production planning optimization using genetic algorithm...

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Production Planning Optimization Using Genetic Algorithmand Particle Swarm Optimization (Case Study: Soofi TeaFactory)

Mansour Soofi 1* and Maryam Mohseni 2

Keywords: production planning, Ge-netic algorithm, ParticleSwarm Optimization Algo-rithm, Securitiesand ExchangeOrganization

Received: 09 November 2016,Accepted: 05 September 2017 Production planning includes complex topics of production

and operation management that according to expansion ofdecision-making methods, have been considerably developed.Nowadays, managers use innovative approaches to solvingproblems of production planning. Given that the productionplan is a type of prediction, models should be such that theslightest deviation from their reality. In order to minimize de-viations from the values stated in the tea industry, two ParticleSwarm optimization algorithm and genetic algorithm wereused to solve the model. The data were obtained through inter-views with Securities and Exchange Organization and those infinancial units, industrial, commercial, and production. Theresults indicated the superiority of birds swarm optimizationalgorithm in the tea industry.

Abstract

International Journal of Agricultural Management and Development (IJAMAD)Available online on: www.ijamad.iaurasht.ac.irISSN: 2159-5852 (Print)ISSN:2159-5860 (Online)Case Report

1 Department of Industrial Management, Rasht Branch, Islamic Azad University, Rasht, Iran2 PhD in Industrial Management, Tehran University * Corresponding author’s email: [email protected]

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INTRODUCTIONOne of the most important tasks of production

management is production planning. Good plan-ning can make the company competitive in astrategic position. Production planning, one ofthe principal duties of managers, aims to meetthe demand for the product on the market in theshortest time and lowest cost. Operations man-agement tries to achieve the organization's goalswith the aim of minimizing the cost of production,without compromising other goals such asproduct quality (Vonderembse & White, 2014).Today, managers tend to have flexible organi-zations consistent with the accelerating changesin market demand and to reduce productioncosts, improve the quality of products or services,promote innovation and risk-taking is so important(Pavão & Ravagnani, 2016). Of course, toachieve these goals, managers must make deci-sions in areas such as production, warehousing,and levels in the workforce. To this end, managerswho designed appropriate mathematical models,according to good demands such as reducingproduction costs and increasing the quality ofproducts, can find appropriate decision variableset by finding an optimal solution to this model(Braune et al., 2000).

In production planning, it can be recognizedhow much production is needed in each courseof planning to meet the demand for the goods.Planning methods that are used to solve pro-duction issues have changed due to improvementsin operation research techniques. Classical andtraditional optimization methods, long used insolving optimization problems, have been un-successful in solving complex problems, becausethey cannot solve problems with complex vari-ables and objective functions. The managers arecurrently facing various goals for the futurewhere these goals are not compatible with eachother (Fatemi Qomi, 2004). Accordingly, nowa-days, managers use heuristic methods to solveproduction planning problems where these methodsaim to look for very justified answers. These in-clude repetitive algorithms that any iteration in-cludes the search for better answers that is betterthan the previous answer (Zha et al., 2016). It

should be noted that the majority of companiesstill rely on the knowledge and experience oftheir experts for production planning and mod-eling, as well optimization of production planning.We should also know that optimization of anyfactory depends on the characteristics, needs,and constraints of the production system. Inother words, optimization goals in each factorymay vary from one factory to another and caninclude a variety of maximization or minimization(Naima et al., 2015).

The tea industry, like other industries, is facedwith more objectives and constraints and itsprocess is composed of many steps and a varietyof stations. For this reason, to use the maximumcapacity of machines and manpower, accurateproduction planning is needed. To have appro-priate production program to meet fluctuationsin demand in the tea industry, it is necessary toprovide a snapshot of conditions for tea productionin our model. This research trying to find a suit-able mathematical model for Soofi Tea Factoryto optimize production planning, determiningthe type and amount of product mix and pro-duction plan tailored to meet seasonal fluctuationsin demand in the factory. For this purpose, asuitable model, due to limitations faced by fac-tories, is introduced for tea industry using theproduction planning techniques and then usingideal planning and advanced techniques of op-erations research (Genetic Algorithm and ParticleSwarm Optimization), the designed model issolved; and by these techniques, the optimalsolution, that is the optimal amount of outputper workstation and normal and overtime hoursthat they work per month within the industrialcompany Soofi Tea is obtained, so that all Teamanufacturing companies by slightly changecan use the model to plan their production andmaximize efficiency.

