- Email: [email protected]
Planning of a multiproduct pipeline integrating blending and distribution
KristV.Gernaey, JakobK.Huusom and RafiqulGani (Eds.), 12th International Symposium on Process Systems Engineering and 25th European Symposium on Computer Aided Process Engineering. 31 May – 4 June 2015, Copenhagen, Denmark © 2015 Elsevier B.V. All rights reserved.
Planning of a multiproduct pipeline integrating blending and distribution Diovanina Dimasa*, Valéria V. Murataa, Sérgio M. S. Neiroa, Susana Relvasb and Ana Paula Barbosa-Póvoab a
Programa de Pós-Graduação em Engenharia Química (PPGEQ), Universidade Federal de Uberlândia (UFU), Avenida João Naves de Ávila, 2121, 38408-100, Uberlândia, Minas Gerais, Brasil b Centro de Estudos de Gestão do Instituto Superior Técnico (CEG-IST), Universidade de Lisboa (UL), Avenida Rovisco Pais 1049-001, Lisboa, Portugal [email protected]
Abstract Pipelines play an important role in the oil supply chain linking different supply chain echelons and acting as one of the most sustainable, safe economical transportation mode. In this context, multiproduct pipeline scheduling is a key issue to be addressed in an optimized form, namely when integrating pipeline operation with the operations of the connected entities. In this paper a MILP discrete time formulation is developed for multiproduct distribution scheduling linking both sides of the pipeline, refinery and distribution centre, so as to generate the best product pumping sequence accounting for material availability at the refinery blending process and delivery needs at the distribution centre. The model was applied to a case based on a real world oil supply chain. Keywords: oil industry, scheduling, multiproduct pipeline, activities integration, MILP.
1. Introduction Typically, downstream distribution in the oil industry can be accomplished via road, railway and pipelines. Pipelines are widely used since they may connect several refineries, depots and terminals transporting crude oil as well as final products in large quantities for long distances in a more sustainable form. The pipeline operator must decide what products and what quantities should be pumped, operational timing range, and how to distribute all products among several destinations (Rejowski and Pinto, 2008). Additionally, this problem often presents some restrictive requirements associated with the pipeline operational conditions such as reverse operation, pumping rate limits, inventory levels, interfaces and lot sizes. All these aspects taken simultaneously make this operation quite complex and decision support tools to help the solution of such complexity are required. Therefore, according to MirHassani, Abbasi and Moradi (2013), distribution scheduling arises as a modeling tool that should be able to determine the transport details and the best way to fulfill several demands at the right time. Several works may be found in the literature addressing pipeline scheduling integrated with either up or downstream operations. Rejowski and Pinto (2004) presented a discrete MILP problem composed by a refinery, pipeline and depots considering
1848
D. Dimas et al.
intermittent pumping time and logical constraints, adding a set of integer cuts and special interface constraint that resulted in better solutions. The same problem was later improved by the same authors (Rejowski and Pinto, 2008) to develop a MINLP continuous time formulation with pumping cost dependent on booster stations yield rate. Magatão et al. (2012) developed a hierarchical decomposition to solve a planning and assignment\sequencing pipeline network model composed by refineries, harbors, depots and clients applied to a real scenario. More recently, Ghaffari-Hadigheh and Mostafaei (2014) proposed a model which provides input and output pipeline sequences to satisfy different terminals simultaneously with minimum operating costs. Pipeline scheduling alone has derived over the last years an intense field for publication, consisting in a complex scheduling problem. These complexities are related with the need to model time and volume decisions efficiently and additionally build flexible models aiming to address multiple i) topologies, ii) products iii) operational and cost issues so as to represent any pipeline-based system. Recent works on the area include the work of Cafaro et al. (2015), where pumping costs are detailed, MirHassani and BeheshtiAsl (2013), who use heuristic procedures as solution method for pipeline scheduling and Relvas et al. (2013) where inventory management at destination depots is tackled along with pipeline scheduling. From the literature review it can be seen that the integration of pipeline scheduling with operations in input and output entities is not widely studied, given the complexity of integrating the pipeline scheduling problem with additional decisions in different echelons. The purpose of this work is to address this problem and to integrate information on product availability at both sides of the multiproduct pipeline (blending and distribution centre) so as to produce an optimal product sequence with minimum operational costs while guaranteeing service levels. The inventory management at the blending and distribution centre is integrated with the pipeline pumping sequence.
