ScienceAsia 28 (2002) : 291-300Aggregate Production Planning UsingSpreadsheet Solver: Model and Case StudyAtthawit Techawiboonwong and Pisal YenradeeIndustrial Engineering Program, Sirindhorn International Institute of Technology,Thammasat university, Pathumthani 12121, Thailand.Corresponding author, E-mail: [email protected] 26 Jul 2001Accepted 6 Feb 2002ABSTRACT Among existing aggregate production planning (APP) approaches, the spreadsheet solverapproach is found to be the most applicable for industries due to the following reasons: (1) the solveron spreadsheet software is readily available on virtually all personal computers, (2) the APP model isrelatively easy to formulate in a spreadsheet format, and (3) the results are easy to interpret. This paperpresents an APP model and a guideline to develop an optimal aggregate production plan using thespreadsheet solver approach. A manufacturing case study is presented to demonstrate how the guidelinecan be applied. The developed APP model is also evaluated whether it is satisfactory and can lead toimmediate implementation.KEYWORDS: Aggregate Production Planning (APP), Application in Industries, Spreadsheet Solver,Optimization, Case Study.INTRODUCTIONAggregate production planning (APP) is amedium term capacity planning that determinesminimum cost workforce and production plans tomeet customer demands. Its aim is to determine theproduction quantity and inventory level in anaggregate term. The aggregate production planusually covers a time period ranging from 12 to 24months. Data in the aggregate plan usually aremonthly or quarterly data. APP has a strong needwhen a demand pattern is highly seasonal.There are many techniques that can solve APPproblems such as trial-and-error, linear and nonlinear programming, linear decision rule, andsimulation search.1-4 Some of these techniques yieldthe optimum solution, while others give only acceptable ones. Additionally, some require models thatare easy to formulate, while others require complicated models. Spreadsheet software is one of thepowerful and practical tools for developing anaggregate production plan since it has a good userinterface and optimization capability.Spreadsheet software has many useful applicationsin production planning and control. For example, aspreadsheet template can provide multiple regressionoptions.5 It is helpful in solving forecasting problemswhen the dependent variable is binary. The spreadsheet models are also used to perform a sensitivityanalysis of performance measures in manufacturingenvironment.6 It can be used to determine whetheravailable capacity and inventory is above the maximumlevel or below the minimum level.7 Kharab alsodeveloped a macro program in the spreadsheetsoftware to solve linear programming problems.8The trial-and-error technique for solving APPproblem can be performed faster if it is applied onthe spreadsheet software. This technique is practicaland very easy to understand since it does not requirean extensive mathematical background. Since thetrials are subjectively determined by a user, it usuallytakes relatively long time to obtain a feasible andsatisfactory solution. Moreover, the solution maynot be the optimal one. There are some papersdemonstrating the way in which APP problems canbe solved using the trial-and-error technique on thespreadsheet software.9-11The spreadsheet solver is an add-in feature foundin recent versions of the spreadsheet software suchas Lotus 1-2-3, Microsoft Excel, and Borland’sQuattro Pro.12 This feature is capable of optimallysolving linear and nonlinear programming problems.Albright et al. demonstrated the use of spreadsheetsolver to solve small examples of APP problems.13Crandall varied some parameters such as inventoryholding cost, back order cost, and hiring and layingoff costs, and determined effects of individual parameters on a production plan in a variable demandenvironment.14 The spreadsheet solver approachgives an optimal solution, does not require extensive
292mathematical background, and is easy to understand,to formulate the problem, and to interpret the results.Furthermore, it does not need additional investmenton the software because the spreadsheet solver isalready included in the spreadsheet software.At present, most manufacturing companies donot systematically perform APP even though it is animportant part for developing the detailed productionscheduling due to the following reasons. Firstly, theAPP model developed based on the requirements andconstraints of their companies is not available.Secondly, most industries are not interested in acomplex approach that requires an extensivemathematical background since they lack wellqualified engineers. Thirdly, most industries requirean approach that is easy to understand and verify inorder to easily convince their management to agreewith its solution. Finally, an approach should notrequire additional investment on any expensivesoftware due to the ongoing economic crisis. Basedon these reasons, this study adopts the spreadsheetsolver approach.This paper has the following objectives:1. To propose a spreadsheet APP model whichis based on the general requirements and constraintsof industries.2. To propose a guideline for developing theoptimal aggregate production plan using spreadsheetsolver approach.3. To study the effectiveness of the spreadsheetsolver approach by evaluating whether the obtainedaggregate production plan is satisfactory and can leadto immediate implementation.This paper is organized as follows. Firstly, ageneral APP model based on the situations andgeneral requirements of industries is presented inSection 2. Then, a