The model is presented in the form of multi-product, multi-stage, and multi-period productionplanning system which contains two target func-tions: the first function is to reduce the cost ofcompany that in this study are non-linear. Asmentioned earlier, it is better to use modeling tooptimize production planning to overcome the

Production Planning Optimization Using Genetic Algorithm ... / Soofi and Mohseni

1 Recently, a fourth dimension has been added:– the institutional dimension of development396

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modern change. Of course, finding the optimalpoint in the case when faced with a complexmodel is not easy. In fact, classical and traditionaloptimization methods have long been used tosolve optimization problems; however, theyhave failed in solving complex problems. Becausethey have not the ability to obtain the globaloptimal point in optimization problems withhigh variables and complex target functions andto solve this problem, give us only one localoptimum point. Most classical optimizationmethods use gradient or higher-order derivativesof target function and start from an initial point,gradually the answer found has been improvedin ascending or descending order. In the gradientmethods, local minimum risk of exposure ishigh (Modares, 2013). One of the ways to over-come this problem is to use intelligent populationoptimization methods such as genetic algorithmsand Particle Swarm Optimization method thatare designed to find the global optimal solutionto complex problems. Production planning is todetermine production targets for a period of timein the future that is called the planning horizonas well as optimal use of resources to meet thespecified requirements (Wang et al., 2015). Thepurpose of production planning is to plan andarrange the order sequence based on strategicobjectives and the actual conditions of the man-ufacturing plant. Production planning attemptsto improve the material flow and efficient useof machinery in its production and includes dif-ferent management goals such as reducing workin process, lead times and costs, as well as im-proving responsiveness to fluctuations in demand(Zolghadri et al., 2008). In some manufacturingunits, the production process is such that thefinal product must pass several stages of pro-duction to complete. The sequence of productionsteps leads the input provide to each stage ofprevious output.

Goal programming was first created in 1960by Charnes and Cooper and is employed byLee in production planning in 1973. Lee pointedout that goal programming models allow disparatevariables to be collected in a single objectivefunction. The main problem of production plan-ning is fluctuating demand over time. Fluctuations

in product demand to be answered by adoptingdifferent strategies, such as changing the speedof production, changes in labor, overtime ornegligence, side contract and change the ware-house level. So far several methods is used tosolve such problems including the decisionsearch programming and linear programmingmethod, but these methods are not widely usedin industry. The main reason for this is thatthese models greatly simplifying the fact andleaves no room to impose manager tastes ormethod to solve problems. In addition, solvingproduction planning problem by any of theabove methods involve actual items productioncosts, staffing and storage that access to realvalues of these costs is very difficult. Becausemost of these cost are not linear and are ingrade two and above and they are not simple es-timate. Since the objective function of each ofthe above methods has cost structure, perhapsthe use of excessive approximation cause thatthe answer obtained is not be reasonable, althoughit may be optimized for used model. Each com-prehensive production planning issue is trying todetermine the optimal production staffing levelsand warehouse, so that at the least cost to meetdemand over the planning horizon. The mainproblem in determining these values is to contrastof the three targets (production, human resources,and warehouse) together. That means access toeach of Purposes undermines other purposes.

Therefore, the above objectives cannot begathered in a single objective function, such aswould be used in linear programming. On theother hand, often for any of these purposes,certain amount to be levied by managers whichmakes full access is not possible yet with goals.Therefore the problem in terms of the abovemodels is impossible. This problem can besolved by using goal programming models. Inaddition, it must be said that the three causes ofthe goal programming method to solve problemsof production planning is recommended, 1)Non-retractable objectives, 2) Fluctuating demandand, 3) Lack of access to the real cost items. Ingoal programming, unwanted deviations fromtarget values set by the decision making can beminimized in order to reach an acceptable solu-


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tion. Unwanted distortions measured by positiveand negative deviation variables that are definedfor every goal. They show the supra and infraachieve to any goal (Liu, et al., 2016). GeneticAlgorithm that highly influenced with naturalphenomena had been provided by Charles Darwinin the mid-19th century (Nunez-Letamendia,2015). Genetic algorithms first introduced byJohn Holland in 1962, then Goldberg expandedit in 1986 (Yand & Chiang, 1996). Due to thehigh potential in solving complex optimizationproblems much attention has been paid (Mitchell,1996). In genetic algorithms, each chromosomerepresents a point in the search space and a pos-sible solution to the problem. Chromosomesitself (solutions) are formed of a fixed numberof genes (variable). Set of chromosomes makeup a colony. With the impact of genetic operatorson each population, the new population is formedof the same number of chromosomes. Steps ofgenetic algorithm can be stated as follows:

1. The initial population is composed of peoplewho are usually randomly selected.

2. Current population estimates are based onthe relative fitness.

3. If the final criterion that is considered to bemeets, the ultimate solution is selected.

4. The new population is created based geneticoperators.

5. Actions are repeated from step 2 again and untilthe end criterion is met, the repetition is continued(Asgarpour Khansary & Hallaji Sani, 2014).