2. Problem description The system considers a single unidirectional multiproduct pipeline that connects a product tank farm at the refinery, blending section, and a distribution centre that has to satisfy the local market, as illustrated in Figure 1. Three different products (gasoline, diesel and jet fuel) are produced and stored at the refinery and transported through a multiproduct pipeline to a distribution centre and to storage tanks with fixed service. When a batch of product arrives at the distribution centre a settling period is required due to regulatory quality assessments.
Figure 1 - Schematic system.
Planning of a multiproduct pipeline integrating blending and distribution
1849
Given: The scheduling horizon; The inventory limits (minimum/maximum storage capacities); Initial volume available at each tank and pipeline; The feeding flow rate from the refinery blending; The pipeline volumetric capacity and batch size limits; The minimum settling period; The matrix of possible/forbidden products sequence; The daily demand; The goal is to determine the products sequence pumped into the pipeline, which satisfy the demand while controlling the inventory tanks at the refinery blending centre and distribution centre.
3. The mathematical formulation A discrete time Mixed Integer Linear Programming (MILP) model is formulated which is an extension of the previous work developed by Relvas et al. (2013). This extension links the previous developed model to the blending tank farm where inventory management is also performed. The main assumptions for this problem are: 1. There is a set of dedicated tanks teach product at refinery and distribution centre; 2. A tank at the refinery is not allowed to load and unload simultaneously; 3. The pipeline should be full at any time; 4. At most one tank can be connected to the pipeline at any time; 5. Changeovers time from one tank to another are disregarded; 6. Not all products sequences are allowed in the pipeline; 7. Settling periods are accounted for at the destination depot, making unavailable the settling product for dispatching to local market; 8. The flowrate is assumed to be variable within an acceptable operational range. This operation is controlled by several constraints that are summarized as follows: 1) Material balance –to determine that the amount of products available in each tank; 2) Timing – to define the initial and final pumping and receiving time of each batch; 3) Inventory control – the minimum and maximum storage tanks limits; 4) Operating rules –referred to allocation constraints; 5) Forbidden sequences – the contact between some products inside the pipeline is prohibited; 6) Demand – to satisfy the local market demand values on time; 7) Batch limits – the volumes pumped should be bounded by the pipeline capacity; 8) Initial conditions –inform on the initial products at each tank and inside the pipeline; Due to space limitations, we will only present the timing constraints and the objective function. Timing constraints are responsible for connecting the blending to the distribution centre, given the pipeline operation, using a reduced amount of problem information. 3.1 Timing constraints These constraints are used to synchronize the operations between refinery, pipeline and distribution centre since these operations are continuous. Then, when a tank b start to feed a pipeline with product p simultaneously a tank d begins to receive a product already pumped at previous time. In this way, at the distribution centre the receiving time for batch i (TDSi) is determined based on the previous receiving time plus the time required to unload the product from the pipeline, as expressed in constraint (1).Similarly, at the refinery the pumping time for batch i (TBSi) depends on the
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D. Dimas et al.
