Optimisation of Production and Transportation Cost of Ashanti Foam Factory Limited, Ghana*

Transcription

1 Optmsato of Producto ad Trasportato Cost of Ashat Foam Factory Lmted, Ghaa* 1 G. Adje, 1 J. Acquah, ad 1 S. Al Hassa 1 Uversty of Mes ad Techology, Box 237, Tarkwa, Ghaa Adje, G., Acquah, J., ad Al-Hassa, S. (2017), Optmsato of Producto ad Trasportato Cost of Ashat Foam Factory Lmted, Ghaa Joural of Techology, Vol. 2, No. 1, pp Abstract Icreasg global competto the busess world ad heghteed expectatos of customers have forced compaes to cosder ot oly the prcg or product qualty, but also relablty ad tmeless of delveres. The cost of producto s the largest cost compoet almost every maufacturg frm followed by trasportato ad vetory costs. Ths hgh cost of producto ad dstrbuto s a major challege to the maagemet of Ashat Foam Factory Lmted ad eeds to make decsos o how to mmse costs so as to maxmse proft. Ths has called for a study to explore ways to effectvely maage producto ad trasportato related problems of the compay. I ths study, Exteded Vogel s Approxmato Method was used to determe the feasble soluto ad the optmalty was tested wth Modfy Dstrbuto Method (MODI). Wth ths, maagemet could reduce producto ad trasportato cost by % ad 42 % respectvely. Keywords: Trasportato Problem, Feasble Soluto, Optmalty 1 Itroducto Icreasg global competto the busess world ad heghteed expectatos of customers have forced compaes to cosder ot oly the prcg or product qualty, but also relablty ad tmeless of delveres. May researchers (Lu, 2003; Sraryawat et al., 2009; Hujet et al., 2002; Gorma, 2006; Eks,o glu, 2002) have establshed that the cost of producto s the largest cost compoet almost every maufacturg frm followed by trasportato ad vetory costs. Frms are to make decsos o producto plag, vetory levels, ad cost of trasportato each level of the logstcs dstrbuto etworks such a way that customers demads are met promptly at a mmum cost (Okrah, 2012). The producto at Ashfoam volves a sgle homogeeous product, whch s to be maufactured over a umber of successve perods to satsfy predetermed demads. Oce maufactured, products ca be trasported to cosumpto ceters or stores; both producto cost ad storage cost ca be determed. O the average, the ut cost of producto ad trasportato of product are GH 415 ad GH 13 respectvely. Maagemet fds ths to be too hgh. Ths has called for a study to explore ways to effectvely maage producto ad trasportato plag related problems of the compay. The study ams at developg a dstrbuto pla for Ashfoam Ghaa Lmted, obta the optmal mothly producto schedule that meets customers demad ad determe optmal mothly haulage of products from sources (warehouses) to destatos (depots) that satsfes customers demad. The ma model used ths study was Trasportato Problem Model. Exteded Vogel s Approxmato Method (EVAM) was used to determe the Ital Basc Feasble Soluto (IBFS); ad, Modfed Dstrbuto Method (MODI) was also used to test for optmalty. 2 Resources ad Methods Used 2.1 Profle of Study Area Ghaa s a West Afrca coutry borderg the Gulf of Guea ad located betwee lattude 5 N ad logtude 0 E. It s sadwched by Burka Faso, Cote d'ivore ad Togo wth a total boudary of km. Ghaa comprses 216 dstrcts, wth the captal cty beg Accra. The total populato of Ghaa s over twety-seve mllo ( ), wth the two most populated ctes beg Accra (2.573M) ad Kumas (2.019M) (Ao., 2015a). The te regos are dvded to two major sectors: Souther ad Norther sectors. Ashat Foam Factory Lmted (Ashfoam Ghaa Ltd) maufactures ad exports polyurethae flexble foam, super deluxe mattress ad pllows. The compay has two plats, oe Accra (Gbawe) ad the other Kumas (Ahesa). The Accra plat s the souther sector of Ghaa, whlst the Kumas plat s the orther sector. The compay has o vetory to beg wth sce uts produced over the year are trasported to the 20

