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An analytical approach to automotive industry

An analytical approach to automotive industry 10.7603/s40690-015-0012-x JOURNAL OF AERONAUTICS AND SPACE TECHNOLOGIES JULY 2015 VOLUME 8 NUMBER 2 (15-23) ø layda ÜLKÜ Serol BULKAN Fadime ÜNEY- YÜKSEKTEPE Istanbul Kültür University, Faculty Marmara University, Faculty of Istanbul Kültür University, of Engineering, Department of Engineering, Department of Faculty of Engineering, Industrial Engineering, Istanbul, Industrial Engineering, Istanbul, Department of Industrial Turkey 34156 (TR), Turkey,34722 (TR), Engineering, Istanbul, Turkey i.karabulut@iku.edu.tr sbulkan@marmara.edu.tr 34156 (TR), f.yuksektepe@iku.edu.tr th th Received: 30 April 2015, Accepted: 23 July 2015 ABSTRACT Inventory control helps to manage or locate materials and any information through the processes in the company. The aim of the inventory management in the companies is to optimize inventory control. Especially, for the manufacturing companies, inventory control has an important goal which satisfies the product to the customer on time. Therefore, the system in the production processes should not have any trouble during the production. This study aims to optimize the production system of a two stage production processes where the bumpers are produced for different type of cars and different colors due to the model of the car. In the first stage there are three injection machines which are parallel, and in the second stage, there is a dying station. A mixed- integer linear programming model is proposed to optimize the production process. With the proposed model, the production of the injection processes is optimized and the lot sizes for each stage are determined. Also, front and back bumpers for each same model is dyed concurrently which prevents the color difference for the same model of each type of car. Keywords: Inventory Control, Lot Size, Mixed-Integer Linear Programming. OTOMOTø V SANAYø Sø NE YÖNELø K ANALø Tø K Bø R YAKLAù IM ÖZET Malzemelerin ve iú süreçlerinin arasÕ ndaki herhangi bir bilginin yönetilmesi veya yerinin saptanmasÕ , envanter kontrolünden faydalanÕ larak yapÕ lmaktadÕ r. ù irketlerdeki stok yönetiminin amacÕ envanter kontrolünü eniyilemektir. Özellikle üretim yapan ú irketler için envanter kontrolünün önemi büyüktür, çünkü müú terinin ürün talebini zamanÕ nda karú Õ lamasÕ gerekmektedir. Bu nedenle, üretim sÕ rasÕ ndaki üretim süreçlerinde herhangi bir sorun olmamalÕ dÕ r. Bu çalÕ ú ma ile farklÕ model ve renkte üretilen otomobil tamponlarÕ n iki aú amalÕ üretim süreçlerinin eniyilemesi hedeflenmektedir. ø lk aú amada paralel durumdaki üç enjeksiyon makinesi, ikinci aú amada ise bir boyama istasyonu bulunmaktadÕ r. Üretim sürecini eniyilemek için karma tamsayÕ lÕ do÷ rusal programlama modeli önerilmektedir. Önerilen model ile enjeksiyon iú lemlerinin üretimi eniyilenmiú olup, her aú ama için parti boyutlarÕ belirlenmiú tir. AyrÕ ca, her biri aynÕ model olan ön ve arka tamponlarÕ n eú zamanlÕ boyanmasÕ sa÷ lanarak, renk farklÕ lÕ klarÕ nÕ n oluú masÕ önlenmiú tir. Anahtar Kelimeler: Envanter Kontrolü, Parti Büyüklü÷ ü, Karma-TamsayÕ lÕ Do÷ rusal Programlama. 1. INTRODUCTION Especially, for the manufacturing companies, inventory control has an important goal which Inventory control helps to manage or locate materials satisfies the product to the customer on time. The and any information through the processes in the motivation behind this study is to see the inventory company. The aim of the inventory management in control, when some important constraints are changed, the companies is to optimize inventory control. such as inventory balance equation. * ÜLKÜ, BULKAN, ÜNEY-YÜKSEKTEPE Corresponding Author 15 An Analytical Approach to Automotive Industry To satisfy a product to the customer on time is one of X is the number of products of model i of type j ijrt the main goals for the manufacturing companies. produced by injection machine r in micro period t, Y Thus, if there is any problem during the production ikt processes, to take precaution is very important. In this is the number of products of model i dyed by dying study, a two stage production processes where station with colour k in micro period t, INY is the ikg different type and different colours of bumpers number of products of model i with colour k held in produced due to the model of the car. There are three injection machines which are paralleling the first buffer stock II at the end of day g, INX is the ijt stage, and there is a dying stationing the second stage. number of products of model i of type j held in buffer stock I at the end of in micro period t, BL is the The obtained data [1] is used in an automotive ikg manufacturer that produces bumpers for different type number of backlogged products of colour k of model i of car models and different colours. The problem has in day g, IDL is the idle time of the dying station in two stages, in the first stage there is three injection micro period t. machines with unequal production rates, and the dying station is the second stage. In the first stage, there are The objective function (1) is to minimize the total cost different moulds used by injection machines. In [1], which includes inventory cost, setup cost, color differentiation occurs between front and back backordering cost, and idleness cost. Inventory cost bumper types due to dying at different periods. includes number of products held in inventory after injection process and number of products held in In this study, a mixed-integer linear programming inventory after the dying process. There are i type of model is proposed to optimize the production process. car models and j type of bumpers on each injection With the proposed model, the production of the injection processes is optimized and the lot sizes for machine, therefore, if there is any production S will ijrt each stage are