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Application of a combined fuzzy multiple criteria decision making and optimization programming model to the container transportation demand split
Applied Soft Computing 10 (2010) 1080–1086
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Applied Soft Computing journal homepage: www.elsevier.com/locate/asoc
Application of a combined fuzzy multiple criteria decision making and optimization programming model to the container transportation demand split Chien-Chang Chou ∗ , Fu-Tsuan Kuo, Rong-Hua Gou, Chaur-Luh Tsai, Chun-Pong Wong, Ming-Cheng Tsou Department of Shipping Technology, National Kaohsiung Marine University Kaohsiung, Taiwan, ROC
a r t i c l e
i n f o
Article history: Received 30 April 2008 Received in revised form 22 May 2010 Accepted 25 May 2010 Available online 8 June 2010 Keywords: Optimization Decision making Fuzzy sets theory Mathematical programming Containerization Marine transportation
a b s t r a c t The container transportation demand split is one of the most important decision issues for government transportation departments and port organizations. In previous studies, many researchers assumed that the shipping carrier would aim to minimize the total operation cost by selecting an appropriate port as the most favorable one to call, and the shipper would aim to minimize the inland freight cost by selecting the nearest port as the most favorable one to import and export international trade containers. Thus, a number of mathematical programming models have been developed. But in practice, the shipping carrier not only aims to minimize the total operation cost but also takes into account other criteria such as the volume of containers and port facility conditions when choosing an appropriate port as the most favorable one to call. The shipper not only aims to minimize the inland freight cost but also takes into account the frequency of ship callings when choosing an appropriate port as the most favorable one to import and export international trade containers. Thus, the purpose of this paper is to formulate a combined fuzzy multiple criteria decision making and optimization programming model for solving the container transportation demand split problem. There are two stages in this combined model: in stage one, we first compute the container transportation demand split rate by using fuzzy multiple criteria decision making (MCDM) method; whereas in stage two, an optimization mathematical programming network model is proposed for determining the inland origin destination (O-D) of import/export containers. The utilization of the proposed model is demonstrated with a case of Taiwanese ports. The results show that the proposed combined fuzzy MCDM and optimization programming model can be used to explain the container transportation demand split practice. © 2010 Elsevier B.V. All rights reserved.
1. Introduction In Taiwan, almost 37.37% (2,210,265 TEUs) of the total volume of imported and exported international trade containers is to/from northern Taiwan, with 23.47% (1,388,000 TEUs) to/from central Taiwan, and 39.16% (2,316,000 TEUs) to/from southern Taiwan, respectively. On the other hand, there are three major international container ports in Taiwan. They are the Port of Keelung in northern Taiwan, the Port of Taichung in central Taiwan and the Port of Kaohsiung in southern Taiwan, respectively. The container throughput splits for the Port of Keelung, the Port of Taichung and the Port of Kaohsiung are 28.64% (1,693,589 TEUs), 13.52% (799,817 TEUs) and 57.84% (3,420,859 TEUs), respectively. That is, many of the international trade containers to/from northern Taiwan and cen-
∗ Corresponding author. E-mail address: [email protected] (C.-C. Chou). 1568-4946/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.asoc.2010.05.021
tral Taiwan were imported/exported via the Port of Kaohsiung in southern Taiwan. In previous studies, many researchers assumed that the shipping carrier would aim to minimize the total operation cost by selecting an appropriate port as the most favorable one to call. Thus, a number of mathematical programming models have been developed. But in practice, the shipping carrier not only aims to minimize the total operation cost but also takes into account other criteria such as the volume of containers, port facility, port location, port operation efficiency and other conditions. The port choice behavior of the carrier is a multiple criteria decision making (MCDM) problem. The MCDM is an appropriate method for solving the port choice problem of the carrier. On the other hand, since 1990s Taiwanese government actively pushed the Port of Kaohsiung to become the transshipment center for the Far Eastern region by improving computer hardware and software, the inland transportation system, the Customs clearance operation and reducing the container handling charges. Therefore the Port of Kaohsiung attracted a lot of liners to call. As a result, the
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Fig. 1. Relationship between port administrators, carriers and shippers. Fig. 2. Structure of Stackerlberg model for port choice.
