AN OPERATIONAL COMPUTERISED SYSTEM TO MANAGE THE SUPPLY CHAIN OF SUGAR CANE

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1 AN OPERATIONAL COMPUTERISED SYSTEM TO MANAGE THE SUPPLY CHAIN OF SUGAR CANE Lluis M. Plà-Aragonés; Esteban López-Milán; Sara V. Rodríguez-Sánchez Department of Mathematics. University of Lleida, Jaume II, 73, 500 Lleida. Spain. Mechanical Engineering Department. University of Holguin. Av. Aniversario, gaveta 57 CP 8000 Holguín Cuba. Department of Mathematics. University of Lleida, Jaume II, 73, 500 Lleida. Spain. Abstract: In this work the authors present a Decision Support System (DSS) for planning daily operations in the sugar cane supply chain for a Cuban sugar mill. The supply chain model is based on a mixed linear programming model. The model objective is to minimize transportation costs while assuring cane supply to the sugar mill. The model determines the fields to harvest, the cutting-loading-transport means for such operation, and the roster for each employee. Keywords: Sugar cane supply chain, Decision support system, Resource allocation. Introduction The international sugar market is in crisis because of the low price of sugar. This is a serious concern for many large producers (e.g., razil and Australia) and for countries that depend on sugar exports (e.g., Cuba). After tourism, sugar is the second must important generator of revenue for Cuba, although its importance is decreasing in favor of other activities. A few years ago, the Ministry of Sugar Industries operated a hundred and fifty six sugar mills. As a result of the sugar market crisis, they operate only forty four sugar mills. The price of sugar in the international market requires constantly lowering production costs in order to increase economic efficiency and increase the chances of some profit. The most important component of production cost in the sugar industry is transportation. This is especially true for developing countries. Cane transport is the largest cost component in the manufacturing of raw sugar as different authors have already shown (Díaz and Pérez, 000; Martin et al., 00). Australian studies estimated the transportation cost to be 30% of the total production cost under their conditions. A complementary strategy to control and reduce the production cost is to concentrate production in larger farms which has a positive effect on transport savings. The sugar cane harvest is a complex logistical operation that involves the cutting and loading of cane in the fields, the transportation by truck or train to the sugar mills, and the unloading of the cane in the mill to be processed. Each sugar mill has a number of teams that cut cane with several harvester machines to meet a daily quota. Depending on the quota and available resources for a particular day, the scheduling is performed by sugar mill managers based upon their own expertise. In view of day-to-day changes in the amount of cane in the fields, the cane ripeness, the unforeseen failures in machinery, and the performance of harvesters, managers must adapt heir schedules daily.

2 In order to cope with daily scheduling changes, there has to be a constant and ongoing analysis of current the organization, the available infrastructure, and future needs. This paper combines computers and mathematical programming in a DSS capable of supporting the operational decisions of sugar mill managers who control the sugar cane supply chain in Cuba. The system is flexible enough to be adapted to other different national conditions of sugar cane harvesting. The sugar cane supply chain The Cuban sugar industry is characterized by large sugar mills that are able to take supplies of cane from surroundings farms. Sugar cane must be cut when it is ripe; otherwise, the sugar quality of the cane deteriorates. As sugar cane is harvested, it is transported to the sugar mill. Generally, sugar cane can be conveyed in two different ways: a) direct transportation to the swing-bolster for just-in-time processing by road transport. b) intermodal transportation that employs road transport to carry the sugar cane to the storage facilities at rail loading stations where it is then cleaned. Later, it is placed in rail carriages and delivered to the sugar mill yard where it is processed. The transportation system has to maintain a constant flow of ripe cane to the sugar mill. Therefore, the planning of the transport of sugar cane from fields to the sugar mill is a difficult task depending on the carriage means available, but is necessary to avoid the waste of valuable resources (Díaz and Pérez, 000). The rail system may operate 4 hours a day, whereas the harvest period may comprise only a part of the day. Therefore, when the road transport stops working at night, the rail system is the only source of supply. In this way, the rail system acts as storage for cut cane, allowing the creation of a reserve that satisfies the demand of the sugar mill, while road transport either is covering other routes at the same time or is stopped at night. Unless a sugar mill failure or break down occurs, railway transportation allows the sugar mill to work 4 hours a day without interruption; however, every 0 days the sugar mill is stopped for technical maintenance. The organisation of the operations prior to processing cane affects sugar quality and productivity at the sugar mill. For instance, harvested sugar cane spoils if it is not processed as soon as possible after harvesting. Therefore, the sugar industry employs the so-called sugar cane freshness as a technical quality indicator (sugar cane freshness is defined as the standard time that sugar cane lasts from being cut in the field until it is processed in the sugar mill). Taking this indicator into consideration, the use of road transport is the best alternative, since it allows the sugar cane to arrive at the sugar mill in optimal conditions to be processed and is therefore preferred. Nevertheless, carriage costs are higher than the ones presented by the railway alternative in Cuban agro-industrial conditions. The second aspect affecting sugar quality is the pol of the cane (i.e., an index related to the ripeness that is used for deciding the cutting moment). If necessary, the ripeness of the cane can be assessed by the supply of reapers to the cane plantations. Reapers improve the pol of the cane; however, a disadvantage is that when using these products, the cane must be cut as soon as possible to avoid its earlier deterioration. In brief, the most important aspect of cane harvesting is being able to determine the optimal combination of