determined. Also, front and back take 1 value in the equation, if there is no production bumpers for each same model is dyed concurrently then S value will take 0 for constraint (2). Constraint ijrt which prevents the colour difference for the same model of the car. The remaining part of this paper is (3) helps to determine number of setups for each organized as follows. In the methodology part, micro period t. Constraint (4) is used to show that proposed optimization model is described in detail. In each model has one mould to be used. That is each comparison study part, data related to the compared injection machine has different mould to produce study is used and the proposed study results are different type of bumpers in each micro period. This compared with the current study. Paper concludes restriction is given by constraint (5). Constraint (6) is with conclusion and suggestions in conclusion part. valid to see the capacity constraint where total available time should not exceed total process and 2. METHODOLOGY setup time. Constraint (7) represents that total inventory level after injection process should not be The parameters below are used to solve the mixed- exceeded. Constraint (8) gives the production balance integer linear programming model. The demand for equation of injection processes for dying station. In constraint (9) demand is balanced with both stages model i in colour k for day g is d , required setup ikg injection and dying. Also, available time of dying time for injection machine r to produce model i of station is restricted with constraint (10). Constraint type j is defined as s . Available time of injection (11), (12), and (13) give restriction for bumpers in ijr dying station. To prevent colour differentiation for machine r in micro period t is at , available time of each model i, each model’s bumpers-frontand back dying station in micro period t is atd . Dying time of should enter at the same time in the dying station in model i with colour k is td , required process time each micro period t. Therefore, it is important to held ik in inventory both type j of model i. Constraint (14), for unit product of model i of type j by injection (15), and (16) satisfy the non-negativity of the machine r is defined as tp , inventory cost and setup ijr decision variables. costs are ic and sc respectively. Backlogging costs In this study, with proposed mixed-integer linear and idleness cost of dying station are bc and idc programming model the production process is respectively. Maximum number of products that can optimized and the lot sizes for each stage are be kept in available inventory is MaxINX . determined. There was colour differentiation between front and back bumper types due to dying at different The following decision variables are used to solve the periods in [1], and with proposed model customer two-stage production processes to find optimal lot satisfaction is increased by preventing color sizes for each stage. differentiation and at the same time the inventory is balanced. ÜLKÜ, BULKAN, ÜNEY-YÜKSEKTEPE 16 An Analytical Approach to Automotive Industry ­ 1 if model i of type j is produced by machine r micro period t; ijrt 0 otherwise ­ 1 setup for model i of type j is produced by machine r micro period t; SI ijrt 0 otherwise The following the mixed-integer linear programming model is used to solve the optimal lot sizes for two stages production problem. minzI NX sc.SI bc.BL ¦¦¦ ¦¦¦¦ ijt ¦¦¦ ijrt ikg (1) ij t i j r t i k g idc.IDL ic.INY ¦¦ti ¦¦ kg tikg Subject to X d MS .  ijrt (2) ijrt ijrt SSd SI  ijrt (3) ijrt ijr(1 t ) ijrt S d 1 ijt ijrt (4) S d 1 rt ¦¦ ijrt (5) ij (. tp Xd st .SI ) at  rt ¦¦ ijr ijrt ijr ijrt (6) ij INX d MaxINX  t ¦¦ ijt (7) ij INX  X INX Y ijt ij(1 t )¦¦ ijrt ijt ikt (8) rk INY  Y BL d INY BL ikg ik(1 g ) ¦ ikt ikg ikg ikg ik( g 1) (9) td .Yd IDL atd ¦¦ ik ikt t (10) ik INX max t INX  ijt (11) it ijt X max t X  ijrt (12) irt ijrt INX max  X max INX max Y it it(1 )¦¦ irt it ikt (13) rk XY,0 t  ijrkt (14) ijrt ikt INX ,, INY BL , IDL t 0  ijkgt (15) ijt ikg ikg t SI ,0 SI  ,1 ijrt (16) ijrt irt 3. COMPARISON STUDY [1] bumpers are put on the hangers and dyed on the hangers. If a color change is occurred a single hanger In this study, real data in [1] is used to see the stays empty. In this study, to reduce the color efficiency of the model. There are five different types differentiation between front and back bumpers, the of bumpers with front and back for each model. The bumper pairs are dyed at the same time together. problem has two stages, in the first stage there is three Therefore, there is no need to leave a hanger empty. injection machines with unequal production rates. For The dying station will be used efficiently with this defined models the production rates are 45, 57, 56, 45, approach. The setup time is ignored, because the 45 unit/hour respectively. Setup time is considered as production rate of dying station is higher than the one hour and setup cost is 600 TL, for the injection setup time. Moreover, setup cost related to the color machines. The dying station is the second stage where change is not necessary to be included in the model at the production rate is 70 bumpers, front and back. In the dying station. Idleness cost is taken as 80 TL, as it ÜLKÜ, BULKAN, ÜNEY-YÜKSEKTEPE 17 An Analytical Approach to Automotive Industry is not preferred to be idle at the dying station. Also, results. The runs were executed on a 1.70GHz Intel there is a capacity for 2472 unit products after the Core i5 notebook with 6 GB of RAM. The micro injection processes. Inventory holding cost is 10 period lengths of 4 hours that is 36 micro period TL/day both for the products after injection process length is obtained in a day [3]. which are not finished and for the products after dying station. As backlogging is not preferred, the Table 1 gives a brief information about the number of backlogging cost