2 varous depots before the begg of the ext producto year. At the ed of each moth (after producto has occurred ad the curret moth s demad has bee satsfed), a vetory cost of $3.3 per ut s curred. The total producto ad trasportato cost of the compay at the ed of the year are $ ad $ respectvely. The growg populato ad mprovemet the lvg stadard of Ghaa has over the years trggered demad for ther products almost all the te regos of the coutry. Although, the cost of producto at each plat s the same, the supply depots are scattered throughout the whole coutry. The regos whch the two major plats supply to are show Fg. 1: Fg. 1 Map of Ghaa Showg Varous Regos (Ao., 2015a) 2.2 Model Formulato I ths study, a Exteded Vogel s Approxmato method coupled wth Modfed Dstrbuto method was appled to solve a trasportato problem to determe the feasble rego. The mathematcal formulato of the trasportato model depeds o the ordary VAM, but a exteded form takg to accout all the ecessary parameters. Let x be the quatty trasported from the source, j to the destato, j. Suppose each plat has the capacty to supply a amout, s to satsfy a requred demad d j to jth destato at a cost c j of th source to jth destato, the the trasportato problem for m sources ad destatos ca geerally be defed as: Mmse: Subject to: Z m cx j j 1 j1 x j s, for = 1, 2, 3,, m j1 m x j d j, for j = 1, 2, 3,, 1 x 0, for all, j j The exteded form of the trasportato problem model for ths study factorg to t the varous plats, ther respectve destatos as well as the varous depots ca further be expressed as: Mmse: A j K j j1 j1 m m Z c x c x j A j j K j 1 j1 1 j1 Subject to: x s, for all = 1, 2, 3,, m m m x x, for all j = 1, 2, 3,, d A j K j j 1 1 x j 0, x where j1 A j a, x j1 K j b,,j Z: Total trasportato cost to be mmzed; C j : Ut trasportato cost of the commodty from each plat to destato j per moth; j : Number of uts of commodty set from source to destato j per moth; a : Level of supply at each source ; b : Level of demad at each destato j; S : Total producto capacty of Ashfoam avalable to be suppled per moth; ad d : Total mothly demad at both depot j. The mmzato cost fuctos formulated out of the trasportato problem model s Equato (1): Subject to supply costrats Equato (2): B: Z 14.0 A1, A1, A1, A1,4 10.5A 1, A1,6 9.5 A1,7 8.5 A1, A1,9 5.6 A1, K 2,1 12.0K 2, K 2,3 14.5K 2,4 4.5 K 2,5 9.5 K 2,6 7.5 K 2,7 7.5K 2,8 14.0K 2, K 2,10 C : Z 15.0 A1, A1, A1, A1, A1, A1, A1,7 8.5 A1,8 12.5A 1,9 6.5 A1, K 2,1 12.5K 2, K 2, K 2,4 5.5 K 2, K 2, K 2, K 2, K 2, K 2,

3 B : A1,1 A1,2 A1,3 A1,4 A1,5 A1,6 A1,7 A1,8 A1,9 A1, K 2,1 K 2,2 K 2,3 K 2,4 K 2,5 K 2,6 K 2,7 K 2,8 K 2,9 K 2, (2) C : A1,1 A1,2 A1,3 A1,4 A1,5 A1,6 A1,7 A1,8 A1,9 A1, K 2,1 K 2,2 K 2,3 K 2,4 K 2,5 K 2,6 K 2,7 K 2,8 K 2,9 K 2, Ad subject to demad costrats for B ad C Equato (3): , A1,1 K2,1 A1,2 K2,2 A1,3 K2,3 A1,4 K2,4 A1,5 K2,5 A1,6 K2,6 A1,7 K2,7 A1,8 K2,8 A1,9 K2,9 A1,10 K2,10 3 where A represets Accra plat, K, Kumas plat, B, cost fuctos for the frst sx moths (Jauary to Jue) ad C, cost fuctos for the ext sx moths (July to December). 2.3 Model Assumptos. The actvtes of Accra ad Kumas operatos are tegrated.. No breakdow producto ad trasportato facltes for the 2014 operatoal year.. All depots are classfed to the te (10) correspodg regos of Ghaa. v. Mothly producto s made up of regular ad overtme producto. 2.4 Methodology The method employed by ths study to fd the Ital Basc Feasble Soluto for the Trasportato Problem model s a Exteded Vogel s Approxmato Method (E-VAM) coupled wth the Modfed Dstrbuto (MODI) Method. Although, there are several methods (Colum Mmum Method (CMM), Row Mmum Method (RMM), North West-Corer Method (NWCM), Least Cost Method (LCM)) for determg the tal basc feasble soluto for a gve trasportato problem model, Vogel s Approxmato Method gves a much better Basc Feasble Soluto (BFS) that s very close to optmalty tha the other methods (Utpal et al., 2014). The VAM thus leads to a allocato wth fewer o-empty cells eve a degeerate case. The algorthm developed for E-VAM s based o the exstg algorthm for Vogel s approxmato Exteded Vogel s Approxmato Method (E-VAM) Algorthm The Exteded Vogel s Approxmato Method makes use of the exstg algorthm for VAM but wth other costrat. The VAM algorthm used here s eumerated the followg steps: Step 1. Idetfy two lowest costs each row ad colum. Fd the row dfferece ad colum dfferece for each cell; Step 2. Idetfy the row or colum wth the largest cost dfferece ad assg the maxmum possble umber of ut to the least cost route that row or colum; Step 3. If the assgmet step two satsfes the demad at that destato, the delete the correspodg colum. Otherwse delete the correspodg row whe t exhausts the supply at the org; ad Step 4. The procedure should be repeated utl every supply ad demad s exhausted or satsfed. Otherwse retur to step oe. Coupled wth the algorthm, the followg codtos were also mposed:. s > 0, = 1, 2, 3,,, ad d j > 0, j = 1, 2, 3,,, that s should ot be egatve or zero at ay staces;. The dfferece s - d j should always be a mmum but ot egatve to satsfy both the customer ad the orgazato; ad. a b 0, ad Z s ( a ) d ( b ) 0 j j 2.5 Model Valdato The formulated model was valdated two ways, frst wth respect to data ad secod wth respect to the authetcty of the wdows terface (POM- QM for wdows (verso 4)) used to smulate the model. The data for the study was acqured from Ashfoam Ghaa Lmted. A year-log secodary data (whch comprses demad, producto ad 22