3 transportation means. The objective of minimizing the global transportation cost while fulfilling the daily sugar mill supply needs with an acceptable level of quality and avoiding cane losses caused by not harvesting. 3 Implementation of the DSS 3. DSS structure The structure and system elements of the DSS are presented in Figure. The heart of the system is the mathematical model representing the supply chain. It is described in the next subsection. The database store inputs and outputs. Inputs are all of the resources available for sugar cane processing. Outputs are represented by the allocation and distribution of resources along the chain, giving priority to transportation cost minimization and sugar quality. The interface allows the user interact with the system, modifying inputs, updating the database, and retrieving outputs. M athem athical M odel M odel input Data base Model output User Interface M ill M anager Figure : Structure of the DSS. 3. Formulation of the model The mathematical model included in the DSS is a mixed integer linear programming model dealing with all of the previously described aspects of the operational problem of sugar cane transport for one day. The model is based on a linear programming model developed by López et al. (005) and summarized in Appendix A. The transportation cost is minimized, and the scheduling of road transports and cutting means are obtained. Quality aspects are considered by means of an opportunity coefficient determined empirically by the decision-maker and by establishing minimum quantities of cane processed just-in-time to preserve cane freshness.

4 3.. Decision variables The decision variables are represented by ijklm, being the quantity of sugar cane transported from origin i to destination j, by transportation mean k during the hour m and harvested by the group l. 3.. Constraints The constraints of the mathematical model are classified in the following groups: Supply of cane to the sugar mill for a working day (see () and (3) in Appendix A) Capacity of the storage facilities (see (6) in Appendix A) Conservation of flow through storage facilities (see (7) in Appendix A) Capacity of transportation by road transportation means (see (8) in Appendix A) Production of the sugar cane fields (see (9) in Appendix A) Constraints related to cutting means used in sugar cane harvesting. This group includes binary variables in the formulation. Therefore, extra constraints related with binary variables are needed (see (4), (5), and (0) to (3) in Appendix A): o Cutting means can work in only one field in one hour o A field can hold up to two groups of harvesters o Movements of cutting means between fields are limited to one o A group of harvesters can only work consecutive hours in a field o The work of harvesters can not overcome the daily hours of work 3..3 Objective function The primary objective is the minimization of daily transportation costs. Hence, the economic coefficients of the objective function establish the transportation cost of sugar cane, as a function of the distances and the transportation means used in each case. Quality aspects are introduced in the objective function through an opportunity coefficient, which represents the preference to cut a sugar cane field Model implementation Due to the constraints, not all decision combinations are feasible. In a complementary way, the binary variables provide the scheduling of transports and cutting tasks for a day s operation. The package embedded in the DSS to solve the model was LINDO (Schrage, 997). The interface was implemented in MS Visual asic v. 6. It interacts with the user and manages the LINDO library in two ways: to formulate the model and to retrieve and show the outcome. With variables representing daily quantities, the system provides a solution in a few milliseconds. If necessary, a detailed solution by hour can be obtained or an initial solution may be refined by modifying the initial inputs. Thus, the system also gives useful