is 1000 TL per day. In addition, products of model i of type j produced by injection there are nineteen types of colors for the bumpers. machine r. There is a daily demand value which is obtained before the start of a week. Proposed model is formulated in GAMS 23.1.2 and solved by using CPLEX 11 [2] solver in order to obtain the optimal Table 1. Number of products of car model i of bumper type j produced by injection machine r for the proposed model. Injection Machine 1 2 3 Total Production Bumper Bumper Bumper Bumper Bumper Bumper Bumper Bumper 1 2 1 2 1 2 1 2 1 500 500 600 500 300 400 1400 1400 2 400 800 300 100 500 300 1200 1200 3 200 0 200 800 500 100 900 900 4 400 400 200 0 0 200 600 600 5 400 0 300 700 0 300 700 1000 Total 1900 1700 1600 2100 1300 1300 Production For each model i, in each injection machine r, total x For injection machine 3, the production number of produced bumpers are shown in Table 1. amount for bumper 1 is 300 units, and for bumper 2 is For instance, for model 1 400 units. x The production amount for bumper 1 and Figure 1 represents a detailed histogram of each model bumper 2 for injection machine 1 is 500 units. i produced by each injection machine r. x For injection machine 2, the production amount for bumper 1 is 600 units, and for bumper 2 is 500 units. Number of products produced for each model by injection machine Model 1 Model 2 Model 3 Model 4 Model 5 Injection Machine 1 Injection Machine 1 Injection Machine 2 Injection Machine 2 Injection Machine 3 Injection Machine 3 Figure 1. Number of products of car model i of bumper type j produced by injection machine r for the proposed model. When the model is compared with the study [1] the represents the production amount of model i of type j following production rates are obtained. Table 2 produced by injection machine r for the current model. ÜLKÜ, BULKAN, ÜNEY-YÜKSEKTEPE Model An Analytical Approach to Automotive Industry Table 2. Number of products of car model i of bumper type j produced by injection machine r for the current model. Injection Machine Injection Machine 1 Injection Machine 2 Injection Machine 3 Total Bumper 1 Bumper 2 Bumper 1 Bumper 2 Bumper 1 Bumper 2 Bumper 1 Bumper 2 Model 1 1100 500 700 1300 1800 1800 Model 2 600 100 300 900 200 100 1100 1100 Model 3 500 400 100 300 100 700 700 Model 4 100 100 100 100 200 200 Model 5 600 200 500 900 500 500 1600 1600 Total 2900 700 900 2700 1600 2000 Figure 2 shows a detailed histogram of each model i model has significant effect in the production amount produced by each injection machine r. When proposed of model 2, 3 and 4. model and current model is compared, proposed Number of products produced for each model by injection machine Model 1Model 2Model 3Model 4 Model 5 Injection Machine 1 Injection Machine 1 Injection Machine 2 Injection Machine 2 Injection Machine 3 Injection Machine 3 Figure 2. Number of products of car model i of bumper type j produced by injection machine r for the current model. Table 3 shows the comparison of number of products products for model 1 is as follows, for the first type of of each model i of type j from injection machines held bumper 500 units and for the second type of bumper in inventory for the proposed model. After the 600 units are held in inventory for the dying station. production process in injection machines, semi- Table 3. The comparison of number of products of car model i of bumper type j from injection machines held in inventory. Bumper Proposed Model Current Model Bumper 1 500 200 Bumper 2 600 100 Bumper 1 200 200 Bumper 2 1300 400 Bumper 1 500 0 Model 3 Bumper 2 200 900 Bumper 1 100 0 Bumper 2 700 200 Bumper 1 31 718 Bumper 2 1131 1518 ÜLKÜ, BULKAN, ÜNEY-YÜKSEKTEPE Model An Analytical Approach to Automotive Industry Figure 3 gives an information to see easily each type dyed together for each model. Therefore, there are of model i and j type of bumpers held in inventory. both front and back bumpers together as the semi- When the proposed situation is compared with the products in the inventory. current situation, the bumper pairs-front and back are Number of products of each model held in inventory from injection machines Bumper 2 Bumper 1 Bumper 2 Bumper 1 Bumper 2 Bumper 1 Bumper 2 Bumper 1 Bumper 2 Bumper 1 0 200 400 600 800 1000 1200 1400 Figure 3. The comparison of number of products of car model i of type j from injection machines held in inventory for the proposed study. Table 4 represents number of products of each model x There are 75 units dyed by color number 3, dyed by painting station with nineteen different color. x 10 unit dyed by color 18 etc. For instance, for car model 1, Table 4. The comparison of number of products of model i dyed by painting station with color k. Proposed Model Current Model 1 2 3 4 5 1 2 3 4 5 1 8 57 57 2 120 185 23 288 3 75 137 141 118 105 108 167 124 47 178 4 297 388 112 12 6 287 486 110 7 5 53 19 553 10 5 6 9 83 22 71 16770831820 214 7 71 58 16 8 9 48 60 9 28 92 347 43 17 413 10 726 142 213 957 185 121 11 9 5 31 90 4 11 108 12 108 29 135 1582280 13 68 47 32 158 43 32 200 14 16 100 150 61 33 35 71 134 28 10 15 7 46 38 16 35 29 16 37 13 31 13 17 23 24 25 23 20 24 13 62 18 10 2 815 8 ÜLKÜ, BULKAN, ÜNEY-YÜKSEKTEPE Model Model Model Model Model Color 1 2 3 4 5 An Analytical Approach to Automotive Industry Number of products of each model dyed by painting station with 19 different colors C1 C2 C3 C4 C5 C6 C7 C8 C9 C10C11C12C13C14C15C16C17C18C19 M1 M2 M3 M4 M5 Figure 4. Number of products of model i dyed by painting station with color k for the proposed study. In figure 4, number of products of each model dyed by current study, for model 1 and 3-eleven different painting station with different colors for the proposed colors, for model 2-nine different colors, for model 4- study are represented. In the proposed model, bumper ten different colors, and for model 5-thirteen different pairs are dyed for model 1, 2, and 3 in