frequency of callings of the Port of Kaohsiung is larger than that of the Port of Keelung and the Port of Taichung. In previous studies researchers assumed that the shippers would aim to minimize the inland freight costs by selecting the nearest port as the most favorable one to import and export international trade containers. These researchers developed some container transportation demand split models by using mathematical programming. In other words, in those models the shippers in northern Taiwan would choose the Port of Keelung for importing/exporting international trade containers, the shippers in central Taiwan would choose the Port of Taichung for importing/exporting international trade containers, and the shippers in southern Taiwan would choose the Port of Kaohsiung for importing/exporting international trade containers. But in fact, many of the shippers in the northern Taiwan area decided to export and import their containers via the Port of Kaohsiung in southern Taiwan because they attached a great deal of importance to the frequency of liner calls when making port choice decision even though it meant added time and additional freight costs. That is why many of the international trade containers to/from northern Taiwan are imported/exported via the Port of Kaohsiung in southern Taiwan. Those models proposed in previous studies neglect that shippers not only aim to minimize the inland freight costs but also take into account the frequency of ship callings when making port choice decision in the real world. Those model proposed in previous studies cannot be used to fully explain the actual port choice behaviors of shippers in Taiwan area. Thus, the purpose of this paper is to formulate a combined fuzzy MCDM and optimization programming model for solving the container transportation demand split problem in Taiwan. There are two stages in this combined model: in stage one, we first compute the container transportation demand split rate by using fuzzy MCDM method; whereas in stage two, an optimization mathematical programming network model is proposed for determining the inland origin destination (O-D) of import/export containers. 2. Literature review 2.1. Port choice Yang [1] discussed that the international trade container transportation market could be regarded as a Stackerlberg market. That is, three players including port administrators, carriers and domestic shippers, can be considered in the international container transportation market. Port administrators can be regarded as the superior players, because they have complete information about the optimal behaviors of both carriers and domestic shippers under a given port management policy. Carriers, on the contrary, can be regarded as superiors and leaders to domestic shippers who are followers in the market, because carriers have complete informa-
tion about the optimal behaviors of shippers under given carriers’ services. This leads to a bi-level Stackerlberg problem. The relationship between port administrators, carriers, and shippers is shown in Fig. 1. In the Stackerlberg model for port choice, the carrier aims to maximize his net revenue by using his strategies of routing, vessel type, call port and frequency of call on each route. While making these strategies, the carriers should take into account all information concerning the behaviors of shippers. For example, carriers first investigate the origin destination of foreign trade containers, then make an estimation of flows of containers, and finally decide the services and declare it. So carriers have complete information about domestic shippers. For this reason carriers can be regarded as leaders and domestic shippers can be regarded as followers in the foreign trade container transportation market. Domestic shippers may choose their port to minimize the total inland transportation cost under a given liner service. They also consider the port access time. However, the port access time is often neglected when modeling. According to the above analysis, the structure of Stackerlberg model for port choice can be constructed in Fig. 2. In Fig. 2, we note that there are two stages in the model. In stage one, the shipping carrier aims to maximize the revenue and choose an appropriate port to call. In stage two, the shipper aims to minimize the inland transportation cost and choose an appropriate port to import/export international trade containers. 2.2. Fuzzy MCDM The location selection is one of the most important decision issues for business organizations. Many precision-based methods for location selection have been developed [2–5]. The MCDM methods were provided to deal with the problem of ranking and selecting locations under multiple criteria [6,7]. In general, the selection of a best location for business organizations from two or more alternatives locations on the basis of two or more factors is a MCDM problem. Under many situations, the values for the qualitative criteria are often imprecisely defined for the decision maker. It is not easy to precisely quantify the ratings of each alternative location, and the precision-based methods as stated above are not adequate to deal with the location selection problem [8–10]. Since human judgments including preference are often vague and can not estimate his preference with an exact numerical value. It is more realistic to use linguistic terms to describe the desired value and important weight of criteria, e.g. “very low”, “low”, “fair”, “high”, “very high”, etc. [11,12]. Due to this type of existing fuzziness in the location selection process, fuzzy set theory is an appropriate method for dealing with uncertainty, and the
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subjective evaluation data can be more adequately expressed in fuzzy linguistic variables [8–10,13,14]. Fuzzy set theory was developed exactly based on the premise that the key elements in human thinking are not numbers, but linguistic terms or labels of fuzzy sets [11,15,16]. Based on the literature review in Sections 2.1 and 2.2, we note that there are two stages in the decision making of transportation demand split, including the decision making of carrier’s port choice in stage one and the decision making of shipper’s port choice in stage two. Furthermore, carrier’s port choice is a MCDM problem. Thus, this paper proposes a mixed fuzzy MCDM and mathematical programming model for solving the container transportation demand split problem.
