the next period.Thisforecastedvalueforthe nextperiod,inconjunctionwiththe lasttwoobservationsof the historical time series, would yield an average that can be used as the forecast for the secondperiod in the future. The calculationof a three-periodmovingaverage isillustratedinfollowingtable.Basedonthe three- period moving averages,the forecastmay predict that 2.55 million new homes are most likely to be sold in the US in year 2008.
  3. 3. Year Actual sale(inmillion) Forecast(inmillion) Calculation 2003 4 2004 3 2005 2 2006 1.5 3 (4+3+2)/3 2007 1 2.67 (3+2+3)/3 2008 2.55 (2+3+2.67)/3 Example:Three-periodmovingaverages In calculatingmovingaveragestogenerateforecasts,the forecastermayexperimentwithdifferent- lengthmovingaverages.The forecasterwillchoose the lengththatyieldsthe highestaccuracyfor the forecastsgenerated.Weightedmovingaveragesmethodisavariantof movingaverage approach.In the movingaveragesmethod,eachobservationof datareceivesthe same weight.In the weightedmovingaverages method,differentweightsare assignedtothe observationsondata that are usedincalculatingthe movingaverages.Suppose,once again,thata forecasterwantsto generate three-periodmovingaverages.Underthe weightedmovingaveragesmethod,the three data pointswouldreceivedifferentweightsbefore the average iscalculated.Generally,the most recentobservationreceivesthe maximumweight,withthe weightassigneddecreasingforolder data values. Year Actual sale(inmillion) Forecast(inmillion) Calculation 2005 2 (.2) 2006 1.5 (.3) 2007 1 (.4) 2008 .42 (2*.2+1.5*.3+1*.4)/3 Example:Weightedthree-periodmovingaveragesmethod A more complex formof weightedmovingaverage isexponential smoothing.Ithismethodthe weightfall off exponentiallyasthe data ages.Exponentialsmoothingtakesthe previousperiod’s forecastand adjustsitby a predeterminedsmoothingconstant,ά (calledalpha;the value foralphais lessthanone) multipliedbythe difference inthe previousforecastandthe demandthatactually occurredduringthe previouslyforecastedperiod(calledforecasterror).Exponentialsmoothingis mathematicallyrepresentedasfollows:New forecast=previousforecast+alpha(actual demand− previousforecast) Orcanbe formulatedas F = F + ά(D− F) Othertime-seriesforecastingmethodsare,forecastingusingtrendprojection,forecastingusing trendand seasonal componentsandcausal methodof forecasting.Trendprojectionmethodused the underlyinglong-termtrendof time seriesof datatoforecastitsfuture values.Trendand seasonal componentsmethodusesseasonal componentof atime seriesinadditiontothe trend
  4. 4. component.Causal methodsuse the cause-and-effectrelationshipbetweenthe variablewhose future valuesare beingforecastedandotherrelatedvariablesorfactors.The widelyknowncausal methodiscalledregressionanalysis,astatistical technique usedtodevelopamathematical model showinghowa setof variablesisrelated.Thismathematical relationshipcanbe usedto generate forecasts.There are more complex time-seriestechniquesaswell,suchasARIMA and Box-Jenkins models.These are heavierdutystatistical routinesthatcancope withdata withtrendsandthe seasonalityinthem. Time seriesmodelsare usedinFinance toforecaststock’sperformance orinterestrate forecast,usedinforecastingweather.Time-seriesmethodsare probablythe simplestmethodsto deployandcan be quite accurate,particularlyoverthe shortterm. Variouscomputersoftware programsare available tofindsolutionusingtime-seriesmethods. For ex., Epidemiologistcanconstruct endemiccurvesbasedonincidence of disease andalso establishthe likelylimitsof variations. If the incidence of adisease exceedsthe expectationbycertainlimits,the occurrence of an increasedincidence orepidemiccanbe anticipated. Activity analysis 2. Work sampling and activity analysis Work samplingisthe statistical technique fordeterminingthe proportionof time spentbyworkers invariousdefinedcategoriesof activity(e.g.settingupamachine,assemblingtwoparts,idle…etc.). It isas importantas all otherstatistical techniquesbecauseitpermitsquickanalysis,recognition,and enhancementof jobresponsibilities,tasks,performance competencies,andorganizational work flows.Othernamesusedforitare 'activitysampling','occurrence sampling',and'ratiodelaystudy'. In a worksamplingstudy,alarge numberof observations are made of the workersoveran extended periodof time.Forstatistical accuracy,the observationsmustbe takenatrandom timesduringthe periodof study,andthe periodmustbe representativeof the typesof activitiesperformedbythe subjects. One importantusage of the work samplingtechnique isthe determinationof the standardtime fora manual manufacturingtask.Similartechniquesforcalculatingthe standardtime are time study, standarddata, and predeterminedmotiontimesystems. Characteristics ofwork samplingstudy The study of worksamplinghassome general characteristicsrelatedtothe workcondition:  One of themisthe sufficienttimeavailable toperformthe study.A worksamplingstudy usuallyrequiresasubstantialperiodof time tocomplete.There mustbe enoughtime available (severalweeksormore) toconduct the study.  Anothercharacteristicismultiple workers. Worksamplingiscommonlyusedtostudythe activitiesof multipleworkersratherthanone worker.