eleven different colors are dyed. In the proposed study, the color type colors, and for model 4 and 5, thirteen different colors is enlarged 18.18% for model 2, and also for model 4 bumper pairs are dyed. On the other hand in the dyed different color types are increased in 23.08%. Table 5.Daily Idle Time (min.) Day 1 11.689 Day 2 12.227 Day 3 9.833 Day 4 11.250 Day 5 11.250 Day 6 11.250 Total Idle Time 67.499 Average Idle Time 11.250 Table 5 shows the summary information about the average idle time of dying station is 11.250 minutes. proposed model. Idle time for dying station of each Also, in figure 5, idle time for dying station of each day is given in minutes. For instance, at the end of day day is given as percentages. For instance, minimum 1, dying station is idle 11.689 minutes, and the daily idle day is day 3 with 14%. Daily Idle Time Day 6 Day 1 17% 17% Day 5 Day 2 17% 18% Day 4 Day 3 17% 14% Figure 5. Daily idle time (%). ÜLKÜ, BULKAN, ÜNEY-YÜKSEKTEPE Daily Idle Time (min.) An Analytical Approach to Automotive Industry 4. CONCLUSION Projects and field works: 7 national and international conference presentations, Member of In this paper, real data from an automotive supplier is Yöneylem Araú tÕ rmasÕ Derne÷ i (YAD). used. A mixed-integer linear programming model is proposed to optimize the production process. With the Dr. Serol BULKAN proposed model, the production of the injection He earned a B.S. degree in Business Engineering at processes is optimized and the lot sizes for each stage Istanbul Technical University in 1986 and a M.S. are determined. Also, front and back bumpers for each degree in Business Engineering from Istanbul type of model is dyed concurrently which prevents the Technical University in 1990 and in Operations color difference for the same model of the car. This Research from Florida Institute of Technology in study helps to increase the customer satisfaction at the 1992. In 1999, he completed his Ph.D. studies in same time with the balancing the inventory. Industrial Engineering program at Cleveland State Moreover, the characteristics of the proposed model University. are given. As the possible future work, micro period lengths can be changed instead of using a fixed micro Between 1998 and 2001, he joined Galatasaray period. In addition, as comparison the run time of the University where he worked as Research Assistant. In model can be changed to see the effects to the model. 2001, he joined the Marmara University’s Faculty of Also, objective function can be changed to see the Engineering as Assistant Professor at Industrial influence to the proposed model. Engineering Department where he currently works as an Associate Professor. “Open Access: This article is distributed under the terms of the Creative Commons Attribution License His current research interests are Optimization, (CC-BY 4.0) which permits any use, distribution, and Mathematical Modeling, Scheduling, Project reproduction in any medium, provided the original Management, Operations Research, Metaheuristics author(s) and the source are credited.” and Production Planning. 5. REFERENCES Publications: 5 international journal papers, 1 national book chapter, 1 national book chapter, 14 [1] Uney-Yuksektepe, F., Ozdemir, R.G., 2011, international conference proceedings. Synchronized Two-Stage Lot Sizing and Scheduling Problem in Automotive Industry, Operations Research Projects and field works: 2 national student projects Proceedings, 477. supported by TUBITAK,41 national and international conference presentations, Member ofÜretim [2] Brooke, A., Kendrick, D., Meeraus, A., Raman, Araú tÕ rmalarÕ Derne÷ i (ÜAD), TMMOB TMO R., 1998. GAMS:A User’s Guide. GAMS, De- ø stanbul ù ubesi, Yöneylem Araú tÕ rmasÕ Derne÷ i velopment Co., Washington, DC. (YAD). [3] Ilog, 2010. CPLEX 12.0 User’s Manual , ILOG S. A. See website www.cplex.com Dr. Fadime ÜNEY-YÜKSEKTEPE She earned a B.S. degree in Chemical Engineering at Istanbul Technical University in 2003 and a M.S. VITAE degree in Industrial Engineering from Koç University in 2005. In 2009, she completed her Ph.D. studies in ø layda ÜLKÜ Industrial Engineering & Operations Management She earned a B.S. degree in Industrial Engineering at program at Koç University. Istanbul Kültür University in 2010 and a M.S. degree in Industrial Engineering from Galatasaray University In 2009, she joined the Istanbul Kültür University’s in 2014. She hasbegun her Ph.D. studies in Industrial Faculty of Engineering as Assistant Professor at Engineering program at Marmara University in 2014. Department of Industrial Engineering where she currently serves an Associate Professor. In 2010, she joined as a Research Assistant in the Istanbul Kültür University Engineering Faculty at Her current research interests are Mathematical Industrial Engineering Department. Programming, Data Mining, Healthcare Applications, Scheduling, and Supply Chain Management. Her current research interests are Mathematical Programming, and Supply Chain Management. Publications: 5 refereed international journal papers, 5 refereed international book chapters, 1 national book Publications: 2 international conference proceedings. chapter, 3 refereed international conference proceedings. ÜLKÜ, BULKAN, ÜNEY-YÜKSEKTEPE 22 An Analytical Approach to Automotive Industry Projects and field works: 2 national student projects supported by TUBITAK, 1 national research project supported by ø stanbul Kultur University, 42 national and international conference presentations, Referee for International Journal of Production Research, European Journal of Operational Research, Machine Learning, Information Sciences, Member of Yöneylem Araú tÕ rmasÕ Derne÷ i (YAD), EURO- CCBM, EUROPT, Depo Yönetimi Derne÷ i. ÜLKÜ, BULKAN, ÜNEY-YÜKSEKTEPE http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Aeronautics and Space Technologies (Havacilik ve Uzay Teknolojileri Dergisi) Springer Journals