3. Fuzzy MCDM model for carrier’s port choice 3.1. Hierarchical analysis structure for carrier’s port choice Hayuth [17] proposed the most common characteristics of a transshipment port are related to: (a) location, (b) operation, (c) infrastructure and (d) degree of integration (EDI). Brian [18] thinks that the transshipment port decision makers are influenced more by price, service considerations of land and ocean carriers than by perceived differences in the ports of entry and exit. Port infrastructures do not appear to play an important role in the routing decisions. Brian uses the following 11 criteria for port selection: (a) port security, (b) size of port, (c) inland freight rates, (d) port charges, (e) quality of Customs handling, (f) free time, (g) congestion, (h) port equipment (i) number of sailings, (j) proximity of port, (k) possibility of inter-modal links. Jansson and Shneers [19] conclude that a shuttle-service/seafeeder transportation seems worthwhile only in exceptional cases where these rout characteristics co-exist: (a) a very low trade density which require a very wide service range relative to the coast-to-coast distance, (b) a large proportion of the total cargo is generated in the hinterland of the base port, (c) the ports are situated deep into the country along a much-indented coast or on scattered islands of an archipelago. James and Gail [20] voice the widespread belief that frequency of shipping services is a main reason for choice of seaport in cargo movement. Time on the route and labor problems at ports is major concerns of freight forwarders. Thomson [21] found that the key successful factors of the transshipment port including: (a) the length of berthing time at port, (b) the loading/discharge rate, (c) the available number of berths, (d) the quantity of containerized cargo, (e) the port facility, (f) the links of port to major consumers market, (g) the working hours of ports. Sternberg [22] stated that the port’s key successful factors are as follows: (a) superior geographical location, (b) the knowledge of market of marine container operators, (c) the flexible operation process, (d) continuous investment in the infrastructure and facility, (e) the operation of related business. Mary [23] suggested that cost and coverage are not the only drivers of the network configuration decision. A carrier’s optimal port call structure is not only a function of voyage distance, steaming time, or port time, but also a complicated interplay of these operational factors with shippers’ needs for transit time, service frequency, special equipment, or other service elements. Ernst [24] found that to achieve large scale transshipment requires: (a) increase in service frequency, (b) build up of shipping and intermodal alliance, and (c) sharing of space on each other’s ships, inland depots, feeders, container terminals, and container inventories. Kuo and Chu [25] construct a decision-making model for the selection of calling container port by using mathematics programming method. Chou et al. [26] discussed some important factors
Table 1 Linguistic variables for the importance weight of criteria. Very low Low Medium low Fair Medium high High Very high
(0.0,0.025,0.075,0.1) (0.0,0.1,0.2,0.3) (0.05,0.15,0.25,0.35) (0.1,0.2,0.3,0.4) (0.15,0.25,0.35,0.45) (0.2,0.3,0.4,0.5) (0.25,0.35,0.45,0.55)
that influent the container port choice and developed a transportation demand split model by using mathematic programming. Chou et al. [27] discussed some important factors that influent the container port choice then compared the Stackerlberg port choice model with the Equilibrium port choice model. They found out factors that influent the port choices of carriers in the Asia-America oceangoing route are different from factors that influent the port choices of carriers in the Intra-Asia coasting route. Chou [28] developed a fuzzy MCDM model for the hub port choice in southeastern Asia. The hub ports include the ports of Hong Kong, Kaohsiung and Shanghai. A sensitivity analysis is performed in the study. Based on the literature review of port choice, Chou [29] summarized and constructed the hierarchical analysis structure for port selection in Fig. 3. 