  5. 5.  The third characteristicislongcycle time.The jobcoveredinthe studyhas relativelyalong cycle time.  The last conditionisthe non-repetitiveworkcycles.The workisnothighlyrepetitive.The jobsconsistof varioustasksrather than a single repetitive task.However,itmustbe possible to classifythe workactivitiesintoadistinctnumberof categories. Stepsin conducting a work samplingstudy There are several recommendedstepswhenstartingtoprepare awork samplingstudy: 1. Define the manufacturingtasksforwhichthe standardtime isto be determined. 2. Define the taskelements.Theseare the definedbroken-downstepsof the taskthatwill be observedduringthe study.Since aworkerisgoingtobe observed,additionalcategorieswill likelybe includedaswell,suchas"idle","waitingforwork",and"absent". 3. Designthe study.Thisincludesdesigningthe formsthatwill be usedtorecordthe observations,determininghowmanyobservationswill be required,decidingonthe number of daysor shiftstobe includedinthe study,schedulingthe observations,andfinally determiningthe numberof observersneeded. 4. Identifythe observerswhowilldothe sampling. 5. Start the study.All those whoare affectedbythe studyshouldbe informedaboutit. 6. Make randomvisitstothe plant andcollectthe observations. 7. Aftercompletingthe study,analyze andpresentthe results.Thisisdone bypreparinga reportthat summarizesandanalyzesall dataandmakingrecommendationswhenrequired. Example A work sampling study was made of a cargo loading operation for the purpose of developing its standard time. The study was conducted for duration of 1500 minutes during which 300 instantaneous observations were made at random intervals. The results of study indicated that the worker on the job was working 80 percent of the time and loaded 360 pieces of cargo during the study period. The work analyst rated the performance at 90 %. If the management wishes to permit a 13 % allowance for fatigue, delays and personal time, what is the standard time of this operation? Ans: Here, total study period = 1500 minutes Working fraction = 80 percent Average rating = 90 percent Number of units loaded = 360 Allowances = 13 % Example
  6. 6. 1: Bulldozer #224 was used 52 hours over the past 14 days, a use rate of 15.5% (52 divided by 336), assuming that a bulldozer, in theory, could be used 24 hours a day. Output rate — units of output produced by a person or machine, divided by time of work or operation. Example: Bulldozer #224 moved 87 cubic tons of material during the five days ending September 22. Workdays were eight hours each, so #224 averaged 2.175 cubic tons of material per hour of uptime during this week. For example:Inastudydone on PHCsnursesinPunjabrevealedthat – 15% of time wasspenton the directservicesincludingactual treatment, – 34% of time wasspenton supportive serviceslike administration,recordkeeping, maintenance,supervision,etc.; – 21% of time wasspenton travel and – 30% time wasspentonpersonal nonproductive. Such analysisthusenablesnotonlyascrutinyof activitesundertakenbutalsosuggestspossible modifications. Mathematical techniques 3. Linear programming Linear programming is one of the widelyused modeling techniques. Linear programming problems consistof an objective function(alsoknow ascostfunction) whichhasto be minimizedormaximized subject to a certain number of constraints. The objective function consists of a certain number of variables. The constraints are linear inequalities of the variables usedin the objective function. This technique is closely related to linear algebra and uses inequalities in the problem statement rather thanequalities.A linearprogrammingproblemcanfall inthreecategories:infeasible,unboundedand an optimal solution.In an infeasible problem values of decision variables do not satisfy constraint condition.A problemisunboundedifthe constraintsdonotsufficientlyrestrainthe