An analytical approach to automotive industry

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10.7603/s40690-015-0012-x JOURNAL OF AERONAUTICS AND SPACE TECHNOLOGIES JULY 2015 VOLUME 8 NUMBER 2 (15-23) ø layda ÜLKÜ Serol BULKAN Fadime ÜNEY- YÜKSEKTEPE Istanbul Kültür University, Faculty Marmara University, Faculty of Istanbul Kültür University, of Engineering, Department of Engineering, Department of Faculty of Engineering, Industrial Engineering, Istanbul, Industrial Engineering, Istanbul, Department of Industrial Turkey 34156 (TR), Turkey,34722 (TR), Engineering, Istanbul, Turkey i.karabulut@iku.edu.tr sbulkan@marmara.edu.tr 34156 (TR), f.yuksektepe@iku.edu.tr th th Received: 30 April 2015, Accepted: 23 July 2015 ABSTRACT Inventory control helps to manage or locate materials and any information through the processes in the company. The aim of the inventory management in the companies is to optimize inventory control. Especially, for the manufacturing companies, inventory control has an important goal which satisfies the product to the customer on time. Therefore, the system in the production processes should not have any trouble during the production. This study aims to optimize the production system of a two stage production processes where the bumpers are produced for different type of cars and different colors due to the model of the car. In the first stage there are three injection machines which are parallel, and in the second stage, there is a dying station. A mixed- integer linear programming model is proposed to optimize the production process. With the proposed model, the production of the injection processes is optimized and the lot sizes for each stage are determined. Also, front and back bumpers for each same model is dyed concurrently which prevents the color difference for the same model of each type of car. Keywords: Inventory Control, Lot Size, Mixed-Integer Linear Programming. OTOMOTø V SANAYø Sø NE YÖNELø K ANALø Tø K Bø R YAKLAù IM ÖZET Malzemelerin ve iú süreçlerinin arasÕ ndaki herhangi bir bilginin yönetilmesi veya yerinin saptanmasÕ , envanter kontrolünden faydalanÕ larak yapÕ lmaktadÕ r. ù irketlerdeki stok yönetiminin amacÕ envanter kontrolünü eniyilemektir. Özellikle üretim yapan ú irketler için envanter kontrolünün önemi büyüktür, çünkü müú terinin ürün talebini zamanÕ nda karú Õ lamasÕ gerekmektedir. Bu nedenle, üretim sÕ rasÕ ndaki üretim süreçlerinde herhangi bir sorun olmamalÕ dÕ r. Bu çalÕ ú ma ile farklÕ model ve renkte üretilen otomobil tamponlarÕ n iki aú amalÕ üretim süreçlerinin eniyilemesi hedeflenmektedir. ø lk aú amada paralel durumdaki üç enjeksiyon makinesi, ikinci aú amada ise bir boyama istasyonu bulunmaktadÕ r. Üretim sürecini eniyilemek için karma tamsayÕ lÕ do÷ rusal programlama modeli önerilmektedir. Önerilen model ile enjeksiyon iú lemlerinin üretimi eniyilenmiú olup, her aú ama için parti boyutlarÕ belirlenmiú tir. AyrÕ ca, her biri aynÕ model olan ön ve arka tamponlarÕ n eú zamanlÕ boyanmasÕ sa÷ lanarak, renk farklÕ lÕ klarÕ nÕ n oluú masÕ önlenmiú tir. Anahtar Kelimeler: Envanter Kontrolü, Parti Büyüklü÷ ü, Karma-TamsayÕ lÕ Do÷ rusal Programlama. 1. INTRODUCTION Especially, for the manufacturing companies, inventory control has an important goal which Inventory control helps to manage or locate materials satisfies the product to the customer on time. The and any information through the processes in the motivation behind this study is to see the inventory company. The aim of the inventory management in control, when some important constraints are changed, the companies is to optimize inventory control. such as inventory balance equation. * ÜLKÜ, BULKAN, ÜNEY-YÜKSEKTEPE Corresponding Author 15 An Analytical Approach to Automotive Industry To satisfy a product to the customer on time is one of X is the number of products of model i of type j ijrt the main goals for the manufacturing companies. produced by injection machine r in micro period t, Y Thus, if there is any problem during the production ikt processes, to take precaution is very important. In this is the number of products of model i dyed by dying study, a two stage production processes where station with colour k in micro period t, INY is the ikg different type and different colours of bumpers number of products of model i with colour k held in produced due to the model of the car. There are three injection machines which are paralleling the first buffer stock II at the end of day g, INX is the ijt stage, and there is a dying stationing the second stage. number of products of model i of type j held in buffer stock I at the end of in micro period t, BL is the The obtained data [1] is used in an automotive ikg manufacturer that produces bumpers for different type number of backlogged products of colour k of model i of car models and different colours. The problem has in day g, IDL is the idle time of the dying station in two stages, in the first stage there is three injection micro period t. machines with unequal production rates, and the dying station is the second stage. In the first stage, there are The objective function (1) is to minimize the total cost different moulds used by injection machines. In [1], which includes inventory cost, setup cost, color differentiation occurs between front and back backordering cost, and idleness cost. Inventory cost bumper types due to dying at different periods. includes number of products held in inventory after injection process and number of products held in In this study, a mixed-integer linear programming inventory after the dying process. There are i type of model is proposed to optimize the production process. car models and j type of bumpers on each injection With the proposed model, the production of the injection processes is optimized and the lot sizes for machine, therefore, if there is any production S will ijrt each stage are determined. Also, front and back take 1 value