Genetic Algorithm uses two different geneticoperator named cutting (link) and mutation thatthe main operator in genetic algorithm is cuttingaction. This operator, by combining the twochromosomes as their parents creates two newchromosomes as children which are somewhatsimilar in terms of specifications to parents andinherit the properties of both. Through this in-heritance is that the gradual evolution arises ul-timately. The population will be modified overtime. It should be noted that interbreedingusually does not apply on all chromosome pairsselected for crossover. Usually the probabilityof crossover is considered for each chromosomepair within 0.6 to 0.95. This number is calledcrossover rate or crossover probability. But the

mutation operator create a sudden or randomchange on some of genes or chromosomes thatcause firstly, the likelihood of algorithm engagingin a locally optimal would be less and secondly,new areas is search and new chromosomes areadded to the cycle. The possibility of mutationaction on each chromosome is called mutationrate mutation or mutations probability. Usuallythis number is considered very small (0.001)(Kuo et al., 2012).

To select members of the next generationfrom among the members of the current gener-ation and offspring from operators, several se-lection methods have been proposed. The mainidea in the selection methods is that good peopleprefer on bad people where the best and worstof people defined by the fitness function f.

In the present study, tournament method isused to select. In this way a few chromosomesare randomly selected and the best of them willgo to the next generation (Depending on thesize of the tournament, which is usually between2 to 7). This work will continue to evolve thenext generation. The number of chromosomesthat are randomly selected called tournamentsize. Usually two people are randomly selectedfrom the population. Then a random number ris chosen between 0 and 1. If r < k (where k is aparameter, for example, 0.75), a more fitnessperson, and otherwise less fit person to beelected as a parent. The two then returned to theinitial population and again place in the selectionprocess (Liu et al., 2016). Usually, differentstop criteria are considered to stopping the al-gorithm. For example, the end time of the algo-rithm, or the number of algorithm iteration areexamples of the algorithm stop criteria.

Particle Swarm Optimization method (PSO)is one of the most recent population-basedsearch methods (Giftson & Rajan, 2015). InPSO, each member of a community called aparticle. These particles all are floating in mul-tidimensional space and moving based on theexchange of information with other members.Change the position of each particle is based onhis experience and knowledge and its neighbors.Thus, the particle in the search space is floatingand moving. And while movement of particles,


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each of them during the way movement store amemory of their best value and its position.From now, Xi (t) is used to show the position ofthe particle Pi at time t.

In PSO, the best value and position of eachparticle is stored in the variable ip best and bestposition of the particles in all the repetitionsstored on ig best (Kennedy, 1997). The newmove of particles takes place based on the re-sultant p best i (The past experience of eachparticle) and g best (best past experience of allthe particles) in the previous moving directionof particles (Mansour et al., 2008).

MATERIALS AND METHODSThe mathematical model designed for this

study is called goal programming model. Themodel consists of 276 decision variables; twoobjectives functions that include minimizingthe cost and maximizing sales; six categoriesof restrictions including restrictions on carsproduction capacity (indicating that each ma-chine cannot produce more than its capacity),balancing limits (to create effective communi-cation between the lines that in this limits theamount of each product at each station isbalance with the required amount of it toproduct in the next step), demand restrictions(storage of one product in one specified monthequal to the product storage in the previousmonth as well as production of that product inthat month minus the projected demand forthat product per month), restrictions of overtimehours and normal hours of work (number ofhours that people work in the area that thecompany has set), restrictions of the numberof people who work extra hours (the numberof people who work extra hours cannot exceedthe number of people in the factory) and re-strictions of the amount of inventory (the

amount of inventory that must be kept in stockcannot exceed the limit that has been set for it).To build capacity constraints and the balance,the production process should be consideredand then presented the respective constraintsfor each station. The production process isshown in Figure 1.

In such systems of production, a balance be-tween the various stages of the production sequenceis very important (Jewski & Ritzman, 2001).

St:

(l=1, 2, …, l) (j=1, 2, …, n )

(i=1, 2, …, m) (j=1, 2, …, n-1)

i=1, 2, ..m

All variables0

where:Xijk: Product i which by the method kmake inj stage

aijk l: The amount of product consumption i bymethod k in the process j in material balancestage 1

bjl: amount of raw material 1 in the process jk: Production methods.The overall goal programming model is as

follows.


Figure 1. The production process in Soofi Tea Factory.