guideline for developing theoptimal aggregate production plan using spreadsheetsolver approach is presented in Section 3. A casestudy to demonstrate the validity of the proposedguideline and to serve as an example for developingthe optimal aggregate production plan is presentedin Section 4. Finally, results are discussed andconcluded in Section 5.THE APP MODELThe proposed APP model was developed withthe requirements of the situations and generalcharacteristics of industries. Therefore, it is differentfrom models available on textbooks and journals andit seems to be more practical in industries.ScienceAsia 28 (2002)Most industries use a monthly planning periodfor their master production plans. Therefore, theaggregate production plan should also adopt themonthly planning period in order to facilitate thedisaggregation of the aggregate plan into the masterproduction plan. The planning horizon of APP mustbe at least one year in order to cover the entire seasonalcycle.Parameters and decision variables of the modelare defined as follows.Parametersm Number of monthly planning periodsin the planning horizonn(t) Number of normal workdays in periodth(t) Number of holidays that can applyovertime in period t.RH Number of regular working hours ineach normal workday Number of allowable overtime hoursOHnin each normal workdayOHh Number of allowable overtime hoursin each holidayMIN W Minimum number of permanentworkers that can operate theproduction lineMAX W Maximum number of permanentworkers to operate the production lineKW Average productivity rate per man-dayof permanent workerKTW Average productivity rate per man-dayof temporary workerD(t) Forecasted demand in period tSS(t) Safety stock level in period tMAX On(t) Maximum overtime man-hours thatcan be applied during normal workdayin period tMAX Oh(t) Maximum overtime man-hours thatcan be applied during holiday inperiod tMAX TW Maximum number of temporaryworkers that can operate the productionlineMAX I Maximum allowable inventory levelMAX Sub Maximum allowable subcontractingunitsCW Average salary per month of a permanent workerCTW Average wages per day of a temporaryworkerCH Hiring cost per person of temporaryworker
293ScienceAsia 28 (2002)CLCICOWnCOWhCOTWnCOTWhCSub Laying off cost per person of temporary worker Average inventory holding cost permonth per unit of product Overtime cost per man-hour of permanent worker during normal workday Overtime cost per man-hour ofpermanent worker during holiday Overtime cost per man-hour of temporary worker during normal workday Overtime cost per man-hour of temporary worker during holiday Subcontracting cost per unitDecision variablesW Number of permanent workersTW(t) Total number of temporary workers inperiod tH(t) Number of temporary workers to behired at the beginning of period tL(t) Number of temporary workers to belaid off at the end of period t Overtime man-hours of permanentOWn(t)worker during normal workday inperiod tOTWn(t) Overtime man-hours of temporaryworker during normal workday inperiod tOWh(t) Overtime man-hours of permanentworker during holiday in period tOTWh(t) Overtime man-hours of temporaryworker during holiday in period tUW(t) Undertime (idle time) man-hours ofpermanent worker in period tUTW(t) Undertime (idle time) man-hours oftemporary worker in period tP(t) Total production quantity in period tI(t) Inventory level in period tSub(t) Amount of subcontracted unit inperiod tObjective functionThe objective of the APP model is to minimizethe sum of permanent worker salary, temporaryworker wages, overtime cost of permanent andtemporary workers, hiring and laying off cost oftemporary workers, subcontracting cost, andinventory holding cost. In this model, the overtimecosts of permanent and temporary workers duringworkdays and holidays are different. Thus, theobjective function as shown in equation (1) musttake this into consideration. The objective functioncan be written as shown below.Min total costsm [CW (W) COWn (OWn(t)) t 1COWh(OWh(t)) CTW (TW(t)) n(t) COTWn (OTWn(t)) COTWh (OTWh(t)) CH (H(t)) CL (L(t)) CSub (Sub(t)) CI (I(t))](1)Constraints1. Permanent worker constraintIn real industrial situation, most industries donot have a policy to repeatedly hire and lay offpermanent workers since laying off incurs a relativelyhigh compensation and results in loss of morale ofemployees and poor image of the companies.Therefore, the number of permanent workers mustbe the same for all periods. However, it may be ofinterest of some industries to know the optimalnumber of permanent workers that minimizes thetotal costs. Generally, if the optimal number ofpermanent workers is higher than the existingnumber, additional permanent workers can be hired.However, if it is lower than the existing number, therewill be no laying off. The company will wait untilsome permanent workers resign. This practice isdifferent from an assumption of past research papersthat allows repeatedly hiring and laying off thepermanent workers.9-10,14-15The number of permanent workers should notbe less than the minimum limit; otherwise theproduction line cannot function. Also, it should notbe more than the maximum limit; otherwise someworkers will be idle.MIN W W MAX W(2)2. Inventory constraintsThe inventory in each period is equal to theinventory from the previous period plus theproduction minus the demand of that period.I(t) I(t-1) P(t) - D(t) for t 1, 2, ., m (3)Moreover, all demands must be satisfied and theinventory level cannot be less than the specifiedsafety stock level.I(t) SS(t) for t 1, 2, ., m(4)The inventory level cannot exceed the maximumallowable limit since there are limited warehousespaces.