in the equation, if there is no production bumpers for each same model is dyed concurrently then S value will take 0 for constraint (2). Constraint ijrt which prevents the colour difference for the same model of the car. The remaining part of this paper is (3) helps to determine number of setups for each organized as follows. In the methodology part, micro period t. Constraint (4) is used to show that proposed optimization model is described in detail. In each model has one mould to be used. That is each comparison study part, data related to the compared injection machine has different mould to produce study is used and the proposed study results are different type of bumpers in each micro period. This compared with the current study. Paper concludes restriction is given by constraint (5). Constraint (6) is with conclusion and suggestions in conclusion part. valid to see the capacity constraint where total available time should not exceed total process and 2. METHODOLOGY setup time. Constraint (7) represents that total inventory level after injection process should not be The parameters below are used to solve the mixed- exceeded. Constraint (8) gives the production balance integer linear programming model. The demand for equation of injection processes for dying station. In constraint (9) demand is balanced with both stages model i in colour k for day g is d , required setup ikg injection and dying. Also, available time of dying time for injection machine r to produce model i of station is restricted with constraint (10). Constraint type j is defined as s . Available time of injection (11), (12), and (13) give restriction for bumpers in ijr dying station. To prevent colour differentiation for machine r in micro period t is at , available time of each model i, each model’s bumpers-frontand back dying station in micro period t is atd . Dying time of should enter at the same time in the dying station in model i with colour k is td , required process time each micro period t. Therefore, it is important to held ik in inventory both type j of model i. Constraint (14), for unit product of model i of type j by injection (15), and (16) satisfy the non-negativity of the machine r is defined as tp , inventory cost and setup ijr decision variables. costs are ic and sc respectively. Backlogging costs In this study, with proposed mixed-integer linear and idleness cost of dying station are bc and idc programming model the production process is respectively. Maximum number of products that can optimized and the lot sizes for each stage are be kept in available inventory is MaxINX . determined. There was colour differentiation between front and back bumper types due to dying at different The following decision variables are used to solve the periods in [1], and with proposed model customer two-stage production processes to find optimal lot satisfaction is increased by preventing color sizes for each stage. differentiation and at the same time the inventory is balanced. ÜLKÜ, BULKAN, ÜNEY-YÜKSEKTEPE 16 An Analytical Approach to Automotive Industry ­ 1 if model i of type j is produced by machine r micro period t; ijrt 0 otherwise ­ 1 setup for model i of type j is produced by machine r micro period t; SI ijrt 0 otherwise The following the mixed-integer linear programming model is used to solve the optimal lot sizes for two stages production problem. minzI NX sc.SI bc.BL ¦¦¦ ¦¦¦¦ ijt ¦¦¦ ijrt ikg (1) ij t i j r t i k g idc.IDL ic.INY ¦¦ti ¦¦ kg tikg Subject to X d MS .  ijrt (2) ijrt ijrt SSd SI  ijrt (3) ijrt ijr(1 t ) ijrt S d 1 ijt ijrt (4) S d 1 rt ¦¦ ijrt (5) ij (. tp Xd st .SI ) at  rt ¦¦ ijr ijrt ijr ijrt (6) ij INX d MaxINX  t ¦¦ ijt (7) ij INX  X INX Y ijt ij(1 t )¦¦ ijrt ijt ikt (8) rk INY  Y BL d INY BL ikg ik(1 g ) ¦ ikt ikg ikg ikg ik( g 1) (9) td .Yd IDL atd ¦¦ ik ikt t (10) ik INX max t INX  ijt (11) it ijt X max t X  ijrt (12) irt ijrt INX max  X max INX max Y it it(1 )¦¦ irt it ikt (13) rk XY,0 t  ijrkt (14) ijrt ikt INX ,, INY BL , IDL t 0  ijkgt (15) ijt ikg ikg t SI ,0 SI  ,1 ijrt (16) ijrt irt 3. COMPARISON STUDY [1] bumpers are put on the hangers and dyed on the hangers. If a color change is occurred a single hanger In this study, real data in [1] is used to see the stays empty. In this study, to reduce the color efficiency of the model. There are five different types differentiation between front and back bumpers, the of bumpers with front and back for each model. The bumper pairs are dyed at the same time together. problem has two stages, in the first stage there is three Therefore, there is no need to leave a hanger empty. injection machines with unequal production rates. For The dying station will be used efficiently with this defined models the production rates are 45, 57, 56, 45, approach. The setup time is ignored, because the 45 unit/hour respectively. Setup time is considered as production rate of dying station is higher than the one hour and setup cost is 600 TL, for the injection setup time. Moreover, setup cost related to the color machines. The dying station is the second stage where change is not necessary to be included in the model at the production rate is 70 bumpers, front and back. In the dying station. Idleness cost is taken as 80 TL, as it ÜLKÜ, BULKAN, ÜNEY-YÜKSEKTEPE 17 An Analytical Approach to Automotive Industry is not preferred to be idle at the dying station. Also, results. The runs were executed on a 1.70GHz Intel there is a capacity for 2472 unit products after the Core i5 notebook with 6 GB of RAM. The micro injection processes. Inventory holding cost is 10 period lengths of 4 hours that is 36 micro period TL/day both for the products after injection process length is obtained in a day [3]. which are not finished and for the products after dying station. As backlogging is not preferred, the Table 1 gives a brief information about the number of backlogging cost is 1000 TL per day. In addition, products of