The 11th Asia Pacific Industrial Engineering and Management Systems Conference The 14th Asia Pacific Regional Meeting of International Foundation for Production Research Melaka, 7 – 10 December 2010
A Time-Space Network based International Transportation Scheduling Problem Incorporating CO2 Emission Levels Yudong Xue † 1 and Takashi Irohara2 Sophia University 7-1 Kioi-Cho, Chiyoda-Ku, Tokyo, Japan 102-8554 Email:
[email protected] [email protected]
Abstract - Environmental problems have received a lot of attention in recent years. Particularly, CO2 emission makes the global warming and other environmental problems worse. In order to reduce the emission effectively, it is necessary to evolve the distribution or transportation processes. The transport sector accounts for 20% of the totalCO2 emission. Therefore, the reduction of the CO2 emission of the transport sector has substantial importance. The purpose of this model is to minimize both the transport cost and the CO2 emission during the transportation. This study considers a transportation scheduling problem in which loads are transported from an overseas production base to three domestic demand centers. Also, the need for time-space network arises naturally when enhancing the possibility of the model. One not only can know how many distance carriers are moving, but also can consider the timetables of carriers during the transportation. Carrier choice, less-than carrier load and domestic transportation among demand centers are considered as the three target areas to reduce CO2 emission during the distribution process. The research model was formulated as a Mixed Integer Programming (MIP) problem. These efforts achieve the cost reduction, and will contribute to the improvement of the environment for the society as well. Keywords: time-space network, timetable, transportation scheduling problem, Mixed Integer Programming (MIP) problem, less-than carrier load
1. INTRODUCTION Recently, CO2 emission exacerbates the global warming and other environmental problems. I n J ap a n , th e total CO2 emission in 2005 increased by more than 6% compared to 1990. The transport field accounts for 20% of the total amount of CO2 emission. Therefore modal shift, shifts of transportation carrier to lower-level CO2 emission ones, such as from truck to freight railway or from airplane to container ship, can make significant contributions to the reduction of the emission. This study focuses on modeling of modal shift, taking into account not only transportation cost and CO2 emission, as traditional studies (Irohara et al. 2009, Kakumoto et al. (2010) and Xue et al. 2010) looked into, but also considering the time-space network problem to improve the modeling of the transportation problems. In
________________________________________ † : Corresponding Author
order to solve this more complicated problem, which includes cost, time and CO2 emission, this study utilizes mixed integer programming (MIP). The following will explain the details of the modeling of this problem with MIP solution. (1) Time-space network model Time-space networks are used for the emergency planning and location based services. Shangyao et al. (2007) developed a time-space network model in order to minimize the length of time needed for emergency repairs. Natalia et al. (2005) applied this time-space network model to a multi-depot bus scheduling problem considering a set of timetable trips. George et al (2008) proposed a timespace network model named an aggregated graph, using less memory to find the shortest path with a fixed start time. However, there are still few studies about transportation
The 11th Asia Pacific Industrial Engineering and Management Systems Conference The 14th Asia Pacific Regional Meeting of International Foundation for Production Research Melaka, 7 – 10 December 2010 scheduling problems. Ohnishi (2007) used time-space network model to solve international transportation problem with consideration of the timetable. This study uses the time-space network model to solve a transportation problem with timetable; our problem consisted of not only international but also domestic transportation. (2) Transportation problem with carrier choice Transportation mode can become more complicated. Some companies manufacture products in a foreign country and import them into the domestic market. In the transportation, the companies confront the problem of choice of the modes. Fujikawa et al. (2004) considered ship and airplane as transportation carriers. There is a trade-off relationship between the two. A ship can transport largerscale volume, at less cost, with less CO2 emission than an airplane, but it consumes more time. Therefore to find the optimal mix of these carriers is critical not only for cost consideration, but also for environmental improvement. (3) Less-than carrier load problem Transportation of small-sized lots with high frequency can reduce the inventory, but it results in large CO2 emission. Okano et al. (2006) considered less-than carrier load problem, which increases the utilization of each carrier’s capacity by packaging different types of smallsized lots, reduces the transportation frequency, and as a result cuts the CO2 emission. The study in this paper incorporates this methodology to reduce the CO2 emission. (4) Domestic transportation among demand centers Ohnishi (2007) considered not only direct transportation but also indirect transportation. For example, there are 3 centers, A (foreign), B (domestic), and C (domestic), and 2 orders, which request transport from A to B and from A to C. Using only direct transportation, it needs 2 international transportation carriers: from A to B and from A to C. Since international transportation costs more than domestic, this method results in higher cost. However using indirect transportation, it can meet this request with one international carrier and one domestic, first transport both from A to B (international), deliver one of the orders for B, and then transport from B to C (domestic) to deliver the rest for C. This method can reduce the number of carriers, the total costs and the CO2 emission.