294ScienceAsia 28 (2002)I(t) MAX I for t 1, 2, ., m(5)3. Production constraintsThe production quantity in each period is equalto the sum of production quantities generated bypermanent and temporary workers during regulartime and overtime (both regular workdays andholidays), plus subcontracted quantities, minus aloss of production due to undertime (idle time) inthat period. Note that undertime can help to reduceunnecessary inventory level during low demandperiods. Constraint (6) allows different productivityrates between permanent and temporary workers.P(t) -W KW n(t) (OWn(t) OWh(t))KW /RH TW(t) KTW n(t)(OTWn(t) OTWh(t)) KTW /RH Sub(t) - UW(t) KW /RHUTW(t) KTW /RHfor t 1, 2, ., m(6)4. Overtime constraintsThe total overtime man-hours of permanent andtemporary workers must not exceed the maximumallowable limit. The limit is calculated based on thetotal number of permanent and temporary workers,number of days, and number of hours in each daythat the overtime can be applied.OWn(t) OTWn(t) MAX On(t)for t 1, 2, ., m(7)OWh(t) OTWh(t) MAX Oh(t)for t 1, 2, ., m(8)where MAX On(t) OHn n(t) (W TW(t))for t 1, 2, ., m(9)andMAX Oh(t) OHh h(t) (W TW(t))for t 1, 2, ., m(10)Since permanent and temporary workers workas a team in the same production line, the numberof overtime man-hours per person applied to bothgroups must be the same. Thus, Constraints (11)and (12) are required.OWn(t) / W OTWn(t) / TW(t)for t 1, 2, ., mOWh(t) / W OTWh(t) / TW(t)for t 1, 2, ., m(11)(12)5. Temporary worker constraintsThe number of temporary workers in each periodis equal to the number of temporary workers inprevious period plus the number of temporaryworkers being hired at the beginning of that periodminus the number of temporary workers being laidoff at the end of the previous period.TW(t) TW(t-1) H(t) - L(t-1)for t 1, 2, ., m(13)The total number of temporary workers in eachperiod cannot exceed the maximum allowable limitsince the production line has limited number ofworkstations where the temporary workers can beassigned.TW(t) MAX TWfor t 1, 2, ., m(14)6. Subcontracting constraintsNumber of subcontracting units cannot exceedthe maximum allowable limit since subcontractorshave limited production capacity.Sub(t) MAX Subfor t 1, 2, ., m(15)7. Non-negativity and Integer conditionsAll decision variables are nonnegative and somedecision variables representing number of workers,namely, W, H(t), L(t), and TW(t) are integer. Sincein real situation the variables W, H(t), L(t), and TW(t)have relatively high values, the integer conditionsfor these variables can be relaxed in order to reducethe computation time. The solutions can be laterrounded to the nearest integer.In conclusion, the proposed APP model hassalient characteristics that make it different from APPmodels in past research works. Firstly, the proposedAPP model explicitly differentiates permanent andtemporary workers since policies to manage thesegroups of workers and labor costs related to thesegroups are different. Secondly, number of permanentworkers must be the same for all periods but thenumber of temporary workers can be varied by hiringand laying off. Thirdly, total working hours (normalworking time plus overtime) for permanent andtemporary workers must be the same because bothgroups work as a team on the same production lines.Finally, the proposed APP model allows differentovertime labor costs during normal workdays andholidays since in practice the overtime labor costduring holidays is more expensive than that duringnormal workdays.The proposed APP model has been tested in threecompanies and presented to eight companies in a