transportation time to the distribution centre and the receiving time at the distribution centre, as shown in constraint (2). Both timings are calculated within an interval given by minimum and maximum pipeline flow rate. 1 ൰ כ ܹௗ,,, ܶܵܦ ݒ௫
ܶܵܦିଵ + ൬
ௗא
1 ൰ כ ܹௗ,,, ݅ ݒ
ܶܵܦିଵ + ൬
ௗא
(1)
݁݅ כ ܴܺ,,, െ ܶܵܦ ܶܵܤ ݒ௫ א
݁݅ כ ܴܺ,,, െ ܶܵܦ ݒ א
݅
(2)
Where vmin/vmax are the minimum/maximum pipeline flowrate, pipe is the pipeline volume, Wd,i,p,k is the volume of batch i with product p received in tank d at time k and XRb,i,p,k a binary variable that indicates if a batch i with product p is unloading from tank b to pipeline at time k. 3.2 Objective Function The objective function is based in operational indicators and is composed by four terms. The first one corresponds to the difference between the total amount received at the distribution center and the total demand. The second term is used to maximize the pipeline usage so as to avoid stoppages/idle times. The third and last terms represent the lowest inventory level at refinery blending and distribution centre, respectively. min ݓଵ כ
ܾ݉݅݊݅
݂݀݅ ܶ|ܵܦூ| െ ݓଶ כ௫ െ ݓଷ ݀݅݊݅݉ כെ ݓସ ܾ݅݊݅݉ כ σ σ ݉݁ܦ, ݄
ܴݒ݊ܫ,,|| ௫ ܴݒ݊ܫ,
and
݉݅݊݅݀
ܶݒ݊ܫௗ,,|| ௫ ݒ݊ܫௗ,
(5) (6)
Where InvRb,p,|K| and InvTd,p,|K| are the inventory of each tank at end of the time horizon as well as their maximum limits, dif is the difference between the volume arrived at the tank at the distribution centre and the volume sent to clients, Demp,k is the demand of each product p at time k, hmax is the time horizon and w1-w4are weights for each of the normalized objective function terms.
4. Results and discussion Having presented the problem at hand, an example to illustrate the model applicability was built based on data reported by Rejowski and Pinto (2008). The input data are detailed in Table 1 regarding inventory limits and initial conditions for each tank. Note that there are two equal tanks for each product at the refinery, since a tank cannot load and unload simultaneously. The product demands for each day for all products are:
Planning of a multiproduct pipeline integrating blending and distribution
1851
Gasoline=2000m3, Jet Fuel=2500m3 and Diesel=6500m3.The pipeline capacity is 18000 m3 and pipeline flowrate range is 450-650 m3/h. A time horizon of 7 days was considered. Table 1 - Input data. Max – Min capacities (m3) Initial Inventory (m3) Product Refinery Distribution centre Refinery Distribution centre Jet Fuel (A1) 100,000-15,000 14,000-3000 31,500 9000 Diesel (GO) 250,000-40,000 40,000-3000 105,000 10,000 Gasoline (U8) 225,000-40000 19,000-5000 100,000 10,000 The model was implemented using GAMS 23.7.3 system version with CPLEX solver on an Intel(R) Core(TM) i7 platform with 6GB of RAM. The model contains 1614 continuous variables, 1008 binary variables and 1547 constraints. The objective function value obtained was -3.4781after 1.061CPU seconds with a gap of 0.0 %. The model solution provides the inventory management in both centres as well as the pipeline scheduling that are shown in Figures 2 and 3, respectively.
Figure 2 - Inventory at the refinery (left) and distribution centre (right)
Figure 3 - Pipeline sequence (input/output of the pipeline).
It can be seen in Figure 2 that the first product delivered from the refinery at the beginning (k = 0) is diesel followed by gasoline and jet fuel (when analysing the slopes). When we look to the distribution centre, it is observed that during the day 1diesel volume is increasing, this corresponding to the volume received from the initial pipeline volume and the volume sent by refinery. This is similar for all products and it demonstrates the synchronization operations. All pumping sequences can be seen through Figure 3. In this figure is shown in different colours the product sequence and the transference time due to the pipeline operation. The time variables values, TBS and TDS, represent the exact moment that the last "volume" of batch i finished its’ pumping or receiving. It is important to note that some products, e.g. in batches 2 and 3, are sent
1852
D. Dimas et al.
at the same day but not at the same time. The constraints which do not allow simultaneous products dispatch as well as loading and unloading simultaneous tanks operations are both satisfied, translated into positive or negative slopes. Additionally, between days 3 and 4 the refinery tanks are loading or stopped and, consequently, there is no pipeline operation and the distribution tanks are just delivering the products.
5. Conclusions This work has presented a model that integrates storage tanks at the refinery blending centre and distribution centre. The scheduling model is capable to coordinate pipeline and the tanks operation at the refinery and distribution centre, while guarantee the demand. Settling periods are considered so as to ensure product quality prior to market delivery. A scenario based on real world data was built to test the model feasibility. This problem allowed testing the model performance even when both pipeline ends are modelled and require having a careful operation with some restrictions. As future work, the model has to be extended in order to include more real world problem features such has blending procedures at the refinery integrated with the market demand, intermediate pipeline inputs/outputs, operational rules at the distribution centre as well as longer time horizons, so as to improve the integration of operations that have different timings along the distribution network.