2. PROPOSED MODEL 2.1 Problem Outline This study considers a transportation scheduling problem, which is not only able to minimize the cost, but also to reduce the CO2 emission. What is more, the timespace network enhances the possibility of the model. It makes it possible to take into consideration the constraint of timetables of each carrier and to allow connection among them. More specifically this network considers whether or not a certain carrier is available at the location and in the time. It finds whether or not other carriers are able to be connected and to carry the order, in case the first carrier is unavailable. The demand information, called “order” in this study, is presented as an order table that provides information on demand quantities of the product, release dates, delivery due dates, and order destinations. Table 1 is an example of the order table, which has 3 orders. For example, order 1 consists of 2 demand quantities of the product. And it will be released on date 1, and must be delivered on date 4 in Tokyo. In this paper, orders are transported from an overseas production base (Shanghai) to three demand centers in Japan (Tokyo, Osaka, and KitaKyusyu). The objective of this model is to minimize the sum of the transportation cost and the CO2 emission. This CO2 emission volume is transformed into the CO2 emission penalty expressed as a money value. This problem of minimization of cost takes into account the constraint of the timetables of the carriers. In other words, this problem is based on time-space network. This study focuses on three target areas to reduce CO2 emissions in the distribution process. First, carrier choices must be carefully considered, since each carrier’s transportation time, transportation cost, and total CO2 emission differ. Second, less-than carrier load should be minimized. This study enables us to consolidate more than two orders and reduce the required number of carrier trips. Third, this study makes it possible the connection among domestic transportation systems and international ones.
Table 1: An example of an order table Order number
Demand quantity
Release date
Due date
Destination
1 2 3 4 …
2 20 5 18 …
1 2 2 3 …
4 6 5 6 …
Tokyo Osaka Kita-Kyushu Tokyo …
The 11th Asia Pacific Industrial Engineering and Management Systems Conference The 14th Asia Pacific Regional Meeting of International Foundation for Production Research Melaka, 7 – 10 December 2010
2.2 Time-Space Network
Table 2: Time table of each carrier
In a time-space network, a node has the information about both time and space, and an arc represents the movements of an order. Each order must follow a one-way path, shown as an arrow, and must reach its destination. Figure 1 shows the time-space network constraints in this study, and we can know how the orders are moved on the network. For example shown in Table 1, order1 is released on date 1, and must be delivered on date 4 in Tokyo. That is modeled as order 1 is to be sent from node (1,1) and delivered to node (4,2) in Figure1. For instance, if order 2 and order 3 can be sent
together, first we send them to Kita-Kyushu, and then order 2 will be sent from Kita-Kyushu to Osaka. Therefore, in Figure 1, less-than carrier load problem is expressed as arrows moving from node (2,1) to (3,4), and finally to (6,3). Instead of direct transportation, which means transport orders from Shanghai to each destination directly, to use indirect transportation is more efficient and causes lower emissions of CO2. It is because international transportation costs are higher than domestic ones.
Ships and airplanes are considered as international transportation carriers. Railways and trucks are used as domestic transportation carriers in this study. As an example, Figure 2 shows a time-space network for ships and railways (airplanes and trucks are omitted for simplicity), and the timetable of these four carriers is shown in Table 2. Table 2 shows that one can use airplane and truck every day, ship in day 2, 5, 8, and railway only in odd days. Ships and railways emit much less CO2 than that of airplanes and trucks. However, we cannot use the ships and the railways as much as we want because of the timetable constraint. And as Figure 2 shows, the orders can only be transported on the arcs connecting two nodes, which represent the movements of the carriers. Space
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Figure 1: The movements of the orders
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Figure 2: The carriers used in the time-space network
2.3 Formulation-1 The formulation for time-space network based transportation problem in this study is as follows. -Suffixes i : number of orders (m,n), (s,t), (r,w) : node information about time and place; (time, space) p,q : the type of carrier (1: ship, 2: airplane, 3: railway, 4: truck) -Decision variables yimnstp :=1: order i is transported by carrier p from node (m,n) to (s,t) : =0: Otherwise. zmnstp :=1: the number of container of carrier p needed to transport from node (m,n) to (s,t) : =0: Otherwise.
The 11th Asia Pacific Industrial Engineering and Management Systems Conference The 14th Asia Pacific Regional Meeting of International Foundation for Production Research Melaka, 7 – 10 December 2010 -Parameters Mp : maximum capacity of carrier p Di : demand quantity of order i Cmnstp : the cost of container of carrier p to transport from node (m,n) to (s,t) Emnstp : the CO2 penalty cost of container of carrier p to transport from node (m,n) to (s,t) Fist : = -1: the order i can be sent after date s to city t : = 0: Otherwise. : = 1: s is the due date and t is the destination for order i Tmnstp : = 1: carrier p can go through node (m,n) to (s,t) : = 0: Otherwise.