295ScienceAsia 28 (2002)Workshop on APP for Thai Industries. Ten out ofeleven companies were satisfied with the conceptsand results of the proposed model after the modelwas slightly modified to match some specificrequirements of the companies. Only one companyrequires significant changes on the model.of temporary workers can be calculated fromrecruitment costs and training costs for new workers.It is recommended that a sensitivity analysis toanalyze the effect of the estimated values on theobtained solution be performed when the estimatedvalues are used instead of the exact values.GUIDELINE FOR DEVELOPING OPTIMAL AGGREGATEPRODUCTION PLAN USING SPREADSHEET SOLVERStep. 2 Formulate APP model in the spreadsheetformatAfter obtaining the necessary information, aspreadsheet APP model will be formulated followingthe objective function and constraints discussedearlier. Some constraints of the proposed APP modelmay be modified or deleted to match specificrequirements of each company. The spreadsheet APPmodel is then solved using the spreadsheet solver.The following guideline is proposed for thecompanies that are interested in developing theirown APP. The objective of this guideline is to providean easy and practical way to develop the aggregateproduction plan using the spreadsheet solver. Theguideline will recommend steps for developingaggregate production plan and necessary informationto be collected. By following this guideline step-bystep, the companies will be able to construct theirown aggregate production plan. The recommendedsteps for developing the aggregate production planusing the spreadsheet solver are summarized inFigure 1.Step 1. Data collectionNecessary data to be collected for developing APPmodel are all parameters in the proposed APP modelpresented in Section 2. In the case that the companydoes not have certain available information or someinformation cannot be exactly determined (such asinventory holding cost, and hiring cost), it can beestimated from other known information. Forexample, the inventory holding cost per year can beestimated to be 20%-30% of the product cost. Ifnecessary, it can be divided by 12 to get the inventoryholding cost per unit per month. The hiring cost1. Collect related data2. Formulate problem into speardsheet formatand solve problem using solver tool3. Evaluate the obtainedsolutionNot satisfy4. Implement the aggregate production planFig 1. Recommended steps for developing the aggregate productionplan.Step 3. Evaluate the obtained solutionsThis step can be done by presenting the constructed spreadsheet APP model and its solutions torelated departments of the company, namely,production, personnel, planning, sales and marketing,and warehousing, and let them judge whether thesolutions are acceptable. The comparison betweenthe existing aggregate production plan and theoptimal plan generated from the APP model maybe done in monetary term. If the solution is notacceptable, values of some input parameters mayneed to be reconsidered or the constraints may needto be modified. The spreadsheet APP model will berevised until the solutions are satisfactory.Step 4. Implement the aggregate productionplanAfter the spreadsheet APP model is satisfactorilydeveloped and solved, the obtained solutions canbe implemented. During the implementation of theaggregate production plan, some parameters of themodel may be changed, for example, demands,productivity rates, related costs, number of workers,and inventory levels. These parameters should beupdated periodically and the APP model is solvedto determine the revised aggregate production plan.CASE STUDYA case study is presented to demonstrate thevalidity of the proposed guideline and to serve as anexample for developing the optimal APP model. Thecompany under consideration is a medium-sizedmanufacturer of air conditioning units located inThailand.