3.2. Solution procedure The concept of linguistic variable is very useful to describe the human judgments or preference in many situations. Terms of linguistic variables could be called “very poor”, “poor”, “medium poor”, “medium”, “medium good”, “good”, “very good”, and so on. These linguistic variables can be also expressed in fuzzy numbers. Owing to the fuzziness of the container port selection problem, the importance weight of various criteria and the preference of each candidate container port are considered as linguistic variables in this paper. These linguistic variables can be expressed in trapezoidal fuzzy numbers. In general, the decision making of the port selection is not made by a committee of many decision makers, but by one top decision maker of the shipping company. Thus the author interviewed the top decision makers of five major shipping companies in Taiwan. And then we obtained the important weight of each criterion in Table 1, the preference for each candidate container port in Table 2, and put the important weight and the preference in Fig. 3. Chou [29] proposed a fuzzy MCDM method for the port choice. In this paper we use Chou’s solution procedure to solve the fuzzy MCDM problem of the carrier’s port choice. The solution procedure is shown as follows. Assume there are M shipping companies (S1 , S2 , Sm . . ., SM ), N container ports (A1 , A2 , An . . ., AN ), I evaluation criteria (C1 , C2 , Ci . . ., CI ) and J sub-criteria (Ci1 , Ci2 , Cij . . ., CiJ ) under criteria i. Let P(Sm,An,Ci,Cij) be the mth shipping company’s fuzzy preference assigned to the nth container port by the top decision maker under criteria Ci and sub-criteria Cij . Wmi and Wmij are the mth shipping company’s importance weights assigned to Ci and Cij , respectively. Let Pmnij = P(Wmi ⊗ Wmij ⊗ P(Sm,An,Ci,Cj) ) be the representation of Wmi ⊗ Wmij ⊗ P(Sm,An,Ci,Cij) , where 1 ≤ n ≤ N, 1 ≤ i ≤ I, 1 ≤ j ≤ J. And Table 2 Linguistic variables for the preference of port. Very poor Poor Medium poor Fair Medium good Good Very good
(0,0,1,2) (1,2,2,3) (2,3,4,5) (4,5,5,6) (5,6,7,8) (7,8,8,9) (8,9,10,10)
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let TPmn =
J I j=1
P i=1 mnij
be the mth shipping company’s total
N
fuzzy preference for the nth container port. Rmn = TPmn / n=1 TPmn be the mth shipping company’s transportation demand split rate M M N for the nth container port. Rn = R / m=1 n=1 Rmn be all m=1 mn shipping companies’ transportation demand split rate for the nth container port. For example, the 1st shipping company’s total preference for the Port of Keelung is
TP11 =
J I
P11ij =
j=1 i=1
J I
P(W1i ⊗ W1ij ⊗ P(S1,A1,Ci,Cij) )
j=1 i=1
= P[(0.05, 0.15, 0.25, 0.35) ⊗ (0.2, 0.3, 0.4, 0.5) ⊗ (8, 9, 10, 10)] +P[(0.05, 0.15, 0.25, 0.35) ⊗ (0.15, 0.25, 0.35, 0.45) ⊗ (5, 6, 7, 8)] +P[(0.05, 0.15, 0.25, 0.35) ⊗ (0.15, 0.25, 0.35, 0.45) ⊗ (5, 6, 7, 8)] +P[(0.2, 0.3, 0.4, 0.5) ⊗ (0.25, 0.35, 0.45, 0.55) ⊗ (5, 6, 7, 8)] +P[(0.2, 0.3, 0.4, 0.5) ⊗ (0.2, 0.3, 0.4, 0.5) ⊗ (4, 5, 5, 6)] +P[(0.2, 0.3, 0.4, 0.5) ⊗ (0.25, 0.35, 0.45, 0.55) ⊗ (5, 6, 7, 8)] +P[(0.1, 0.2, 0.3, 0.4) ⊗ (0.15, 0.25, 0.35, 0.45) ⊗ (5, 6, 7, 8)] +P[(0.1, 0.2, 0.3, 0.4) ⊗ (0.15, 0.25, 0.35, 0.45) ⊗ (5, 6, 7, 8)] +P[(0.1, 0.2, 0.3, 0.4) ⊗ (0.25, 0.35, 0.45, 0.55) ⊗ (7, 8, 8, 9)] +P[(0.15, 0.25, 0.35, 0.45) ⊗ (0.2, 0.3, 0.4, 0.5) ⊗ (5, 6, 7, 8)] +P[(0.15, 0.25, 0.35, 0.45) ⊗ (0.05, 0.15, 0.25, 0.35) ⊗ (7, 8, 8, 9)] +P[(0.15, 0.25, 0.35, 0.45) ⊗ (0.15, 0.25, 0.35, 0.45) ⊗ (7, 8, 8, 9)] +P[(0.15, 0.25, 0.35, 0.45) ⊗ 0.15, 0.25, 0.35, 0.45) ⊗ (7, 8, 8, 9)] +P[(0.15, 0.25, 0.35, 0.45) ⊗ (0.25, 0.35, 0.45, 0.55) ⊗ (5, 6, 7, 8)] +P[(0.15, 0.25, 0.35, 0.45) ⊗ (0.2, 0.3, 0.4, 0.5) ⊗ (8, 9, 10, 10)] +P[(0.0, 0.1, 0.2, 0.3) ⊗ (0.1, 0.2, 0.3, 0.4) ⊗ (7, 8, 8, 9)] +P[(0.0, 0.1, 0.2, 0.3) ⊗ (0.05, 0.15, 0.25, 0.35) ⊗ (5, 6, 7, 8)] +P[(0.0, 0.1, 0.2, 0.3) ⊗ (0.00, 0.025, 0.075, 0.1) ⊗ (2, 3, 4, 5)] The basic fuzzy arithmetic operations on fuzzy numbers have been proposed in previous literature [9,10,12,14,30–43]. This paper calculates the total preference for the port by using the canonical representation of multiplication operation on fuzzy numbers proposed by Chou [42].