5 information for scheduling. The quantity of cane transported to the sugar mill, the location where cane is collected, the transportation means used, the way cane is cut, and transportation time are all provided in the solution. In addition, sugar mill managers are able to determine the amount of transportation means needed, the exact time of shipment and the amount of petrol in reserve. 4 DSS operation The DSS was developed to manage the sugar cane supply chain around a specific sugar mill situated in the Holguín province (Cuba) that processes cane from 39 fields. All inputs are related to this specific case, but the parameters can be adapted to represent different situations. The database contains data representing the specific conditions of this chain. For instance, on a regular work day, this sugar mill is supplied with cane cut in different surrounding fields and sent directly by train from five storage facilities. The fields are selected by the user from the database. The harvesting labor on the fields is a maximum of 4 hours per day. The daily processing capacity of the sugar mill, a minimum quantity of cane to be processed, the maximum and minimum quantities of sugar cane supplied to the sugar mill per hour, and the limited management capacity of each storage facility have to be set. Available road transportation with the corresponding technical and operational characteristics, the number of groups of harvesting means (mechanical or manual), and the corresponding work capacity also have to be set. For this purpose, the DSS interface has a set of windows and displays where all these parameters can be selected and corresponding figures introduced (Figure ). Figure. Selection of harvesting means and corresponding technical and operational characteristics The cane is transported to the sugar mill straightaway after being cut or passed through storage facilities. All available origins and destinations for each feasible combination between origin and destination also have to be set. Distances are stored in the database. The problem as it is formulated generates H[ + A + ( + )(L + C)+ + K] (L + C)( - ) constraints and (L+C)[+ H [()(K-) +]] +AH variables, being H the total number of hours of work; A the number of storage facilities; the number of fields to cut; L the number of harvesting machines; C the number of groups of manual cutting and

6 K the number of transport means. Hence, a total of (L+C)(+ H) variables are binary (López et al., 005). These figures can vary if managers consider daily information. The solution, as it is shown in Figure 3, represents the daily quantity of sugar cane transported. The solution indicates how direct transportation is not always preferred; because all related constraints are not fully satisfied and thus the maximum processing capacity of this kind is not attained. Generally, direct transportation involves the nearest fields to the sugar mill for which road transportation is cheaper. On the other hand, the nearest storage facility to each field is the preferred one to store cane when needed. Figure 3. Display of DSS outputs 5 Discussion and conclusions The complexity in developing the DSS presented here is inherited from its embedded mathematical model. What was more problematic was handling of the large number of variables, although this problem is unappreciated for the user and remains inside the DSS. In a preliminary step, a reduced case considering just one day is proposed to be solved in order to approximate the solution of the problem (Plà et al., 00). This first step serves to verify and refine the real needs of all kind of means to perform the harvesting, and thus superfluous variables can be ignored in subsequent runs of the model. The real problem can become more complex depending on the changes in the number of constraints from one day to another. For instance, the availability of cutting and transportation means, the possible destinations and origins, and the number of working hours may all vary. It is the user who has to select the actual parameters daily. If the number of fields and the number of harvesting machines increase and the available transportation means and their working hours increase, then the number of decision variables in the model also increases. Therefore, solving this kind of complex model daily, this automated solution system is seen as very profitable. The DSS presented is capable of solving the problem of cost minimization of sugar cane transport from fields to the sugar mill for one working day. The model determines the capacities of the road and rail transport

7 facilities for transporting cane to ensure an uninterrupted supply to the sugar mill. Moreover, the scheduling of road transportation and harvesting quotas of cutting means are derived from an optimal solution that simplifies the daily task of the mill s managers. However, specific railway scheduling is not considered in detail. The mathematical formulation of the model integrates rail and road transport systems emphasising the reduction of transportation cost. The model also controls sugar cane freshness through the minimum supply constraints to the sugar mill with direct transport. Furthermore, the model allows sugar mill managers to schedule daily transport plans automatically, based on either objective criteria or on considerations that have been acquired through professional experience. Professional software permits solving huge linear programming models, but managers find them difficult to handle. ecause of this, it is helpful to elaborate custommade software based on a friendly interface that simplifies dealing with large amounts of variables and making the mathematical model transparent to the user. In this way, the reformulation of the problem and its daily update will be easier and feasible, saving a lot of time and money for the mill s managers. To combine models in a custom-made software package, combining the possibilities of specific systems for solving mixed integer linear programming models with the knowledge and the experience of people who are familiar with the cutting-loading-transportation system for sugar cane allows the users of the model to make a more flexible allocation decisions of harvesting and road transportation means. Moreover, it also provides the scheduling of these resources in place and time according to their daily availability. 6 References Díaz, J. A. and I. G. Pérez, (000). Simulation and optimization of sugar cane transportation in harvest season. In the proceedings of: Winter Simulation Conference, Miami, December 000, 4-7. Higgins, A.J. (999). Optimizing cane supply decisions within a sugar mill region. Journal of Scheduling Higgins, A.J. (00). Australian sugar mills optimize harvester rosters to improve production. Interfaces 3(3) 5-5. Higgins, A.J. and R.C. Muchow (003). Assessing the potential benefits of alternative cane supply arrangements in the Australian sugar industry. Agricultural Systems López, E., S. Miquel and L.M. Plà (004). El problema del transporte de la caña de azúcar en Cuba. Revista de Investigación Operacional López, E., S. Miquel and L.M. Plà (005). Sugar cane transportation in Cuba, a case study. European Journal of Operational Research. In press. Martin, F., A. Pinkney and. Yu inghuo (00). Cane railway scheduling via constraint logic programming: labelling order and constraints in a real-live application. Annals of Operational Research Plà, L.M., E. López and S. Miquel (00). Planning transports of sugar cane in Cuba. I Congreso Latinoamericano de Investigación Operativa. Concepción, Chile.