296ScienceAsia 28 (2002)Step 1. Data collectionBy visiting and interviewing the company thecollected data can be summarized as follows:1. The planning horizon is 12 months.2. Forecasted demands, number of holidays thatcan apply overtime, and number of normalworkdays, in each period are shown in Table1.3. The regular working hours is 8 hours per day.4. Numbers of allowable overtime hours for eachnormal workday and holiday are 2 and 8hours, respectively.5. Minimum and maximum numbers ofpermanent workers to operate the productionline are 600 and 1,100 workers, respectively.Maximum number of temporary workers tooperate the production line is 500 workers.6. Average productivity rates of permanent andtemporary workers are 5 and 4.5 units perman-day, respectively.7. Amount of required safety stock in eachperiod is zero.8. Maximum allowable inventory level isunlimited.9. Maximum subcontracting units is unlimited.10. Average monthly salary per permanentworker is 5,500 Baht.11. Average wage per day per temporary workeris 162 Baht.12. Each temporary worker cannot be hiredlonger than four months according to Thailabor law. Otherwise the temporary workermust be transferred to become a permanentone.13. Average cost of hiring one temporary workeris 1,200 Baht.14. Laying off cost of temporary worker isnegligible.15. Average inventory holding cost per unit permonth is 200 Baht.16. Overtime costs per man-hour per permanentworker during normal workday and holidayare 34.38 and 45.83 Baht, respectively.Overtime costs per man-hour per temporaryworker during normal workday and holidayare 30.38 and 40.50 Baht, respectively.17. Subcontracting cost is 300 Baht per unit.18. Amount of inventory at the beginning of thefirst period is zero.19. The required amount of inventory at the endof the last period is zero.20. There are currently 600 permanent workersand it is the company policy to keep thenumber at this level.21. The company hired 150, 150, and 100 temporary workers three periods ago, two periodsago, and one period ago. They were hired atthe beginning of periods.Step 2. Formulate the APP model in the spreadsheet formatBased on the collected data, the APP model (inmathematical form) is formulated to clearly showthe objective function and constraints as follows.Objective function12Min Z [5500 W 34.38 OWn(t) t 145.83 OWh(t) 162 TW(t) n(t) 30.38 OTWn(t) 40.50 OTWh(t) 1200 H(t) 300 Sub(t) 200 I(t)](16)Constraints1. Permanent worker constraintW 600(17)2. Inventory constraintsI(t) I(t-1) P(t) - D(t)for t 1, 2, ., 12I(t) 0 for t 1, 2, ., 12(18)(19)3. Production constraintP(t) 3000 n(t) 0.625 (OWn(t) OWh(t)) 4.5 TW(t) n(t)Table 1. Number of workdays and holidays that can apply overtime, and forecasted demand in each period.period1234567Number of23222520212417normal workdaysNumber of4444444holidays thatcan apply OTForecasted136,000 140,000 146,000 147,000 160,000 140,000 82,000demand 5,000 117,000
297ScienceAsia 28 (2002) 0.5625 (OTWn(t) OTWh(t)) Sub(t) 0.625 UW(t)- 0.5625 UTW(t) for t 1, 2, ., 12(20)4. Overtime constraintOWn(t) OTWn(t) MAX On(t)for t 1, 2, ., 12OWh(t) OTWh(t) MAX Oh(t)for t 1, 2, ., 12where MAX On(t) 2 n(t) (600 TW(t))for t 1, 2, ., 12and MAX Oh(t) 8 h(t) (600 TW(t))for t 1, 2, ., 12OWn(t) / 600 OTWn(t) / TW(t)for t 1, 2, ., 12OWh(t) / 600 OTWh(t) / TW(t)for t 1, 2, ., 12(21)(22)(23)(24)(25)(26)5. Temporary worker constraintThai labor law stated that temporary workerscould not be continuously hired longer than fourmonths. After four months they must becomepermanent workers. Hence, Thai industries will layoff temporary workers after four months if they donot want to transfer them to permanent ones.Therefore, the Constraint (13) that is a general onemust be specifically modified into Constraint (27)and (28). Constraint (27) shows that the totalnumber of temporary workers working in the currentperiod is the sum of the numbers of temporaryworkers hired at the beginning of the last threeperiods and the current period. Constraint (28)indicates that temporary workers hired three periodsago will be laid off at the end of the current period.APP models developed from literature do not havethese constraints.9-10, 14-15TW(t) H(t-3) H(t-2) H(t-1) H(t)for t 1, 2, ., 12(27)L(t) H(t-3)for t 1, 2, ., 12(28)TW(t) 500for t 1, 2, ., 12(29)6. Non-negativity and integer conditionsAll decision variables are non-negative. H(t) areinteger for t 1, 2, ., 12.Spreadsheet modelThe spreadsheet APP model is shown in Table 2.The model is divided into two sections. The firstsection (the top part of the table) is the input datasection. All collected information will be enteredinto the corresponding cells. The second sectionis the calculation section. There are formulasembedded in cells to calculate the needed output.The decision variables are the number of temporaryworkers to be hired at the beginning of each period,numbers of overtime man-hours for permanent andtemporary workers during normal workdays andholidays in each period, number of undertime manhours in each period, and number of subcontractedunits in each period. The spreadsheet APP model issolved and the optimal aggregate production plan isshown in Table 2. The related costs are calculatedand shown in the bottom part of Table 2. The grandtotal cost which is the objective function of the modelis shown in the lower right cell of the table.Step 3: Evaluate the obtained solutionsAfter the spreadsheet APP model and theobtained optimal aggregate production plan arepresented to the company, there are comments asfollows. Firstly, the