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4. Mathematical programming model for shipper’s port choice In this section, a mathematical programming model for the port choice of the shipper is presented. Chou [44] took into account the frequency of ship callings and developed a mathematical programming model for the port choice of the shipper. We applied the model proposed by Chou [44] to solve the problem of shipper’s port choice. First of all, decision variables and deterministic parameters are introduced and then the model for port choice of shipper is presented as follows. Decision variables Xkijk : the volume of foreign trade containers assigned by shippers, origin zone is k, departure port is port i, discharge port is port j, and destination zone is k . Deterministic parameters • • • • •
k: origin zone of foreign trade container, k = 1, 2, . . .., K. k : destination zone of foreign trade container, k = 1, 2, . . .., K . CIki : inland transportation cost from zone k to port i. CIjk : inland transportation cost from port j to zone k . Q: the total volume of exported/imported trade containers from/to Taiwan. • Ri : the share rate of the capacities of vessels assigned by carriers to visit port i. • Qk : the volume of foreign trade containers from origin zone k.
4.1. Model for shipper’s port choice As previously mentioned, domestic shippers not only aim to minimize their inland freight costs under a given marine transportation service presented by carriers, but also to take into account the frequency of callings. Thus the shippers’ objective function is formulated in Eq. (1) and constraints are formulated in Eqs. (2)–(7). Objective function
Min
k
i
(CIki + CIjk )Xkijk
(1)
k
j
Subject to P(A1 ⊗ A2 ⊗ A3 ) =
1 1 (c1 + 2a1 + 2b1 + d1 ) × (c2 + 2a2 + 2b2 + d2 ) 6 6 ×
1 (c3 + 2a3 + 2b3 + d3 ) 6
Xkijk ≥ 0,
k
Thus, we can obtain quickly the total preference for the Port of Keelung TP11 = 10.52. Similarly, we can obtain easily the 1st shipping company’s total preference for the Port of Taichung TP12 = 8.80 and the total preference for the Port of Kaohsiung TP13 = 12.08. Thus the 1st shipping company’s transportation demand split rates for the Port of Keelung, the Port of Taichung and the Port of Kaohsiung are
∀k, i, j, k
i
j
k
j
k
k
j
k
(3)
k
Xkijk = Ri Q
(4)
Xkijk = Qk
(5)
=
Ri Ri+1
k= / i, i + 1
(6)
=
Ri Ri+2
k= / i, i + 2
(7)
Xkijk
Xkijk = Q
(2)
R11 = 10.52/(10.52 + 8.80 + 12.08) = 0.3350 R12 = 8.80/(10.52 + 8.80 + 12.08) = 0.2803 R13 = 12.08/(10.52 + 8.80 + 12.08) = 0.3847
Xk(i+1)jk
Similarly, we can obtain easily the other 4 shipping companies’ transportation demand split rates for the Port of Keelung, the Port of Taichung and the Port of Kaohsiung are R21 = 0.2785, R22 = 0.1675, R23 = 0.5540, R31 = 0.2873, R32 = 0.1766, R33 = 0.5361, R41 = 0.2628, R42 = 0.1945, R43 = 0.5427, R51 = 0.2789, R52 = 0.1534, R53 = 0.5677. Finally, we can compute all shipping companies’ transportation demand split rates for the Port of Keelung, the Port of Taichung and the Port of Kaohsiung are R1 = 0.2885, R2 = 0.1945, R3 = 0.5170, respectively.