2.4 Formulation-2
min . Z Cmnstp z mnstp
3. NUMERICAL EXPERIMENTS
m n
s
t
i
m n
s
s.t. Di yimnstp M p z mnstp
t
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p
m, n, s, t , p (2)
i
yimnstp yistrwq Fist i, s, t (3) p
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yim 1stp 1 m s
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w q
i (4)
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yimnstp Tmnstp yimnstp {0,1} z mnstp 0
min.
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-Parameter Q: maximum quantity which can be dispatched in a day
p
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m n
Formulation-2 takes into consideration the maximum quantity Q that a distribution center can send every day.
i, m, n, s, t , p (5) i, m, n, s, t , p (6) m, n, s, t , p (7)
Equation (1) is an objective function, which consists of transportation cost and CO2 emission penalty cost. Equation (2) expresses the constraints of numbers of carriers. The total use of carriers must be equal to or lower than their total capacity. Equation (3) constraints the transportation routes and the orders that must be transported to the destination node on the network. Equation (4) means that at least one order emerges from Shanghai, and the order must be delivered to certain places at the end. Equation (5) represents timetable constraint. If Tmnstp = 0, that means there is no carrier available for delivering from time-space (m,n) to (s,t). In other words, there is no route. Then in this case, yimnstp must be zero. Equation (6) and Equation (7) indicates the decision variables binary y and non-negative integer z. Formulation-1 considers neither the capacity of the factory and the number of carriers nor the capacity of the distribution centers. To make the formulation more realistic, one needs to consider the maximum flow of the distribution centers
In this study, mathematical programming software CPLEX 10.1.0 is used to solve the MIP problem.
3.1 The Experimental Results of Formulation-1 Table 3 compared the execution results of this study with those of the model that does not consider time-space network (Irohara et al. 2009). Row E1 is the result of not considering the timetable, and Row E2 is the result of considering the timetable of the carriers. The experiment of Row E2 uses the timetables shown in Table 2: the ship departs every three days, the railway departs every two day, and the others depart every day. In row E2, with tighter and more realistic constraints, which consider the timetables, the result has both higher transportation cost and higher CO2 emission cost. Also the timetable constraint results in more uses of the airplane and less of the container ships than E1. In traditional study, there is no constraint of timetable. Thus, we can use ships and railways anytime. However, in E2, one uses the time table shown in Table 2, we know the numbers of ships and railways are fewer than those of the airplanes and trucks, and that causes the airplanes and trucks to be selected more often then the ships and railways in E2. Table 3 : The experimental result of the model Ship E1 E2
38 32
Number of containers Airplane Railway Truck 12 18
21 14
13 24
E1= traditional study (Irohara et al. 2009) E2= the proposed model C1 = transportation cost C2 = CO2 emission penalty cost
Cost C1 C2 101670 109988
446 785
The 11th Asia Pacific Industrial Engineering and Management Systems Conference The 14th Asia Pacific Regional Meeting of International Foundation for Production Research Melaka, 7 – 10 December 2010
Table 4: The timetable of the carriers Ship Every 3 day
a.m. p.m.
Airplane
○ ○
×
Railway
Truck
×
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Every 3 day
Table 5: The experimental result of the time-division Number of containers Airplane Railway Truck
Ship E2 E3
32 28
18 22
9 14
19 21
Cost 110773 119838
140 120
One day (No division)
250
Transportation Quantity
The timetable of the carrier can be set in more detail. Table 4 shows the detailed timetable of each carrier, and now one day is divided into two parts: a.m. and p.m. The ship departs every three day in the morning and the railway departs every two days at night, and the airplane and the truck depart at both the a.m. and the p.m. Table 5 shows the execution result of the time-division, where E2 does not consider the time-division and E3 does consider it. This shows that taking the time-division into consideration (E3 compared to E2) increases the cost. Figure 3 shows how the time-division impacts the execution time as the number of orders increases. It is found that the more one day is divided, the more calculation time is necessary to solve the problems. As Figure 4 shows, because there is no constraint in the maximum quantity that the distribution center can deal with, if the due dates are concentrated within the several days in the month, a large number of orders are sent at once and on a certain day in order to save cost and reduce CO2 emission. However, it is unrealistic.
