MATHEMATICAL MODELING ON TRANSPORTATION OF SUGAR CANE: MINIMIZATION OF SUGAR LOSSES DUE TO TRANSPORTATION DELAYS

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1 Bulletin of the Marathwada Mathematical Society Vol. 14, No. 2, December 2013, Pages MATHEMATICAL MODELING ON TRANSPORTATION OF SUGAR CANE: MINIMIZATION OF SUGAR LOSSES DUE TO TRANSPORTATION DELAYS V.A. Chougule, U.K. Shirke and R.D. Khalate Department of Mathematics, S.V.P.Ms College Of Engineering, Malegaon (Bk), Taluka Baramati, Dist. Pune. (chouguleva@gmail.com, ushagulunkar@rediffmail.com, khalaterahul@yahoo.co.in) Abstract Sugar industry bears loss of raw material (Suagcane) quality due to hectic transportation and labor problems. This is the main reason to find out an optimized solution to minimize sugar losses due to transportation delays or many other problems. Several studies and research are carried out in this regard in many countries, but the results obtained or methods derived are local to the environment and facilities available there. Thus it is essential to optimize such methods in accordance with labor problems and local transportation facilities like Bullock Carts, Tractors, trucks etc. Our work is step in this regard. In this paper we tried to construct a Mathematical Model to minimize the losses of sugar during the sugarcane harvesting and transportation. Here we have focused on Cost and time required during the sugarcane harvesting and transportation, and we have added one example without solution. 1 1 INTRODUCTION India has been known as the original home of sugar and sugarcane. India has more than 566 sugar mills in the country, of which 56 per cent are in the co-operative sector, 34 per cent in the private sector and the remaining 10 per cent are in the public sector. These processing units are located in 80 major districts of India and a large number of these units are in Maharashtra (142 in the co-operative sector and 12 in the private sector during ). The sugarcane supply system for mills has been of great interest for several researchers, due to the increasing world consumption of sugar and ethanol. In this context, studies on the analysis of the cost and time 1 Keywords: modeling, sugarcane, transportation, road conditions, lead time, optimization, sugar Marathwada Mathematical Society, Aurangabad, India, ISSN

2 10 V.A.Chougule, U.K.Shirke and R.D.Khalate that the sugarcane takes from the time of cutting to milling facilities in the mill are noteworthy. More specifically, the time (here called lead time)refers to the period of waiting about the time between the beginning and end of the operations of handling the raw material. That is, the lead time begins to be considered from the moment of cutting sugarcane, through the subsequent operations of loading, transportation, reception, unloading until the starting of grinding for processing within the mill. The lead time is important because it has direct bearing on the quality of the juice of the sugarcane and thus, in turn, has influence on the quality of sugar and ethanol produced by the mill. The sugarcane has better productivity when the lead time is shorter. It is critical to this system when the lead time is more than forty-eight hours. Thus to control the quality of sugarcane (Raw Material) Losses due to lead time has to be minimized. Here we are considering the Sugar Factories in Maharashtra, India, as these factories are running on co-operative basis and are of great interest of people. 2 SUGARCANE TRANSPORTATION SYSTEM In Mahrashtra state of India, harvesting of sugar cane is mainly done with the help of labors and transportation is done using bullock Carts, Tractor-trailer, Trucks. Road conditions at countryside are very poor, labor problem is also the great issue. Harvested sugarcane is to be sent for crushing to the factories concerned. Main thing is to transport this sugarcane from fields to the factory. For that each route, distance between source to the destination, number of units of sugarcane to be transported, cost of transportation of one unit of sugarcane along the routes should be calculated.cost and time of loading and unloading is to be minimized. Depending upon the road conditions the vehicle is so chosen that, transportation time should be reduced. At the time of unloading, we can apply queuing theory so that waiting time and unloading time is reduced. 3 NOTATIONS Let us define the variables as, Vehicle Type :V 1, V 2, V 3, V 4,..., V i,... Load on Vehicle :V i = L i, i.e.l 1, L 2, L 3, L 4,..., L i,... Route :R 1, R 2, R 3, R 4,..., R j,... Distance of a route :d 1, d 2, d 3, d 4,..., d j,... Cost factor and Time factor 2 Loading charges per ton :C L1, C L2, C L3, C L4,..., C Li... Transportation cost per unit distance per ton :C T1, C T2, C T3, C T4,..., C Ti... Unloading charges per ton :C U1, C U2, C U3, C U4,..., C Ui... 2 Depends upon vehicle type