Acknowledgements The authors ackowledge finantial support from CAPES (Grant 99999.002568/2014-04).
References A. Ghaffari-Hadigheh and H. Mostafaei, 2014, On the scheduling of real world multiproduct pipelines with simultaneous delivery, Optimization and Engineering, Springer, DOI 10.1007/s11081-014-9263-9. 55HMRZVNL-UDQG-03LQWR(I¿FLHQW0,/3IRUPXODWLRQVDQGYDOLGFXWVIRUPXOWLSURGXFW pipeline scheduling, 28, 1511–1528. R. Rejowski Jr and J.M. Pinto, 2008, A novel continuous time representation for the scheduling of pipelinesystems with pumping yield rate constraints, Computers and Chemical Enginnering, 32, 1042–1066. 6$0LU+DVVDQL0$EEDVL60RUDGL2SHUDWLRQDOVFKHGXOLQJRIUH¿QHGSURGXFWSLSHOLQH with dualpurpose depots, Applied Mathematical Modelling, 37, 5723–5742. S.A. MirHassani, N. BeheshtiAsl, 2013, A heuristic batch sequencing for multiproduct pipelines, Computers and Chemical Engineering, 56, 58–67. S. N. B. Magatão, L. Magatão, H. L. Polli, F. NevesJr.,L. V. R. Arruda, S. Relvas and A. P. F. D. Barbosa-Póvoa, 2012, Planning and Sequencing Product Distribution in a Real-WorldPipeline Network: An MILP Decomposition Approach, Industrial and Engineering Chemistry Reserach, 51, 4591–4609. S. Relvas, S. N. B. Magatão, A. P. F.D.Barbosa-Póvoa and F. NevesJr., 2013, Integrated scheduling and inventory management of an oil products distribution system, Omega, 41, 955–968. V.G Cafaro, D.C. Cafaro, C.A. Mendéz, J. Cerdá, 2015, MINLP model for the detailed scheduling of refined products pipelines with flow rate dependent pumping costs, Computers and Chemical Engineering, 72, 210-221.
Planning of a multiproduct pipeline integrating blending and distribution Diovanina Dimasa*, Valéria V. Murataa, Sérgio M. S. Neiroa, Susana Relvasb and Ana Paula Barbosa-Póvoab a
Programa de Pós-Graduação em Engenharia Química (PPGEQ), Universidade Federal de Uberlândia (UFU), Avenida João Naves de Ávila, 2121, 38408-100, Uberlândia, Minas Gerais, Brasil b Centro de Estudos de Gestão do Instituto Superior Técnico (CEG-IST), Universidade de Lisboa (UL), Avenida Rovisco Pais 1049-001, Lisboa, Portugal [email protected]
Abstract Pipelines play an important role in the oil supply chain linking different supply chain echelons and acting as one of the most sustainable, safe economical transportation mode. In this context, multiproduct pipeline scheduling is a key issue to be addressed in an optimized form, namely when integrating pipeline operation with the operations of the connected entities. In this paper a MILP discrete time formulation is developed for multiproduct distribution scheduling linking both sides of the pipeline, refinery and distribution centre, so as to generate the best product pumping sequence accounting for material availability at the refinery blending process and delivery needs at the distribution centre. The model was applied to a case based on a real world oil supply chain. Keywords: oil industry, scheduling, multiproduct pipeline, activities integration, MILP.