model has a very good userinterface. The outputs (worker plan, productionplan, and summary of costs) of the model containuseful information and are easy to understand. Themodel requires some inputs, which are not currentlyavailable, but they are possible to be estimated.Secondly, the model can be verified easily sincevalues of all parameters, decision variables, objectivefunction, and constraints are explicitly shown ononly one page. Correctness of mathematical formulacan be simply checked using a calculator. Management team of the company is rapidly convinced totrust the correctness of the model.Thirdly, the obtained optimal aggregate production plan shown in Table 2 is acceptable. Duringlow-demand periods (e.g., August and September),the numbers of temporary workers are very low orzero, there is no overtime work, and some workersmust work undertime to avoid producing unnecessaryinventories. During moderate-demand periods (e.g.,October), some temporary workers are hired, butthere is no overtime work and no undertime. Duringhigh-demand periods (e.g., January), temporaryworkers are hired and they must work overtimeduring workdays. However, there is no overtimework during holidays. During very-high-demandperiods (e.g., May), temporary workers are hired,and they must work overtime during workdays andholidays. Subcontracting is not recommended inany period since it is the highest cost alternative.At the end of April (before entering the highestdemand period), creating 1,187 units of inventoryis recommended since carrying inventory for one
Table 2. Spreadsheet APP model.298ScienceAsia 28 (2002)
299ScienceAsia 28 (2002)period is less costly than subcontracting in May. Thisis due to the fact that the overtime schedules duringworkdays and holidays reach their maximum limitsin May. With this situation, the production quantitycannot be increased unless (costly) subcontractingis allowed. Thus, producing additional units in Apriland carrying them over to May can avoid utilizingsubcontracting.Based on the optimal aggregate production planwith an objective to minimize the total cost, theoptimal policy for adjusting production rates for Thaiindustries is recommended and presented in Table3. To increase the production rate, the first priorityis to hire temporary workers, the second priority isto apply overtime work during workdays, andthe last priority is to apply overtime work duringholidays. The undertime may be applied during lowdemand periods to reduce production rate and avoidunnecessary inventory.This optimal policy is different from the currentnormal practice of Thai industries that is alsopresented in Table 3. Thai industries firstly applyovertime work during workdays, and then duringholidays, and finally use temporary workers sinceapplying overtime work is the most convenient(but costly) method. Moreover, they never allowundertime, which results in carrying unnecessaryinventory. The normal practice of Thai industries isdifferent from the optimal policy since Thaiindustries do not explicitly consider costs related toAPP and do not try to minimize the total cost.Therefore, the proposed spreadsheet APP model isvery useful for Thai industries.Step 4. Implement and revise the aggregateproduction planSince the optimal aggregate production plan issatisfactory, it is immediately implemented in thecompany. After one month, the aggregate productionplan is regenerated using a rolling horizon concept.We need to add forecasted demand, number ofworkdays, and number of holidays that can applyovertime of the last period to the spreadsheet APPmodel and update forecasted demands of otherperiods. The inventory at the beginning of the firstperiod, target inventory at the end of the last period,and number of workers hired during last threemonths are also updated. Updating the input databefore regenerating the optimal aggregate productionplan takes less than 10 minutes, and it takes lessthan one minute of computation time by the spreadsheet solver to obtain the optimal solution using a500 MHz, Pentium III PC. The company currentlytakes about one day for manually generating anacceptable (but not optimal) aggregate productionplan. Therefore, the company can save significanttime of a planner in using the spreadsheet APP modelinstead of manually generating the aggregateproduction plan.DISCUSSION AND CONCLUSIONSThis paper proposes a four-step guideline fordeveloping the optimal aggregate production planfor industries. A general APP model is developedbased on real situations and requirements ofindustries. A case study is presented to demonstratehow to develop the optimal aggregate productionplan using the proposed guideline.The proposed APP model and the obtainedoptimal aggregate production plan are useful formost industries since they supply useful informationand recommend appropriate actions. They recommendthe optimal number of temporary workers to be hiredat the beginning of each period, the optimal numberof temporary workers to be laid off at the end ofeach period, and the number of temporary workersthat should be available in each period. These piecesof information are useful for managing humanresources of the company. They also recommendthe optimal number of overtime man
Aggregate production planning (APP) is a medium term capacity planning that determines minimum cost workforce and production plans to meet customer demands. Its aim is to determine the production quantity and inventory level in an aggregate term. The aggregate production plan u