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St:

(J=1, 2,…,n) (I =1, 2, …, m)

(r=0,1, 2,…,s) (j=1, 2, …, n)

cXj , di+ , di- ≥0

Xj: Model decision variables that can adoptany non-negative number

Di+, di-: Show Positive and negative deviationsfrom the ideal variables

Bi: Express the right number or level of desireof its goal i

Pn: specifies the kth priorities (k=1,2, ...., N)ofgoal.

Arj: Provides technical coefficients of themodel

Cij: Coefficients of the decision variablesbr: The right numbers of functional limitations To implement a fitness-proportionate selection,

several sampling methods have been proposedsuch as roulette wheel. Fitness or the selectionprobability of each chromosome is calculatedas follows:

where f j, is the value of chromosomes matchingfunction.

The particles movement rate i is defined asfollows:

The following steps are to be taken when em-ploying the Particle Swarm Optimization method:(Karimi et al., 2010)

1. Choose the initial population (populationof particles are randomly selected in the searchspace).

2. Calculate the value of particles using itspresent position (for every particles, its value isobtain according to the criterion function).

3. Compare the present value of the particlesand best experience and the following conditionalGreen Leaf Tea ((In fact, the value of eachparticle compared with pi besti and if it's currentvalue is pi pest, we replace the value of thecurrent position by p best I and the positionrelated it). If f (pi) p best I , then:

f(pi)=p best i (A

(B

4. Compare the current value of each particlewith the best previous experience on all Popu-lation particles and Green Leaf Tea of below:(In fact, the value of each particle comparedwith g besti and if the particles value is morethan g besti, we replace the value of the positionby g besti and the position related it). If f (pi) gi best, then:

f(pi)=p best i (A

(B

5. Change the speed of the particles accordingto the following equation:

where 1 and 2 are positive random numbers.6. Move the particle to its new position

7. Go to step 2 and repeat algorithm until con-vergence.

Decision variablesf1: Values greater than the cost of products

specified in Octoberf2: Values greater than the cost of products

specified in Novemberf3: Values greater than the cost of products

specified in Decemberf4: Values greater than the cost of products

specified in January


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f5: Values greater than the cost of productsspecified in February

f6: Values greater than the cost of productsspecified in March

h1: Values less than the sale of productsspecified in October

h2: Values less than the sale of productsspecified in November

h3: Values less than the sale of productsspecified in December

h4: Values less than the sale of productsspecified in January

h5: Values less than the sale of productsspecified in February

h6: Values less than the sale of productsspecified in March

PC1ijt: Oxidation and fermentation Tea that isgenerated in the band i with difficulty j inperiod t.

PC2ijt: Product that is generated in the Fixationi with difficulty j in period t.

Iptt: The Green Leaf Tea that is stored in thewarehouse of raw materials in band during theperiod t.

RM jt: The oxidation Tea produced with diffi-culty j in period t.

RSt: Oxidation Tea amount stored in the period tIot: The Natural flavors of tea is stored in the

intermediate product warehouse in period t.CM ijt: The amount of tea which are produced

by the mill i with the genus j in period t.ZLt: The additives for production in the period tIlt: The amount of tea stored in the period t in

the warehouse number one.IMt: The amount of tea stored in the period t

in the warehouse numbers two.ISt: The amount of tea stored in the period t in

the warehouse number three.Sijt: The amount of tea are ready to sell from

the final station with a label i with genus j inperiod t.

Nt: Normal hours of work per worker in period tLt: Number of employees who work extra

hours during tMt: The number of hours of overtime work

per worker in period tISijt: The final balance of the tea with label i

and genus j in period t.

Model parametersThe model parameters include projected de-

mand of different products according to thetype of material and the period of maximum-band capacity and the efficiency of various de-vices and the beginning inventory of productswith label i for genus j in period t. Goals amountof sales and the cost of the salary of regularworking hours, overtime, the cost of one squaremeter warehousing product, the number of work-ers who work in overtime; minimum number ofnormal working hours and the maximum andminimum number of overtime hours per workerand the selling price and cost of production perKg of product. C.cap1ijt: The maximum capacity of the

circling to dry i to produce a production withdifficulty j in period t.M.cap2ijt: The maximum capacity of each

Oxidation and Fermentation device i to producea production with difficulty j in period t.I.capt: The maximum capacity of Green Leaf