4 trasportato cost) was used to valdate the model due to varato prces of the product. The set of data used s show Table 1. The frst set of data Table 1, s o Producto Capacty ad Ut Cost of Producto. The table shows the respectve cost of producto from Jauary to December for each ware house (Accra ad Kumas warehouses) as well as the ut total cost for each moth for the two warehouses. The secod set of data s also o Mothly Demads at Varous Depots. The expected mothly demad from Jauary to December for each rego (Depots) ad the overall aual demad for each rego are also show Table 2. The two sets of data were used to valdate the model to acheve optmalty. I ascertag the authetcty of the wdows terface used, POM- QM for wdows (verso 4) was used to ru a exstg data wth kow results from two dfferet referece softwares (Ldo ad Excel) ad the three results compared. The data used for the valdato was obtaed from two dfferet compaes Ghaa (Guess Ghaa Ltd ad GHACEM). From the results obtaed, t ca be ferred that there s o sgfcat dfferece the optmal solutos ad the dstrbuto plas of all the three softwares. It ca thus be cocluded that the POM-QM for wdows (verso 4) s relable, ad ca be used to smulate the model. Tables 5 ad 6, show the outputs obtaed usg POM-QM softwares. 3 Results ad Dscusso Tables 3 ad 4 show the results obtaed whe the formulated model equatos (1) - (3) was smulated wth data from Ashfoam Ghaa Lmted. The result obtaed, Table 3, shows the Optmal Mothly Producto Schedule for the compay, whlst Table 4 gves the mothly Optmal Dstrbuto Pla from Jauary to December. Tables 3 ad 4 were both used to expla the producto ad trasportato schedule for the compay. From Tables 3 ad 4 t ca be ferred that for the moth of Jauary Accra Plat should produce uts ad dstrbute uts to Wester Rego, uts to Easter Rego, uts to Volta Rego ad uts to Greater Accra rego. Also, that same moth, Kumas Plat should produce uts ad haul uts to Brog Ahafo Rego, uts to Norther Rego, uts to Upper East Rego, uts to Upper West Rego, uts to Ashat Rego, uts to Wester Rego ad uts to Cetral Rego. Table 1 The Producto Capacty ( thousad) ad Ut Cost of Producto (Dollars) MONTH WHS Ja Feb Mar Apr May Ju Jul Aug Sept Oct Nov Dec Total ACC WHS KSI WHS COST (Source: Ao., 2015b) Table 2 Expected Mothly Demads at Varous Depots (Quatty) MONTH DEPOTS Ja Feb Mar Apr May Ju Jul Aug Sept Oct Nov Dec Total BA/R N/R UE/R UW/R AS/R W/R C/R E/R V/R G/R Total (Source: Ao., 2015b) 23

5 Table 3 Optmal Mothly Producto Schedule for Ashfoam Ghaa Lmted Table 4 Mothly Optmal Dstrbuto Pla Soluto for Jauary to December 24