model i of type j produced by injection there are nineteen types of colors for the bumpers. machine r. There is a daily demand value which is obtained before the start of a week. Proposed model is formulated in GAMS 23.1.2 and solved by using CPLEX 11 [2] solver in order to obtain the optimal Table 1. Number of products of car model i of bumper type j produced by injection machine r for the proposed model. Injection Machine 1 2 3 Total Production Bumper Bumper Bumper Bumper Bumper Bumper Bumper Bumper 1 2 1 2 1 2 1 2 1 500 500 600 500 300 400 1400 1400 2 400 800 300 100 500 300 1200 1200 3 200 0 200 800 500 100 900 900 4 400 400 200 0 0 200 600 600 5 400 0 300 700 0 300 700 1000 Total 1900 1700 1600 2100 1300 1300 Production For each model i, in each injection machine r, total x For injection machine 3, the production number of produced bumpers are shown in Table 1. amount for bumper 1 is 300 units, and for bumper 2 is For instance, for model 1 400 units. x The production amount for bumper 1 and Figure 1 represents a detailed histogram of each model bumper 2 for injection machine 1 is 500 units. i produced by each injection machine r. x For injection machine 2, the production amount for bumper 1 is 600 units, and for bumper 2 is 500 units. Number of products produced for each model by injection machine Model 1 Model 2 Model 3 Model 4 Model 5 Injection Machine 1 Injection Machine 1 Injection Machine 2 Injection Machine 2 Injection Machine 3 Injection Machine 3 Figure 1. Number of products of car model i of bumper type j produced by injection machine r for the proposed model. When the model is compared with the study [1] the represents the production amount of model i of type j following production rates are obtained. Table 2 produced by injection machine r for the current model. ÜLKÜ, BULKAN, ÜNEY-YÜKSEKTEPE Model An Analytical Approach to Automotive Industry Table 2. Number of products of car model i of bumper type j produced by injection machine r for the current model. Injection Machine Injection Machine 1 Injection Machine 2 Injection Machine 3 Total Bumper 1 Bumper 2 Bumper 1 Bumper 2 Bumper 1 Bumper 2 Bumper 1 Bumper 2 Model 1 1100 500 700 1300 1800 1800 Model 2 600 100 300 900 200 100 1100 1100 Model 3 500 400 100 300 100 700 700 Model 4 100 100 100 100 200 200 Model 5 600 200 500 900 500 500 1600 1600 Total 2900 700 900 2700 1600 2000 Figure 2 shows a detailed histogram of each model i model has significant effect in the production amount produced by each injection machine r. When proposed of model 2, 3 and 4. model and current model is compared, proposed Number of products produced for each model by injection machine Model 1Model 2Model 3Model 4 Model 5 Injection Machine 1 Injection Machine 1 Injection Machine 2 Injection Machine 2 Injection Machine 3 Injection Machine 3 Figure 2. Number of products of car model i of bumper type j produced by injection machine r for the current model. Table 3 shows the comparison of number of products products for model 1 is as follows, for the first type of of each model i of type j from injection machines held bumper 500 units and for the second type of bumper in inventory for the proposed model. After the 600 units are held in inventory for the dying station. production process in injection machines, semi- Table 3. The comparison of number of products of car model i of bumper type j from injection machines held in inventory. Bumper Proposed Model Current Model Bumper 1 500 200 Bumper 2 600 100 Bumper 1 200 200 Bumper 2 1300 400 Bumper 1 500 0 Model 3 Bumper 2 200 900 Bumper 1 100 0 Bumper 2 700 200 Bumper 1 31 718 Bumper 2 1131 1518 ÜLKÜ, BULKAN, ÜNEY-YÜKSEKTEPE Model An Analytical Approach to Automotive Industry Figure 3 gives an information to see easily each type dyed together for each model. Therefore, there are of model i and j type of bumpers held in inventory. both front and back bumpers together as the semi- When the proposed situation is compared with the products in the inventory. current situation, the bumper pairs-front and back are Number of products of each model held in inventory from injection machines Bumper 2 Bumper 1 Bumper 2 Bumper 1 Bumper 2 Bumper 1 Bumper 2 Bumper 1 Bumper 2 Bumper 1 0 200 400 600 800 1000 1200 1400 Figure 3. The comparison of number of products of car model i of type j from injection machines held in inventory for the proposed study. Table 4 represents number of products of each model x There are 75 units dyed by color number 3, dyed by painting station with nineteen different color. x 10 unit dyed by color 18 etc. For instance, for car model 1, Table 4. The comparison of number of products of model i dyed by painting station with color k. Proposed Model Current Model 1 2 3 4 5 1 2 3 4 5 1 8 57 57 2 120 185 23 288 3 75 137 141 118 105 108 167 124 47 178 4 297 388 112 12 6 287 486 110 7 5 53 19 553 10 5 6 9 83 22 71 16770831820 214 7 71 58 16 8 9 48 60 9 28 92 347 43 17 413 10 726 142 213 957 185 121 11 9 5 31 90 4 11 108 12 108 29 135 1582280 13 68 47 32 158 43 32 200 14 16 100 150 61 33 35 71 134 28 10 15 7 46 38 16 35 29 16 37 13 31 13 17 23 24 25 23 20 24 13 62 18 10 2 815 8 ÜLKÜ, BULKAN, ÜNEY-YÜKSEKTEPE Model Model Model Model Model Color 1 2 3 4 5 An Analytical Approach to Automotive Industry Number of products of each model dyed by painting station with 19 different colors C1 C2 C3 C4 C5 C6 C7 C8 C9 C10C11C12C13C14C15C16C17C18C19 M1 M2 M3 M4 M5 Figure 4. Number of products of model i dyed by painting station with color k for the proposed study. In figure 4, number of products of each model dyed by current study, for model 1 and 3-eleven different painting station with different colors for the proposed colors, for model 2-nine different colors, for model 4- study are represented. In the proposed model, bumper ten different colors, and for model 5-thirteen different pairs are dyed for model 1, 2, and 3 in eleven different colors are dyed. In the