3 Mathematical Modeling on transportation of sugar cane 11 Loading time:t L1, t L2, t L3, t L4,..., t Li... Transportation time per unit distance :t T1, t T2, t T3, t T4,..., t Ti... Waiting time 3 :t W1, t W2, t W3, t W4,..., t Wi... Unloading time :t U1, t U2, t U3, t U4,..., t Ui... The function of sugar loss after time t is denoted by R(t). 4 4 MATHEMATICAL MODELLING Consider the route R j and vehicle V i,...for i = 1, 2, 3,..., n and j = 1, 2, 3,...m. The total time(lead time) required for the transportation of sugarcane from field to processing starts in factory be t ij = [t Li + (t Ti.d j ) + t Wi + t Ui ]. The total cost of transportation of sugarcane for j th route and i th vehicle, C ij = L i.[c Li + (C Ti.d j ) + C Ui + R(t ij )]. Minimize, C ij, subject to the constraints, L i 0 d j 0, C Li 0 C Ui 0 C Ti 0, CLi C L CUi C U CTi C T tli t L tti t T tui t U and t wi 0 5 EXAMPLE Reduction of Sugarcane Weight after Harvesting R(t) Reduction of weight of sugarcane in Kg/M.tons Sr.No. After Harvesting Sugarcane crushing period 1 After 00 Hrs After 08 Hrs After 16 Hrs After 24 Hrs After 32 Hrs After 40 Hrs After 48 Hrs After 56 Hrs After 64 Hrs After 72 Hrs Reduction of sugar in Kg/M.Tons The following data is made avalable for the year from The Malegaon Shakari Sakhar Karkhana, Shivnagar, Malegaon(Bk),Tal:Baramati,Dist:Pune. 3 time between vehicle rich at factory site and unloading starts 4 In terms of recovery of sugarcane and weight loss converted in terms of cost of sugarcane

4 12 V.A.Chougule, U.K.Shirke and R.D.Khalate Routes and their Distance R j and d j Route R j Village /(GAT) 0 Distance d j Km Route 1 Malegaon 02 to 05 Km Route 2 Pandare 10 to 13 Km Route 3 Sangavi Kambaleshwar 10 to 15 Km Route 4 Khandaj Shiravali 06 to 10 Km Route 5 Baramati Malad 08 to 10 Km Route 6 Nira Waghaj 15 to 20 Km Vehicle and their Load V i and L i Sr. No. Vehicle type V i Load L i M.Tons 1 Bullock Cart 1.5 to Tracter- Trolley 12 to 14 3 Truck 14 to 16 4 Harvester Trolley 12 to 14 Vehicle V i and their lead time t ij in Hours Vehicle Type V i Loading Transportation Waiting Unloading Time t Li Timet Ti per Km time t Wi time t Ui Hr Hr Hr Bullock Cart 2 to to Tractor Trolley 3 to to Truck 3 to to Harvester Trolley 2 to to Vehicle V i, Harvesting Costs C ij Bullock Cart C ij = 186 Rs. Per M.Ton 5 Tractor Trolley C Li + C Ui = 186 Rs.,Transportation Cost C Ti = 145 Rs., per Km Per M.Ton Truck C Li + C Ui = 186 Rs.,Transportation Cost C Ti = 145 Rs. per Km Per M.Ton Harvester Trolley C Li + C Ui = 305 Rs.,Transportation Cost C Ti = 145 Rs. per Km Per M.Ton 6 CONCLUSION One can use a software tool like MATLAB or even one can design a C programme to solve a problem like this, using this theoretical model. As the reduction of sugarcane weight affects the income of farmer, while the 0 Group of villages suitablly made 5 Fixed

5 Mathematical Modeling on transportation of sugar cane 13 reduction of sugar(recovery) affects the loss in production of sugar, i.e. both factors are affected. The cost of harvesting and transportation is almost fixed for a particular year, main factor in minimization of sugar losses is the lead time i.e. the time between the harvesting of sugarcane and crushing at factory site. For that, we have to minimize the lead time t ij especially the waiting time t Wi. To minimize this, a well management (with past experience) of harvesting and transportation of sugarcane is important. To minimize the lead time at factory site, one has to minimize the factory stoppages(ideal time due to maintenance in factory), over or less supply of raw material(sugarcane) etc. This may be a part of research of a management student. ACKNOWLEDGEMENTS : The authors are thankful to all officials of The Malegaon Shakari Sakhar Karkhana for giving the details about sugarcane supply system, and all the persons who inspired us to write this article. We always welcome your valuable suggestions. References [1] P. Saravanamoorthi and V. Navaneethakumar, Mathematical Analysis on Transportation of sugarcane: A qualitative approach, International Journal of Mathematics and Application.(2010), p.p [2] Frank R. Giordano and Willam P. Fox, Mathematical Modelling, Principles and Applications, Cengage Learning,(2009). [3] Harris AJ, Bezuidenhout CN, Lagrange LF and Lyne PWL, Development of a sugarcane transport route planning model in a geographical information system, Proc S Afr Sug Technol Ass.(2008), p.p [4] AJ Barnes, E Meyer, AC Hansen, ER DE La Harpe and PWL Lyne, Simulation Modelling of a sugarcane harvesting transport delays, Proc S Afr Sug Technol Ass.72 (1998), p.p [5] Esteban Lopez Milan, Silvia Miquel Fernandez and Lluis Miquel Pla Aragones, Sugar cane transportation in Cuba, a case study, European Journal of Operational Research.174 (2006), p.p [6] Paitoon Chetthamrongchai, Aroon Auansakul and Decha Supawan, Assessing the Transportation problems of the sugarcane industry in Thailand, Transport and Communications Bulletin for Asia and the Pacific.70 (2001), p.p