Tea warehouse to store raw materials crushedin the period t. RM.capjt: The maximum capacity of the Oxi-

dation and Fermentation batching machine toproduce a production with difficulty j in period t.IO.capt: The maximum capacity of the central

warehouse to store the Shaping Tea in band inthe period t.RS.capt: Maximum capacity of the form in

period t.K.capt:The maximum capacity of the roasting i

to produce a production with degree j in period t.CM.capijtt: The maximum capacity of Oxida-

tion and Fermentation device to produce a pro-duction with degree j in period t.IL.capt: The maximum capacity of the device

number one to shaping tea in period t.IM.capt: The maximum capacity of the device

number two to shaping tea in period t.IS.capt: The maximum capacity of the device

number three to shaping tea in period t.S.capijt: The maximum capacity of the selling

station of products with devices i with genus jin period t.N t min: Normal minimum number of hours

each employee works in period t

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N t max: Normal maximum number of hourseach employee works in period tL t max:Maximum employees who work in period tM t max:Maximum hours that each worker has

overtime in the period tM t min: Minimum hours that each worker has

overtime in the period tIS ijt-1: The amount of tea inventory with label

i and genus j at the beginning of the first month.D ijt: The demand for teas with label i and

genus j in period t.C ijt: The cost of one Kg tea with label i and

genus j in period t.P ijt: Sale price of Kg products with label i

and genus j in period t.C RL: The cost of one normal work hours per

worker in period tC RO: The cost of one hour of overtime per

worker in period t.C IO: The cost of inventory per square meter

products in the period t.gt: The goal set for maximizing sales rev-

enue.%X: The efficiency of Oxidation and fer-

mentation unit%Y: Efficiency of shaping devices%A: Tea percent% (1-A): % of additives

The mathematical model

(1)

(2)

N t min N t N t max (3) L t L tmax (4) S ijt + IS ijt-1 - Isijt D ijt (5) M tmin M t M t max (6) PC 1ijt C.cap 1ijt (7)PC 2ijt C.cap 2ijt (8) IP t I.cap t (9)

RM jt RM.cap jt (10)RS t RS.cap t (11) K ijt K.cap ijt (12)IO t IO.cap t (13)CM ijt CM.cap ijt (14)IL t IL.cap t (15) IM t IM.cap t (16) IS t IS.cap t (17)S S.cap ijt (18)

(19)

(20)

(21)

(22)

(23)

(24)

(25)

(26)

(27)

(28)

As mentioned, the study aimed to satisfiedtwo objectives: Reducing costs and increasingsales that two equations (1) and (2) in the above


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model reflects the two objectives functions.Thus, the (1) relate to 4 group of cost includescost of production, normal wage labor costs,the cost of overtime wage and factory storagecost and Ct represents the goal cost. Equation(2) is also refer to the second goal, that is theproceeds from the sale of tea products and gtrefers to goal sale. Equation (3) ensures thatnormal hours of labor in the factory does notexceed from less than the minimum workinghours and the maximum working hours.

Equation (5) ensures that labor overtimehours in the factory does not exceed from lessthan the minimum overtime hours and the max-imum overtime hours. As equation (6) suggests,the amount of a product inventory in the previousmonth in addition to the amount of product inthat month minus the amount of inventory inthat month must be greater than anticipated de-mand for the product on the same month. Equa-tion (7) indicates the capacity constraints ofOxidation and fermentation device and equation(8) indicates the form capacity constraints andensures that the product produced by the moldfor a given period and certain hardness cannotexceed the maximum capacity of Fixation /Kill-green devices. Equation (9) refers to rawmaterial storage capacity constraints.

Equation (19) means that the products of dif-ferent machines in the first station are equal tothe input to the warehouse of Green Leaf Teas.Equation (10) states that the prepared oxidationTea should not exceed the maximum amount ofFixation / Kill-green devices to produce pro-duction. Equation (20) means that the inputGreen Leaf Tea to oxidation Tea constructionequipment is equal to the amount of material inthe warehouse for raw materials. According toequation (11) the amount of material stored ineach period cannot exceed the maximum capacityof vibrating table. Equation (21) means theamount of input material in the silo of raw ma-terials is equal to manufactured products fromraw mill minus waste moisture produced by thegrinding of raw materials. The main part takesplace when drying that according to (12) theproduct is not more than the maximum capacityof the Fixation / Kill-green devices.

Equation (22) indicates that total powderedmaterial stored in the silo of raw materials isequal to imported materials to oxidation Teamachine building. This means that all materialsgo from silo of raw materials into the devices.Equation (13) ensures that the additive that isstored in the intermediate products stock ineach period does not exceed the maximumstorage capacity. Equation (24) states that allmaterials that are inserted into the machine isnot converted into oxidation Tea, but dependsto station efficiency (% y); So, the materialleaves the device to the next round is not equalto the material inserted into the machine. Equation(13) refers to the limited capacity of oxidationtea shaping for the production. According toequation (23), a percentage of additives areadded to the tea that is removed from the deviceto achieve oxidation tea in the next step. Equations(15), (16) and (17) refers o the limited capacityof three Oxidation Tea silos. And according tothe equation (25), (26) and (27), all productswill be imported to the warehouse where theyare stored. Equation (19) refers to labels of pro-duced oxidation Tea and limited capacity to acertain degree production. Equation (28) meansthat all products go to sales station.