proposed study, the color type colors, and for model 4 and 5, thirteen different colors is enlarged 18.18% for model 2, and also for model 4 bumper pairs are dyed. On the other hand in the dyed different color types are increased in 23.08%. Table 5.Daily Idle Time (min.) Day 1 11.689 Day 2 12.227 Day 3 9.833 Day 4 11.250 Day 5 11.250 Day 6 11.250 Total Idle Time 67.499 Average Idle Time 11.250 Table 5 shows the summary information about the average idle time of dying station is 11.250 minutes. proposed model. Idle time for dying station of each Also, in figure 5, idle time for dying station of each day is given in minutes. For instance, at the end of day day is given as percentages. For instance, minimum 1, dying station is idle 11.689 minutes, and the daily idle day is day 3 with 14%. Daily Idle Time Day 6 Day 1 17% 17% Day 5 Day 2 17% 18% Day 4 Day 3 17% 14% Figure 5. Daily idle time (%). ÜLKÜ, BULKAN, ÜNEY-YÜKSEKTEPE Daily Idle Time (min.) An Analytical Approach to Automotive Industry 4. CONCLUSION Projects and field works: 7 national and international conference presentations, Member of In this paper, real data from an automotive supplier is Yöneylem Araú tÕ rmasÕ Derne÷ i (YAD). used. A mixed-integer linear programming model is proposed to optimize the production process. With the Dr. Serol BULKAN proposed model, the production of the injection He earned a B.S. degree in Business Engineering at processes is optimized and the lot sizes for each stage Istanbul Technical University in 1986 and a M.S. are determined. Also, front and back bumpers for each degree in Business Engineering from Istanbul type of model is dyed concurrently which prevents the Technical University in 1990 and in Operations color difference for the same model of the car. This Research from Florida Institute of Technology in study helps to increase the customer satisfaction at the 1992. In 1999, he completed his Ph.D. studies in same time with the balancing the inventory. Industrial Engineering program at Cleveland State Moreover, the characteristics of the proposed model University. are given. As the possible future work, micro period lengths can be changed instead of using a fixed micro Between 1998 and 2001, he joined Galatasaray period. In addition, as comparison the run time of the University where he worked as Research Assistant. In model can be changed to see the effects to the model. 2001, he joined the Marmara University’s Faculty of Also, objective function can be changed to see the Engineering as Assistant Professor at Industrial influence to the proposed model. Engineering Department where he currently works as an Associate Professor. “Open Access: This article is distributed under the terms of the Creative Commons Attribution License His current research interests are Optimization, (CC-BY 4.0) which permits any use, distribution, and Mathematical Modeling, Scheduling, Project reproduction in any medium, provided the original Management, Operations Research, Metaheuristics author(s) and the source are credited.” and Production Planning. 5. REFERENCES Publications: 5 international journal papers, 1 national book chapter, 1 national book chapter, 14 [1] Uney-Yuksektepe, F., Ozdemir, R.G., 2011, international conference proceedings. Synchronized Two-Stage Lot Sizing and Scheduling Problem in Automotive Industry, Operations Research Projects and field works: 2 national student projects Proceedings, 477. supported by TUBITAK,41 national and international conference presentations, Member ofÜretim [2] Brooke, A., Kendrick, D., Meeraus, A., Raman, Araú tÕ rmalarÕ Derne÷ i (ÜAD), TMMOB TMO R., 1998. GAMS:A User’s Guide. GAMS, De- ø stanbul ù ubesi, Yöneylem Araú tÕ rmasÕ Derne÷ i velopment Co., Washington, DC. (YAD). [3] Ilog, 2010. CPLEX 12.0 User’s Manual , ILOG S. A. See website www.cplex.com Dr. Fadime ÜNEY-YÜKSEKTEPE She earned a B.S. degree in Chemical Engineering at Istanbul Technical University in 2003 and a M.S. VITAE degree in Industrial Engineering from Koç University in 2005. In 2009, she completed her Ph.D. studies in ø layda ÜLKÜ Industrial Engineering & Operations Management She earned a B.S. degree in Industrial Engineering at program at Koç University. Istanbul Kültür University in 2010 and a M.S. degree in Industrial Engineering from Galatasaray University In 2009, she joined the Istanbul Kültür University’s in 2014. She hasbegun her Ph.D. studies in Industrial Faculty of Engineering as Assistant Professor at Engineering program at Marmara University in 2014. Department of Industrial Engineering where she currently serves an Associate Professor. In 2010, she joined as a Research Assistant in the Istanbul Kültür University Engineering Faculty at Her current research interests are Mathematical Industrial Engineering Department. Programming, Data Mining, Healthcare Applications, Scheduling, and Supply Chain Management. Her current research interests are Mathematical Programming, and Supply Chain Management. Publications: 5 refereed international journal papers, 5 refereed international book chapters, 1 national book Publications: 2 international conference proceedings. chapter, 3 refereed international conference proceedings. ÜLKÜ, BULKAN, ÜNEY-YÜKSEKTEPE 22 An Analytical Approach to Automotive Industry Projects and field works: 2 national student projects supported by TUBITAK, 1 national research project supported by ø stanbul Kultur University, 42 national and international conference presentations, Referee for International Journal of Production Research, European Journal of Operational Research, Machine Learning, Information Sciences, Member of Yöneylem Araú tÕ rmasÕ Derne÷ i (YAD), EURO- CCBM, EUROPT, Depo Yönetimi Derne÷ i. ÜLKÜ, BULKAN, ÜNEY-YÜKSEKTEPE

Journal

Journal of Aeronautics and Space Technologies (Havacilik ve Uzay Teknolojileri Dergisi) – Springer Journals

Published: Nov 2, 2015

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