1. Introduction Typically, downstream distribution in the oil industry can be accomplished via road, railway and pipelines. Pipelines are widely used since they may connect several refineries, depots and terminals transporting crude oil as well as final products in large quantities for long distances in a more sustainable form. The pipeline operator must decide what products and what quantities should be pumped, operational timing range, and how to distribute all products among several destinations (Rejowski and Pinto, 2008). Additionally, this problem often presents some restrictive requirements associated with the pipeline operational conditions such as reverse operation, pumping rate limits, inventory levels, interfaces and lot sizes. All these aspects taken simultaneously make this operation quite complex and decision support tools to help the solution of such complexity are required. Therefore, according to MirHassani, Abbasi and Moradi (2013), distribution scheduling arises as a modeling tool that should be able to determine the transport details and the best way to fulfill several demands at the right time. Several works may be found in the literature addressing pipeline scheduling integrated with either up or downstream operations. Rejowski and Pinto (2004) presented a discrete MILP problem composed by a refinery, pipeline and depots considering
1848
D. Dimas et al.
intermittent pumping time and logical constraints, adding a set of integer cuts and special interface constraint that resulted in better solutions. The same problem was later improved by the same authors (Rejowski and Pinto, 2008) to develop a MINLP continuous time formulation with pumping cost dependent on booster stations yield rate. Magatão et al. (2012) developed a hierarchical decomposition to solve a planning and assignment\sequencing pipeline network model composed by refineries, harbors, depots and clients applied to a real scenario. More recently, Ghaffari-Hadigheh and Mostafaei (2014) proposed a model which provides input and output pipeline sequences to satisfy different terminals simultaneously with minimum operating costs. Pipeline scheduling alone has derived over the last years an intense field for publication, consisting in a complex scheduling problem. These complexities are related with the need to model time and volume decisions efficiently and additionally build flexible models aiming to address multiple i) topologies, ii) products iii) operational and cost issues so as to represent any pipeline-based system. Recent works on the area include the work of Cafaro et al. (2015), where pumping costs are detailed, MirHassani and BeheshtiAsl (2013), who use heuristic procedures as solution method for pipeline scheduling and Relvas et al. (2013) where inventory management at destination depots is tackled along with pipeline scheduling. From the literature review it can be seen that the integration of pipeline scheduling with operations in input and output entities is not widely studied, given the complexity of integrating the pipeline scheduling problem with additional decisions in different echelons. The purpose of this work is to address this problem and to integrate information on product availability at both sides of the multiproduct pipeline (blending and distribution centre) so as to produce an optimal product sequence with minimum operational costs while guaranteeing service levels. The inventory management at the blending and distribution centre is integrated with the pipeline pumping sequence.
2. Problem description The system considers a single unidirectional multiproduct pipeline that connects a product tank farm at the refinery, blending section, and a distribution centre that has to satisfy the local market, as illustrated in Figure 1. Three different products (gasoline, diesel and jet fuel) are produced and stored at the refinery and transported through a multiproduct pipeline to a distribution centre and to storage tanks with fixed service. When a batch of product arrives at the distribution centre a settling period is required due to regulatory quality assessments.
Figure 1 - Schematic system.
Planning of a multiproduct pipeline integrating blending and distribution
1849
Given: The scheduling horizon; The inventory limits (minimum/maximum storage capacities); Initial volume available at each tank and pipeline; The feeding flow rate from the refinery blending; The pipeline volumetric capacity and batch size limits; The minimum settling period; The matrix of possible/forbidden products sequence; The daily demand; The goal is to determine the products sequence pumped into the pipeline, which satisfy the demand while controlling the inventory tanks at the refinery blending centre and distribution centre.
3. The mathematical formulation A discrete time Mixed Integer Linear Programming (MILP) model is formulated which is an extension of the previous work developed by Relvas et al. (2013). This extension links the previous developed model to the blending tank farm where inventory management is also performed. The main assumptions for this problem are: 1. There is a set of dedicated tanks teach product at refinery and distribution centre; 2. A tank at the refinery is not allowed to load and unload simultaneously; 3. The pipeline should be full at any time; 4. At most one tank can be connected to the pipeline at any time; 5. Changeovers time from one tank to another are disregarded; 6. Not all products sequences are allowed in the pipeline; 7. Settling periods are accounted for at the destination depot, making unavailable the settling product for dispatching to local market; 8. The flowrate is assumed to be variable within an acceptable operational range. This operation is controlled by several constraints that are summarized as follows: 1) Material balance –to determine that the amount of products available in each tank; 2) Timing – to define the initial and final pumping and receiving time of each batch; 3) Inventory control – the minimum and maximum storage tanks limits; 4) Operating rules –referred to allocation constraints; 5) Forbidden sequences – the contact between some products inside the pipeline is prohibited; 6) Demand – to satisfy the local market demand values on time; 7) Batch limits – the volumes pumped should be bounded by the pipeline capacity; 8) Initial conditions –inform on the initial products at each tank and inside the pipeline; Due to space limitations, we will only present the timing constraints and the objective function. Timing constraints are responsible for connecting the blending to the distribution centre, given the pipeline operation, using a reduced amount of problem information. 3.1 Timing constraints These constraints are used to synchronize the operations between refinery, pipeline and distribution centre since these operations are continuous. Then, when a tank b start to feed a pipeline with product p simultaneously a tank d begins to receive a product already pumped at previous time. In this way, at the distribution centre the receiving time for batch i (TDSi) is determined based on the previous receiving time plus the time required to unload the product from the pipeline, as expressed in constraint (1).Similarly, at the refinery the pumping time for batch i (TBSi) depends on the