6 Table 5 POM-QM Trasportato Output of Guess Gh. Ltd., July 2007-Jue 2008 OPTIMALVALUE =$ FTA RICKY OBIBAJK KADOM NAAT LESK DCEE JOAMA KBOA ACH KAS Table 6 POM QM Trasportato Output of Ghacem Ltd. OPTIMAL VALUE= MK1 MK2 MK3 MK4 MK5 MK6 MK7 MK8 MK9 PLANT PLANT DUMMY For the moth of February, Accra Plat should produce uts ad haul to Easter Rego uts, Volta Rego uts ad uts to Greater Rego. Aga, Kumas Plat o the other had, should produce uts order to meet customers demad ad shp uts to Brog Ahafo Rego, uts to Norther Rego, uts to Upper East Rego, uts to Upper West Rego, uts to Ashat Rego, uts to Wester Rego, uts to Cetral Rego, ad uts to Easter Rego. Ths scearo cotues for the subsequet moths. It was also realsed that there were o producto ad supply the moths of Aprl ad May at both Accra ad Kumas Plats. Ths s due to the fact that the proposed model takes to accout the stock at varous depots before producto ad supply commece. Thus, the optmal aual cost for producto was foud to be $ ad that of trasportato was $ Coclusos ad Recommedato 4.1 Coclusos The research work sought to reduce the trasportato ad producto cost of Ashfoam Ghaa Ltd. Ths was acheved by the use of Exteded Vogel Approxmato Method to reduce producto ad trasportato cost, ad at the same tme satsfy the customers demad. Wth ths schedulg pla, the compay wll reduce ts producto ad trasportato cost by 12.18% ad 42% respectvely. The applcato of the model also shows the optmal way to trasport goods from the ware to the depots to meet customers demad. 4.2 Recommedato It s recommeded that maagemet of Ashfoam Ghaa Lmted adopt the proposed model for optmzg producto to meet the requred demad at mmal cost. Ackowledgemets We are very grateful to all the staff of Ashat Foam Factory Lmted, Kumas, Ghaa who provded the data for ths research. Refereces Ao. (2015a), Iteratoal Health ad Developmet Network (IHDN), Accessed: August 2, Ao. (2015b), Ashfoam Ghaa Lmted, Accessed: August 2, Asamoah, K. M. (2011), Optmal Trasport Prcg of Ilad Freght for Cemet Haulage at Ghacem Lmted, Upublshed MSc thess, Kumas, pp Chadra, P., ad Fsher, M. L. (1994), Coordato of Producto ad Dstrbuto Plag Europea Joural of Operatoal Research 72 (3), pp Che, J. (2004), Achevg Maxmum Supply Cha Effcecy, IEE Solutos, pp Eks o glu, S. A. (2002), Optmsg Itegrated Producto, Ivetory ad Dstrbuto Problems Supply Chas, A PhD dssertato, Uversty of Florda, pp Gorma, M. F. (2006), Trasportato ad the World Ecoomy, Maagemet for a Itegrated producto-dstrbuto, Europea Joural of Operatoal Research 195, pp Hujet, D., Mlovc, M., Luka, N. ad Lajos, S. (2002), Producto-Trasportato Problem ad ts Extesos, Operatoal Research Proceedgs KOI, pp Lu, S. (2003), O the Itegrated Producto, Ivetory ad Dstrbuto Routg Problem, A PhD. Dssertato, The State Uversty of New Jersey, pp Okrah, K. C. (2012), Optmal Producto Trasportato Problem of Latex Foam Ghaa, upublshed Mph. thess, KNUST, Kumas, pp Sraryawat, N. ad Zuder, T. (2009), Impacts of Lea Producto System to Trasportato Sector, 25

7 documets/sraryawat.pd. Accessed: August 2, 2014, pp Utpal, K. D., Ashraful B., Amur, R. K., Md. Abu, H., Sharf, U. (2014), Logcal Developmet of Vogel s Approxmato Method (LDVAM): A Approach to Fd Basc Feasble Soluto of Trasportato Problem, Iteratoal Joural of Scetfc & Techology Research (IJSTR), Vol. 3, No. 2, pp Authors Mr Gabrel Adje holds M.Phl. Mathematcs from Uversty of Mes ad Techology (UMaT), Tarkwa. He s curretly a Mathematcs Tutor at Atebubu Seor Hgh School ad a part-tme Lecturer at Gold Star College. Hs research area of terest s Rsk Modellg ad Hedgg. Mr Joseph Acquah s a Lecturer at the Departmet of Mathematcal Sceces of the Uversty of Mes ad Techology (UMaT). He obtaed hs MPhl ad BSc degrees from Uversty of Cape Coast (UCC), Cape Coast, Ghaa. Hs research terest s verse problems. He s curretly pursg hs PhD degree at UMaT. He s a member of Ghaa Isttute of Mathematcal Sceces. Prof Sulemaa Al-Hassa s a Assocate Professor the Mg Egeerg Departmet at the Uversty of Mes ad Techology, Tarkwa. He obtaed hs BSc (Hos.) ad Postgraduate Dploma Mg Egeerg from the Uversty of Mes ad Techology 1982 ad 1983 respectvely. He obtaed hs PhD from the Uversty of Wales, Cardff, UK Hs research areas clude Meral Reserve Estmato, Me Plag ad Desg, Meral Ecoomcs ad Small Scale Mg. He s a Member of Ghaa Isttuto of Egeers (MGhIE), Ghaa Isttuto of Geoscetsts (MGhIG) ad Australasa Isttuto of Mg ad Metallurgy (MAusIMM). 26