Transportation quantity 200
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Figure 4: The concentration of the release date
3.2 Experimental Results of Formulation-2 With the Equation (8), it is impossible to dispatch the orders more than the maximum quantity of the distribution center can dispatch every day. Thus, the constraint of the order dispatched from Shanghai is tighter than the Formulation-1. Figure 5 shows the experimental result with the constraint of the maximum flow and compared to Formulation-1. When the due dates are concentrated within several days in the month, it costs less if one sends them together. However, it is impossible, because there have the limitation of the capacity of the distribution center. Therefore, compared to Formulation-1, Formulation-2 is more realistic in the case of the concentration of the due dates. Through Figure 6, we learn that the execution time of the Formulation-2 is longer because of the stricter constraint. Thus, if the due dates of the orders are not concentrated, Formulation-1 can reach the optimal solution quicker. The execution time of the traditional model (Kakumoto et al. 2010) is also shown in Figure 6. Even for the small-scale problem, it takes longer to reach the optimal solution. And in the case of the order number being larger than 50, it cannot find the optimal solution.
One day divided into 2 parts 80
250
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One day divided into 4 parts
60 40 20 0 10
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30
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40
50
Figure 3: The execution time of the time-division
Transportation Quantity
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100
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200
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Figure 5: The experimental result of Formulation-2
The 11th Asia Pacific Industrial Engineering and Management Systems Conference The 14th Asia Pacific Regional Meeting of International Foundation for Production Research Melaka, 7 – 10 December 2010 K. Kakumoto and T. Irohara, (2010) Optimization and sensitivity analysis of an international transportation scheduling problem incorporating CO2 emission levels, Journal of Japan Industrial Management Association, Vol.61, No.2, pp.46-53
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N. Kliewer, T. Mellouli and L. Suhl (2006) A time– space network based exact optimization model for multidepot bus scheduling. European Journal of Operational Research, Vol. 175, pp. 1616-1627
# of order
Figure 6: Execution time of the formulations
4. CONCLUSION This study focuses on modeling of modal shift, taking into account not only transportation cost but also CO2 emission. The objective is to minimize both the transportation cost and the CO2 penalty cost. In several traditional studies, the authors looked into the same model and considered the heuristics to deal with the large-scale problem, but it was impossible for them to consider the timetable. This study also considers the time-pace network problem, in order to deal with the timetable of each carrier. Thus, time-space network is one of the most important parts in this study. With the constraint of the timetable of each carrier, the more detailed schedule of the orders can be considered. In addition, compared to the traditional method, this study also can deal with large-scale problem and can get the optimal solution in a shorter time. Some experiments prove the efficiency of the time-space network constructed in this study.
REFERENCES B. George and S. Shekhar (2008) Time-aggregated graphs for modeling spatio-temporal networks. Journal on Data Semantics XI, LNCS 5383, pp.191-212 H. Fujikawa, T. Nezuka, and T. Irohara (2004) Transportation carrier selection problem to minimize operation cost in global manufacturing environment. Proceedings of Japan Industrial Management Association, pp. 186-187 T. Irohara, and K. Kakumoto (2009) Optimization model for freight transportation planning incorporating CO2 emission levels. Institutional Supply Chain Management (ISCM), Xi’an, China,8-10
H. Okano, H. Yanagisawa, and K. Yorita (2006) Less-Than Truckload Network Design Problem with Leadtime. Proceedings of the Eighteenth RAMP (Research Association of Mathematical Programming) symposium, Operations Research Society of Japan, 77-91 M. Ohnishi (2007) An international transport route optimization problem with timetables of ships and airplanes. Proceedings of the Nineteenth RAMP Symposium, Oper. Res. Soc. of Japan, 151-161 S. Yan and Y. Shih (2007) A time-space network model for work team scheduling after a major disaster. Journal of the Chinese Institute of Engineers, Vol.30, No. 1, pp. 63-75 Y. Xue and T. Irohara (2010) Multi-objective Optimization for International Transportation Scheduling Problem Incorporating CO2 Emission Levels. Proceedings of Japan Industrial Management Association, pp. 18-19
AUTHOR BIOGRAPHIES Yudong Xue is a graduate student at Sophia University in the Department of Information and Communication Sciences. She received her B.S. in Mechanical Engineering from Sophia University, Tokyo. Takashi Irohara is a Professor at Sophia University in the Department of Information and Communication Sciences. He received his B.S., M.S., and Ph.D. in the Department of Industrial and Management Systems Engineering of Waseda University, Tokyo. His research interests include facility layout and material handling, manufacturing scheduling and logistics optimization. His papers have been published in International Journal of Biomedical Soft Computing and Human Sciences, Computers and Industrial Engineering, Journal of Japan Industrial Management Associations, Transactions of the Japan Society of Mechanical Engineers and elsewhere.