RESULTSAfter making the appropriate model, decision

maker can act on any kind of experience andapplied it. As described earlier, the present studywith the help of Genetic Algorithm and ParticleSwarm simulation algorithm sought to solvethe proposed mathematical model. In the firststep, the basic parameters of the algorithmshould be determined. In Particle Swarm simu-lation algorithm, each particle is a potential an-swer. As such, each particle has 276 decisionvariables. In addition, in genetic algorithms,every chromosome is a potential answer thathas 276 decision variables. Accordingly, thesearch space in each of these two algorithmswill have 276 dimensions. In the studied factory,as mentioned the value of all objective functionto manage all the same and rate the weightedfactor for both functions is considered one. Inthe optimization model in genetic algorithm,


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the extended sampling space is considered andselection method is tournament. Basic parametersof GA and PSO are shown in Tables 1 and 2.

Moreover, r1 and r2 random numbers in theperiod [0, 1] and , the inertia weight decreaseslinearly during the iterations of the algorithm. Inthe beginning, is considered equal to 1 and finallycan reach 0.5 with trial and error to achieve betterresults (Soleimani & Kannan, 2014). Next, by col-lecting the necessary data from the Soofi TeaFactory and after importing the inputs to the modelby the programming software called MATLAB,the obtained model using GA and PSO were solvedand the optimum solutions were obtained. The an-swers of the model include the amount of outputper workstation, the number of overtime hours andthe normal number of hours that employees work

per month and the number of employees who workextra hours per month, end inventory for eachproduct per month, and the deviation rate of the ob-jective functions from the goals assigned to them.

Data collectionIt is noteworthy that before entering data and

parameters into the model in the present study,the data were obtained through interviews withSEO and those in financial units, industrial,commercial and production. Storage cost perKg of tea is 1000. The factory has 350 workersat its manufacturing plant in normal time work.The cost of each worker's salary for normalworking hours is 2000 and the cost of wagesper worker per hour of overtime is 3500.Thecollected information is shown in Tables 3 to 6.


Parameters Value

Mutation rateCrossover rateInitial population sizeNumber of generations

0.10.840100

Table 1Parameters of Genetic Algorithm

Parameters Value

Number of particlesNumber of generationsAcceleration coefficient g best (c2)Acceleration coefficient p best (c1)

4010022

Table 2PSO algorithm parameters

Goal October November December January February March

CostSale

22100000004210000000

22000000004162000000

19000000003580000000

18900000003570000000

196500000003710000000

21600000004130000000

Table 3Data on Goals (IRR)

Teascost of perKg (to IRR)

selling priceper Kg (to IRR)

Max inventory ofend period (to kg)

Tea stock at the beginning ofthe first month planning (to kg)

Black

Green

Tea bag

IIIIIIIII

2500030000260003150002550032500

500005650051500580005100057500

030000

30000

3500

030000

20000

3000

Table 4Data on the Genus Product and Related Information (IRR)

Tea Type October November December January February March

Black

Green

Tea bag

IIIIIIIII

25000400004000300060003000

24000380003000200050005000

20000300003000200050006000

20000300003000200050006000

22000300004000300040006000

25000400003000300030007000

Table 5Data on Projected Demand for the Next 6 Months (kg)

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The answerers obtained from the modelTo solve the problem in two ways Genetic

Algorithm and Particle Swarm algorithm, theoptimum amount of product on each work-station according to number of machine,

genus, as well as tag of product and productionrate in different months/Kg can be obtained.Tables 7 and 8 show the values obtainedfrom the algorithm:

The regular working hours overtime and the


Specifications

Loading Place

Green leaf tea stock

Oxidation tea production

Additives Stock

Fixation / Kill-green devicesNumber of shaping devices

Green Leaf tea storageTea

Oxidation tea

Products storage

Total: 2Power loading of Tea in months/ kg: 90000Total: 3Capacity in kg: 20/180/160Monthly production capacity in kg: 2000For each ton of entries: 600 kgMonthly capacity in kg: 90000Scrap percentage: 40%Total capacity of mold in months: 264000Total: 12Power Monthly: 178000Capacity in Kg/ Month: 528000Monthly production power/hours: 800Monthly production power/ kg: 70000Monthly production power/hours:200Monthly production power/ kg: 40000-Additives for oxidation Tea capacity per month: 900000 kg ; Combined ratio: 95%-Capacity of oxidation Tea corrective materials/month: 300000Combined ratio: 5%