objectivefunction so that for any given feasible solution, another feasible solution can be found that makes further improvement to the objective function. In an optimal solution, the objective function has a unique maximum or minimum value. Linear programming problems can be solved using graphical analysis method. Sensitive analysisis extensionto solution foundin linear programming to find out effect of parameter changes on the optimal solution. The parameters are called coefficients and can be quantity or value used in objective function. In linear programming results are rounded to get reasonable output, however rounded solution might not be feasible and many not give an optimal solution.Therefore,Integerprogrammingmodel isusedwithfractional values.Linearprogrammingis alsouse tosolve transportation,transshipment,andassigningproblems.Linearprogrammingiswidely usedinproductionplanningandscheduling.Itisverywellusedinairlineindustryforaircraftandcrew scheduling.
  7. 7. Example Revisit the above example of the farmer who may grow wheat and barley with the set provision of some L land, F fertilizer and P pesticide. Assume now that y unit prices for each of these means of production (inputs) are set by a planning board. The planning board's job is to minimize the total cost of procuring the set amounts of inputs while providing the farmer with a floor on the unit price of each of his crops (outputs), S1 for wheat and S2 for barley. This corresponds to the following linear programming problem: To each variable in the primal space corresponds an inequality to satisfy in the dual space, both indexed by output type. To each inequality to satisfy in the primal space corresponds a variable in the dual space, both indexed by input type. The coefficients that bound the inequalities in the primal space are used to compute the objective in the dual space,input quantities in this example. The coefficients used to compute the objective in the primal space bound the inequalities in the dual space, output unit prices in this example.Both the primal and the dual problems make use of the same matrix. In the primal space,this matrix expresses the consumption of physicalquantities of inputs necessary to produce set quantities of outputs. In the dual space, it expresses the creation of the economic values associated with the outputs from set input unit prices. Since each inequality can be replaced by an equality and a slack variable, this means each primal variable corresponds to a dual slack variable, and each dual variable corresponds to a primal slack variable. This relation allows us to speak about complementary slackness. Example Covering and packing LPs commonly arise as a linear programming relaxation of a combinatorial problem and are important in the study of approximation algorithms.[4] For example, the LP relaxations of the set packing problem, the independent set problem, and the matching problem are packing LPs. The LP relaxations of the setcover problem, the vertex cover problem, and the dominating set problem are also covering LPs.Finding a fractional coloring of a graph is another example of a covering LP. In this case, there is one constraint for each vertex of the graph and one variable for each independent set of the graph. Example Restaurants uselinear programming for menu planning. It uses basicalgebrato optimize meal production and thereby increase restaurant profits. Linear algebra reflects a direct relationship between an increase or decrease in food resources, and an increase or decrease in meal production. For example, if the kitchen has only half its needed supply of cream base, then it can only prepare half its normal amount of cream soups. Additionally, management can determine the cost of preparing different menu items to decide how many of each menu item to prepare for optimal profit.