8 Schrage, L., (997). Optimization modeling with LINDO. 5th Ed. Duxbury Press, ITP. New York. Rizzoli, A.E., N. Fornara and L.M. Gambardella (00). A simulation tool for combined rail/road transport in intermodal terminals. Mathematics and computers in simulation Semenzato, R., (995). A simulation study of sugar cane harvesting. Agricultural Systems iography LLUÍS M. PLÀ is an associate professor in the Department of Mathematics at University of Lleida (UdL) and a Senior Researcher in the Area de Producción Animal at the UdL-IRTA Center. His main research interests include operational research methods applied in agriculture and forest management, with special reference to Simulation, Supply Chain Planning and Markov decision processes. Coordinator of the EURO-Working group: Operational Research in Agriculture and Forest management < He is a member of INFORMS and EURO. His Web address is < ESTEAN LOPEZ is Auxiliary Professor at University of Holguin, Cuba. He is the Industrial Machines and Transport Group Chief and professor of courses about exploitation and repairing automotive transport. He investigates the development of mathematical models to organize and planning the transportation. He has investigated in reliability tires, optimization of sugar railway traffic and optimization of sugar cane of railway and trucks transportation. He has experience as Visual asic programmer. SARA V. RODRÍGUEZ is a PhD student in the Department of Mathematics at University of Lleida (UdL). His main research interest is Supply Chain Management and optimization. Appendix A: The mathematical model K O.F. : Minimize Subject to: j= k= L+ H l= m= C ijklm Co i ijklm () A H m m= k = A H K L+ C + H i + iklm Mmax () m m= k = l= m= K L+ H i + iklm Mmin (3) l= m= K L+ k = l= iklm Smax m m =,,, H (4)

9 K L+ k = l= K L+ k = l= iklm ijklm Smin SP j m m =,,, H (5) m =,,, H and j =, 3,..., (6) K L+ j m ijklm = k= l= 0 m =,,, H and j =, 3,..., (7) L+ j= l= CR ijkl ijklm TM k m =,,, H and k =, 3,..., K (8) K L+ H ijklm j= k = l= m= Cap i i = A +, A +,..., (9) A + K j= k = A + ilm ijklm Prod l ilm i = A +, A +,..., ; (0) l =, 3,..., L+ and m=,,,h l =, 3,..., L+ and m=,,,h () L + C + ilm l= L + C + il l= A + il H m= t+ H i = A +, A +,..., and m=,,,h () Y i = A +, A +,..., (3) Y l =, 3,..., L+ (4) ilm m= ilm ( H t) il, t+ + ( H t) il, t H i = A +, A +,..., H Y il l =, 3,..., L+ and t=,,,h- (5) i = A +, A +,..., and l =, 3,..., L+ (6) where: C ijklm = c k d i,j : represents the economic coefficients. Co i : represents the opportunity coefficients. ijklm : are the decision variables.

10 c k : is the specific economic coefficient related to transport k. As it is shown, the way and time in which the cane is cut make no difference because these economic coefficients are just representing transportation costs. d ij : is the distance between origin i and destination j. Co i : opportunity coefficient which represents the preference to cut a field, Co i. TM k : total transport force of means type k expressed in hours of work CR ijkl where: Dij + Vcck Vsck = Cc k + Tc D ij : Distances from origin i to destination j Vcc k : Speed of the given carriage means k, with load. Vsc k : Speed of the given carriage means k, without load. Tc kl : Waiting time of carriage means k, with cutting system l. Cc k : Loading capacity of carriage means k. Cap i is the production of sugar cane in field i. kl ilm {0,} is the binary variable controlling possible combinations origin-cutting mean per hour. Prod l : production per hour of each l-group of cutting means Y il {0,} is the binary variable representing if the cutting mean l has been working or not on field i during the working day. (7)