Table 6Other Data

Production station

Type of

genus pro-

duce

Production

October

Production

Novem

ber

Production

Decem

ber

Production/

January

Production

February

Production

March

Loading Place

Fixation Tea

Shaping

Stock intermediateproductsAmendmentsDryerRaw materials SiloRaw MillRaw material storageCircling 1Circling 2Additive

Lot By Lot

Quantity

Fixation IM1Fixation IL2Fixation IH3

i=1i=2i=3i=1

i=1i=1i=1i=1i=1i=1i=2i=3

BlackGreenTea bagBlackGreenTea bagAll threeAll threeAll threeAll threeAll threeAll threeAll three

All threeAll threeAll threeAll threeAll threeAll threeAll threeAll three

2500040006000370003500250026000260002600026010260102601071580

200000238590238600477180477190178590178590120000

2400030005000380002000500025670256702567025680256802568070530

200000235080235090470190470180175080175080120000

2000030005000300102000600022010220102201022020220202202058970

200000196560196560393120393110136560136560120000

2000030005000334801000350021990219902199021990219902199058930

200000196440196430392850392850136440136440120000

2200040004000300001500700022830228302283022830228302283061580

200000205260205260410520410530145260145260120000

2500030006000365003000300025500255002550025500255002550070000

200000233340233330466680466670173340173340120000

Table 7Optimum Amount of Product in Each Station Using GA (kg)

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number of people who work overtime per monthin studied plants are expressed in terms of vari-ables and values obtained from using geneticalgorithm and Particle Swarm algorithm shownin Tables 9 and 10.

The amount of each product must be in storageper month using Genetic Algorithm and Particle

Swarm also shown in tables 11 and 12.Tables 13 and 14 shows the deviation from

the objective functions, each of which hasbeen implemented five times by each of thealgorithms. In different performances of thetwo algorithms, the amount of output perworkstation was identical, while the number


Production station

Type of

genus

produce

Production

October

Production

Novem

ber

Production

Decem

ber

Production/

January

Production

February

Production

March

Loading Place

Fixation Tea

Shaping

Stock intermediateproductsAmendmentsDryerRaw materials SiloRaw MillRaw material storageCircling 1Circling 2

Lot By Lot

Quantity

Fixation IM1Fixation IL2Fixation IH3

i=1i=2i=3i=1

i=1i=1i=1i=1i=1i=1i=2

BlackGreenTea bagBlackGreenTea bagAll threeAll threeAll threeAll threeAll threeAll threeAll three

All threeAll threeAll threeAll threeAll threeAll threeAll three

250004000600370303500250026010260102601026020260202602071610

200000238690238700477380477390178695178695

2400030005000380002000502025675256752567525685256852568570580

200000235270235280470540470550175275175275

2000030005000300202000608022030220302203022040220402204059070

200000196900196900393800393790136895136895

2000030005000334501500340022115221152211522125221252212559240

200000197800197800395600395600137800137800

2200040004000300001700700022900229002290022910229102291061820

200000206070206070412150412150146070146070

2500030006000365003100300025530255302553025530255302553070094

200000233650233660467300467310173655173655

Table 8Optimum Amount of Product in Each Station Using PSO (kg)

Month Regular hours Overtime hours number of people who work overtime

OctoberNovemberDecemberJanuaryFebruaryMarch

160150140130130150

505050505050

304030405030

Table 9Number of Hours Worked and the Number of People Who Work Overtime Based on GA

Month Regular hours Overtime hours number of people who work overtime


160150140130130150

505050505050

405040305540

Table 10Number of Hours Worked and the Number of People Who Work Overtime Based on PSO

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of overtime hours, the number of regular work-ing hours and the number of designated peoplewere fixed. Because the changes of overtimehours, regular hours, and the number of peoplework overtime per month affect only the costsobjective function and will not affect the salesobjective function.

The model was aimed at reducing the total

distortions. According to the results that havebeen obtained by PSO, whole unwanted devi-ations from target values set by the expertsparticipating in PSO is less than when themodel is solved using GA. And from this, itcan be concluded that the results obtained fromof PSO are better than the ones that can beachieved by GA.