  8. 8. Financial techniques 4. Cost accounting and analysis Cost Accounting refers to "Accounting for Costs" and Management Accounting refers to "Accounting for management". If the term Cost & Management is analysed, it consists of three words – Accounting, Management and cost. 'Accounting' refers to art and science of recording, classifying, summarizing and interpreting the financial transactions of a business. 'Management' refers to planning, organizing, directing and controlling of resources to attain stated objectives. Cost refers to expenditure incurred in the business. So, it can be said that Cost and management accounting in simple terms means recording, classifying, summarizing and interpreting the cost transactions for the management's decision-making. Recent developments in cost & management accounting stands for development in the area of cost and management accounting in addition to its traditional techniques viz., Standard Costing, Responsibility Accounting, Marginal Costing, etc. Modern techniques used by the management in Cost & Management Accounting for its decision making are as follows: * Back Flush Accounting – It is a system in which costing is delayed until goods are finished. Standard costs are then flushed backward through the system to assign costs to products. The result is that detailed tracking of costs is eliminated. The system is best suited to companies that maintain low inventories because costs then flow directly to cost of goods sold. Work-in- progress is usually eliminated, journal entries to inventory accounts may be delayed until the time of product completion or even the time of sale, and standard costs are used to assign costs to units when journal entries are made, that is, to flush costs backward to the points at which inventories remain. This system is possible only with a JIT type system of operation. * Throughput Accounting – It seeks to increase the pace with which products move through an organization by eliminating the bottlenecks with in the organization. The purpose of throughput accounting is not to control costs but as to demonstrate ways of improving profit by increasing production flow. Throughput Accounting is the only management accounting methodology that considers constraints as factors limiting the performance of organizations. It is based on Theory of Constraints (TOC). The theory focuses on constraints or bottlenecks to speedy production within an organization, cost gets reduced if raw materials are turned into products for immediate shipment to customers at minimum possible time. Throughput accounting's primary concern is the rate at which a business can generate profits. * Alternative Costing – ABC (Activity based Costing) is an alternative to the traditional way of accounting. ABCis a costing model thatidentifies the costpool, or activity centers, in an organization and assignscoststo productsandservices(costdrivers) basedon thenumberof eventsortransactions involved in theprocessof providing a productorservice. Asa result,ABCcansupportmanagersto see how to maximize shareholdervalue andimprove corporate performance.Ina businessorganization, the ABCmethodologyassignsanorganization'sresource coststhroughactivitiestothe products and services provided to its customers. It is generally used as a tool for understanding product and customer cost and profitability. An activity-based cost system provides management with an economicmapof theirenterprise;itidentifieswhere money isbeingmade andlost.Assuch,ABChas
  9. 9. predominantlybeenusedtosupportstrategicdecisionssuchaspricing,outsourcingandidentification and measurement of process improvement initiatives. Examples MANUFACTURING VS. NON-MANUFACTURING COSTS Manufacturing costs are those costs incurred by a producer of goods that are needed to transform raw materials into finished products, ready to sell. These costs consist of the cost of basic materials and components, plus the costs of labor and factory overhead needed to convert the materials into finished products. Materials and labor canbe classifiedas eitherdirect or indirect in relation to the final product. Direct materials are those major components that can be easily traced to the finished good and are accounted for carefully due to their significance to the product. In the case of manufacturing a lawn mower, for example, these types of materials would include the engine, housing, wheels, and handle. Indirect materials would include those minor items that are essential but which cannot be easily traced to the finished product. Examples of these would be screws, nuts, bolts, washers, and lubricants. One might say that the cost of keeping an account of each of these indirect items exceeds the benefit derived from having the information. Consequently, the costs of these items are accumulated as part of factory overhead and prorated to products on some appropriate basis. Direct labor refers to the efforts of factory workers that can be directly associated with transforming the materials into the finished product, such as laborers who assemble the product. Indirect laborers are those whose efforts cannot be traced directly or practically to the finished product. The indirect laborers would include maintenance personnel and supervisors. COMPUTING THE COSTS OF PRODUCING A PRODUCT OR SERVICE Manufacturing companies use a variety of production processes in creating goods. These processes include job shops, batch flows, machine-paced line flows, worker-paced line flow, continuous flows, and hybrids that consist of more than one of the previous separate flow process. The type of production process to a certain extent determines the type of product costing system that a company utilizes. Job shops, such as machine shops, receive orders for products that are manufactured to the unique blue-print specifications of the requesting customer. As such, it would be rare for these products to meet the needs of any other customer. Thus each "job" must be accounted for separately as the goods are produced and no goods would be produced on a speculative basis. An appropriate method to determine the cost of each unique item produced is activity- based costing (ABC). This method is discussed in detail elsewhere in this publication; please see Activity-Based Costing. The essence of ABC costing is that the exact costs of materials and labor, and a highly accurate estimate of factory overhead costs basedon the specificactivities (cost drivers) incurred to produce the goods, are determined for each unique product.