1850
D. Dimas et al.
transportation time to the distribution centre and the receiving time at the distribution centre, as shown in constraint (2). Both timings are calculated within an interval given by minimum and maximum pipeline flow rate. 1 ൰ כ ܹௗ,,, ܶܵܦ ݒ௫
ܶܵܦିଵ + ൬
ௗא
1 ൰ כ ܹௗ,,, ݅ ݒ
ܶܵܦିଵ + ൬
ௗא
(1)
݁݅ כ ܴܺ,,, െ ܶܵܦ ܶܵܤ ݒ௫ א
݁݅ כ ܴܺ,,, െ ܶܵܦ ݒ א
݅
(2)
Where vmin/vmax are the minimum/maximum pipeline flowrate, pipe is the pipeline volume, Wd,i,p,k is the volume of batch i with product p received in tank d at time k and XRb,i,p,k a binary variable that indicates if a batch i with product p is unloading from tank b to pipeline at time k. 3.2 Objective Function The objective function is based in operational indicators and is composed by four terms. The first one corresponds to the difference between the total amount received at the distribution center and the total demand. The second term is used to maximize the pipeline usage so as to avoid stoppages/idle times. The third and last terms represent the lowest inventory level at refinery blending and distribution centre, respectively. min ݓଵ כ
ܾ݉݅݊݅
݂݀݅ ܶ|ܵܦூ| െ ݓଶ כ௫ െ ݓଷ ݀݅݊݅݉ כെ ݓସ ܾ݅݊݅݉ כ σ σ ݉݁ܦ, ݄
ܴݒ݊ܫ,,|| ௫ ܴݒ݊ܫ,
and
݉݅݊݅݀
ܶݒ݊ܫௗ,,|| ௫ ݒ݊ܫௗ,
(5) (6)
Where InvRb,p,|K| and InvTd,p,|K| are the inventory of each tank at end of the time horizon as well as their maximum limits, dif is the difference between the volume arrived at the tank at the distribution centre and the volume sent to clients, Demp,k is the demand of each product p at time k, hmax is the time horizon and w1-w4are weights for each of the normalized objective function terms.
4. Results and discussion Having presented the problem at hand, an example to illustrate the model applicability was built based on data reported by Rejowski and Pinto (2008). The input data are detailed in Table 1 regarding inventory limits and initial conditions for each tank. Note that there are two equal tanks for each product at the refinery, since a tank cannot load and unload simultaneously. The product demands for each day for all products are:
Planning of a multiproduct pipeline integrating blending and distribution
1851
Gasoline=2000m3, Jet Fuel=2500m3 and Diesel=6500m3.The pipeline capacity is 18000 m3 and pipeline flowrate range is 450-650 m3/h. A time horizon of 7 days was considered. Table 1 - Input data. Max – Min capacities (m3) Initial Inventory (m3) Product Refinery Distribution centre Refinery Distribution centre Jet Fuel (A1) 100,000-15,000 14,000-3000 31,500 9000 Diesel (GO) 250,000-40,000 40,000-3000 105,000 10,000 Gasoline (U8) 225,000-40000 19,000-5000 100,000 10,000 The model was implemented using GAMS 23.7.3 system version with CPLEX solver on an Intel(R) Core(TM) i7 platform with 6GB of RAM. The model contains 1614 continuous variables, 1008 binary variables and 1547 constraints. The objective function value obtained was -3.4781after 1.061CPU seconds with a gap of 0.0 %. The model solution provides the inventory management in both centres as well as the pipeline scheduling that are shown in Figures 2 and 3, respectively.