MonthEnding inventory

Black Green Tea bag


LBLi=1000000

Qi=20020350035000

LBLi=1000000

Qi=2250025002500150000

LBLi=1000000

Qi=2250025002500000

Table 11The Ending Inventory Based on GA (kg)

MonthEnding inventory

Black Green Tea bag


LBLi=1000000

Qi=2303050350035000

LBLi=1000000

Qi=22500250025002000700800

LBLi=1000000

Qi=2250025202600000

Table 12The Ending Inventory Based on PSO (kg)

Performance 1 2 3 4 5

f1f2f3f4f5f6h1h2h3h4h5h6F

154000012660006752600052460005405000025400001075000020000001344100095590001550000010750000194168000

60850004369800025256000177280008435000262580001075000020000001344100095590001550000010750000177180000

3405500040000

558880005809000290000254000010750000200000013441000955900015500000750000

160622000

67330002715000026525000222310003336900089100010750000200000013441000955900015500000750000

186918000

434300037340000992100028446000128900001199100010750000200000013441000955900015500000750000

186931000

Table 13The Deviations from GA with the Population Size 40

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CONCLUSIONAccording to the results and outputs of the

model by the Genetic Algorithm and ParticleSwarm optimization algorithm, it can be con-tended that the production rate by PSO is higherthan that of GA. As we know, organizations aretrying to produce more to gain further profit. Inthe answer obtained from Genetic Algorithmand Particle Swarm Optimization Algorithm(see Table 7), the total products that achieved insales within the six months that the organizationis planning using genetic algorithms is 433 990(the sum of all values in station sales) and usingParticle Swarm Optimization Algorithm is 434800 (Table 8). This amount associated with anincrease of 810 Kg of tea than to use genetic al-gorithms. Also compared to tables 7 and 8, itcan be seen that the production in other productionstations is more obtained by PSO algorithm.This means that the production stations capacitymore used. As such, given that in any organiza-tion, management aims to increase productionin view of the costs, we can argue that theanswer obtained from birds swarm optimizationalgorithm is better than the one obtained fromthe genetic algorithm.

Moreover, given that the objective function inour model is to reduce the sum of cost and salesrevenue deviations, in comparison to Table 13and 14, it can be argued that the total target de-viation (cost and sales revenue) in the valuesspecified in Genetic Algorithm is higher in

amount compared to Particle Swarm algorithm.According to what was explained it can be con-cluded that particle Swarm Optimization algo-rithm performance is better than genetic algorithm,and by using it, more satisfactory results can beachieved.

Given the results of the model using GA, thecompany is able to produce 433990Kg in 6months for which production planning has takenplace and launch it to the consumer market forsales. This amount is compared to the company'spresent production that is 367 788 Kg, whichhas increased to 18% over six months. It can,then, be contended that the obtained resultsfrom GA are satisfactory. On the other hand,according to the results yielded by the model,the company is able to produce 434800Kg in 6months for which production planning has takenplace and launch it to the consumer market forsales using PSO. This amount can be comparedto the company's present production, which is367 788 Kg and shows an increase by 18.2 per-cent. Values of, f, h, or deviation from the idealsmeans that the solutions obtained to what extentare different from the ideals set for an object.Values of suggest to what degree the obtainedanswers are different from the ideal of cost. Forexample, to solve model using PSO, the amountof 1 is corresponds to obtain 2440000. Thisnumber means that the cost obtained for themonth of October in 2440000 is more than theideal cost. The values h also indicated the extent


Performance 1 2 3 4 5

f1f2f3f4f5f6h1h2h3h4h5h6F

2440000690000702100016846000659000049075000905500085000082760005000039000004950000109743000

419400058950007021000168460006590000569000090550008500008276000500003900000495000073317000

2440000690000546010002526700065900005690000905500085000082760005000039000004950000122359000

209400004232000070210001684600065900008840000905500085000082760005000039000004950000129638000

34430005669000070210001684600065900005691000905500085000082760005000039000004950000123362000

Table 13The Deviations from PSO with the Population Size 40

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to which the obtained answers are differentfrom the ideal of sales. For example, to solvethe model using PSO, the amount of h1 corre-sponds to 9055000. This number means thatthe sales revenue obtained for the month Octoberin 9055000 is less than the ideal sales. Thevalues F also represents the total difference incost goal objective function and ideal sales fromobjective function. For example, to solve themodel using PSO, the amount of F correspondsto obtained109750000. This number means thatthe total objective function is different from thecost ideals and sales ideals from the objectivefunction is 109750000.

ACKNOWLEDGEMENTWe are thankful to Dr. Alireza Amirteimoori

professor in Applied Mathematics and OperationsResearch, for his scientific comments on thisstudy.

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How to cite this article:Soofi, M., & Mohseni, M. (2017). Production planning optimization using genetic algorithm and particleswarm optimization (case study: Soofi tea factory). International Journal of Agricultural Managementand Developmen, 7(3), 395-410.URL: http://ijamad.iaurasht.ac.ir/article_530260_c1d9cb79551007e80a0d0d2d24122d84.pdf

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