  10. 10. 5. Zero Based Budgeting According to Sarant, ZBB is a technique which complements and links to existing planning, budgeting and review processes. It identifies alternative and efficient methods of utilizing limited resources . It is a flexible management approach which provides a credible rationale for reallocating resources by focusing on a systematic review and justification of the funding and performance levels of current programs.” A method of budgeting in which all expenses must be justified for each new period. Zero- based budgeting starts from a "zero base" and every function within an organization is analyzed for its needs and costs. Budgets are then built around what is needed for the upcoming period, regardless of whether the budget is higher or lower than the previous one. ZBB allows top-level strategic goals to be implemented into the budgeting process by tying them to specific functional areas of the organization, where costs can be first grouped, then measured against previous results and current expectations Zero Base Budgeting (ZBB) in the public sector and the private sector are very different processes, and this must be understood when implementing a ZBB process in the public sector. “The use of ZBB in the private sector has been limited primarily to administrative overhead activities (i.e. administrative expenses needed to maintain the organization…)”. For example, Peter Pyhrr used ZBB successfully at Texas Instruments in the 1960s and authored an influential 1970 article in Harvard Business Review. In 1973, President Jimmy Carter, while governor of Georgia, contracted with Pyhrr to implement a ZBB system for the State of Georgia executive budget process. President Carter later required the adoption of ZBBby the federal government during the late 1970s. “Zero-Base Budgeting (ZBB) was an executive branch budget formulation process introduced into the federal government in 1977. Its main focus was on optimizing accomplishments available at alternative budgetary levels. Under ZBB agencies were expected to set priorities based on the program results that could be achieved at alternative spending levels, one of which was to be below current funding.” According to Peter Sarant, the former director of management analysis training for the US Civil Service Commission during the Carter ZBB implementation effort, “ZBB means “different things to different people.” Some definitions are implying that zero-base budgeting is the act of starting budgets from scratch or requiring each program or activity to be justified from the ground up. This is not true; the acronym ZBB, is a misnomer. ZBB is a misnomer because in many large agencies a complete zero-base review of all program elements during one budget period is not feasible;itwould result in excessivepaperwork and be an almost impossibletask if implemented.” In many respects the “common misunderstanding” of ZBB noted above resemble a “sunset review” process more than a traditional public sector ZBB process.
  11. 11. Examples There are many ways to create company budgets. Let's take the marketing department of Company XYZ as an example. Lastyear, the department spent $1 million. What's the right way to set a budget for next year? You might simply give the department $1 million again, but this might not reflect the changes in the marketing programs next year, the need to hire more marketing people due to additional sales, or other factors. Another way might be to give all departments a 10% increase or decrease based on what the board of directors would like earnings per share to be next year. This would give the department $1.1 million or $900,000, depending on which way the board goes. A third way would be zero-based budgeting, whereby the department starts with no budgeted funds and must justify every person and expense that should be included in the budget for the coming year. This might result in a budget of, say, $1,024,314, which is higher than last year but reflective of the actual needs next year. Use in Government Zero-base budgeting was introduced in the federal government by President Jimmy Carter in 1977 as a means to control program costs. It has since been heavily modified or replaced in various governments, but severalstates,such as Iowa for example, stilluseamodified version of zero-base budgeting to allocate funding. In Iowa, state agencies prepare for the governor performance measures and goals based on their statutory mission, and each budget item is considered in terms of its causal link to those performance measures. Legislators may opt to review or adopt this zero-base budget approach in their appropriations decisions. Use in Private Business Zero-base budgeting became popular with private businesses about the same time it was adopted for use in the federal government. In some cases,private businesses havebeen more successful with implementation than governments. In one example, the Florida Power and Light Company began using zero-based budgeting in 1977 -- the same year it was introduced in the U.S. Congress -- to administer the budgets for each of its staff departments. The company's systemtreated new and old problems the samewhen management developed the budget, where budgets based on prior years' expenditures may be more likely to treat older problems as higher priorities because money was budgeted for them already. According to the Encyclopedia of Management, the company's director found the strategy highly effective in controlling costs.