Figure 2 - Inventory at the refinery (left) and distribution centre (right)
Figure 3 - Pipeline sequence (input/output of the pipeline).
It can be seen in Figure 2 that the first product delivered from the refinery at the beginning (k = 0) is diesel followed by gasoline and jet fuel (when analysing the slopes). When we look to the distribution centre, it is observed that during the day 1diesel volume is increasing, this corresponding to the volume received from the initial pipeline volume and the volume sent by refinery. This is similar for all products and it demonstrates the synchronization operations. All pumping sequences can be seen through Figure 3. In this figure is shown in different colours the product sequence and the transference time due to the pipeline operation. The time variables values, TBS and TDS, represent the exact moment that the last "volume" of batch i finished its’ pumping or receiving. It is important to note that some products, e.g. in batches 2 and 3, are sent
1852
D. Dimas et al.
at the same day but not at the same time. The constraints which do not allow simultaneous products dispatch as well as loading and unloading simultaneous tanks operations are both satisfied, translated into positive or negative slopes. Additionally, between days 3 and 4 the refinery tanks are loading or stopped and, consequently, there is no pipeline operation and the distribution tanks are just delivering the products.
5. Conclusions This work has presented a model that integrates storage tanks at the refinery blending centre and distribution centre. The scheduling model is capable to coordinate pipeline and the tanks operation at the refinery and distribution centre, while guarantee the demand. Settling periods are considered so as to ensure product quality prior to market delivery. A scenario based on real world data was built to test the model feasibility. This problem allowed testing the model performance even when both pipeline ends are modelled and require having a careful operation with some restrictions. As future work, the model has to be extended in order to include more real world problem features such has blending procedures at the refinery integrated with the market demand, intermediate pipeline inputs/outputs, operational rules at the distribution centre as well as longer time horizons, so as to improve the integration of operations that have different timings along the distribution network.
Acknowledgements The authors ackowledge finantial support from CAPES (Grant 99999.002568/2014-04).
References A. Ghaffari-Hadigheh and H. Mostafaei, 2014, On the scheduling of real world multiproduct pipelines with simultaneous delivery, Optimization and Engineering, Springer, DOI 10.1007/s11081-014-9263-9. 55HMRZVNL-UDQG-03LQWR(I¿FLHQW0,/3IRUPXODWLRQVDQGYDOLGFXWVIRUPXOWLSURGXFW pipeline scheduling, 28, 1511–1528. R. Rejowski Jr and J.M. Pinto, 2008, A novel continuous time representation for the scheduling of pipelinesystems with pumping yield rate constraints, Computers and Chemical Enginnering, 32, 1042–1066. 6$0LU+DVVDQL0$EEDVL60RUDGL2SHUDWLRQDOVFKHGXOLQJRIUH¿QHGSURGXFWSLSHOLQH with dualpurpose depots, Applied Mathematical Modelling, 37, 5723–5742. S.A. MirHassani, N. BeheshtiAsl, 2013, A heuristic batch sequencing for multiproduct pipelines, Computers and Chemical Engineering, 56, 58–67. S. N. B. Magatão, L. Magatão, H. L. Polli, F. NevesJr.,L. V. R. Arruda, S. Relvas and A. P. F. D. Barbosa-Póvoa, 2012, Planning and Sequencing Product Distribution in a Real-WorldPipeline Network: An MILP Decomposition Approach, Industrial and Engineering Chemistry Reserach, 51, 4591–4609. S. Relvas, S. N. B. Magatão, A. P. F.D.Barbosa-Póvoa and F. NevesJr., 2013, Integrated scheduling and inventory management of an oil products distribution system, Omega, 41, 955–968. V.G Cafaro, D.C. Cafaro, C.A. Mendéz, J. Cerdá, 2015, MINLP model for the detailed scheduling of refined products pipelines with flow rate dependent pumping costs, Computers and Chemical Engineering, 72, 210-221.