Eq. (2) ensures that decision variable Xkijk is a positive number. Eq. (3) means that the total volume of foreign trade containers assigned by shippers equals to the actual total volume of foreign trade containers to/from the Taiwan area. Eq. (4) guarantees that the volume of foreign trade containers assigned by shippers to departure from port i equals to the number of capacities of vessels assigned by carriers to call port i. Eq. (5) means that the total volume of foreign trade containers assigned by shippers in origin zone k equals to the actual volume of foreign trade containers from/to
Xkijk Xk(i+2)jk
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Fig. 3. Hierarchical analysis structure for port choice.
Table 3 The volumes of containers from/to northern/central/southern Taiwan. Northern Taiwan Import Export Total
1,305,449 (45%) 904,816 (30%) 2,210,265 (37.37%)
Central Taiwan 725,000 (25%) 663,000 (22%) 1,388,000 (23.47%)
Southern Taiwan
Total
870,000 (30%) 1,446,000 (48%) 2,316,000 (39.16%)
2,900,449 (100%) 3,013,816 (100%) 5,914,265 (100%)
Source: Annual statistical reports of Ministry of Transportation and Communications, Taiwan, Republic of China. (Unit: TEU).
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Table 4 The inland transportation distance and freight in Taiwan. Origin (Keelung) → Destination (as follows)
Distance
Freight (Taiwan dollar)
Origin (Kaohsiung) → Destination (as follows)
Basic freight Taipei city Taipei county Taoyuan city Chungli city Taoyuan county Hsinchu city Hsinchu county Miaoli county Taichung county Taichung city Changhua county Nantou county Chiayi county Tainan county Tainan city Kaohsiung city Ilan county
Within 12 km 100 km 120 km 140 km 160 km 180 km 230 km 260 km 300 km 360 km 400 km 440 km 520 km 560 km 600 km 680 km 760 km 240 km
3,500 5,000 6,000 6,300 6,800 7,200 8,000 8,500 9,000 10,000 11,000 12,000 14,000 15,000 16,000 17,000 19,000 9,000
Basic freight Kaohsiung county Tainan city Tainan county Hsining city Chiayi city Chiayi county Yunlin county Nantou county Changhua county Taichung city Taichung county Hsinchu county Taoyuan county Chungli city Taoyuan city Keelung city
Source: Association for Truck Container Transportation, Taiwan, Republic of China.
Table 5 The results for the shipper’s port choice model. Imported containers to northern Taiwan Keelung Port Taichung Port Kaohsiung Port Total
376,622 253,858 674,969 1,305,449 Exported containers to northern Taiwan
Keelung Port Taichung Port Kaohsiung Port Total
Keelung Port Taichung Port Kaohsiung Port Total
261,039 175,951 467,826 904,816
Imported containers to central Taiwan 209,163 140,984 374,854 725,000
Imported containers to southern Taiwan 250,995 169,180 449,825 870,000
Exported containers to central Taiwan 191,276 128,927 342,798 663,000
Total 836,780 564,021 1,499,648 2,900,449
Exported containers to southern Taiwan
Total
417,171 281,189 747,640 1,446,000
869,486 586,067 1,558,263 3,013,816
Imported/Exported containers to/from northern Taiwan
Imported/Exported containers to/from central Taiwan
Imported/Exported containers to/from southern Taiwan
Total
637,661 429,808 1,142,795 2,210,265
400,438 269,910 717,652 1,388,000
668,166 450,369 1,197,465 2,316,000
1,706,265 1,150,088 3,057,912 5,914,265
(Unit: TEU).
origin zone k. Eqs. (6) and (7) mean that there is a positive relationship between the preference for port choice of shipper and the frequency of ship callings. 4.2. Data and results for shipper’s port choice model The data required for the port choice models are shown in Tables 3 and 4. Table 3 is the volumes of import/export international trade containers to/from northern Taiwan, central Taiwan and southern Taiwan. Table 4 presents the distances and the freights among all major cities and counties in Taiwan. By the way, according to the report from the Ministry of Transportation and Communications of Taiwan, Keelung city, Taipei city, Taipei county, Taoyuan city, Chungli city, Taoyuan county, Hsinchu city and Hsinchu county belong to the northern Taiwan area, and Miaoli county, Taichung county, Taichung city, Changhua county, Nantou county, and Chiayi county belong to the central Taiwan area, and Tainan county, Tainan city, Kaohsiung city and Kaohsiung county belong to the southern Taiwan area. The results for the shipper’s port choice model proposed in this paper are shown in Table 5. In Table 5, we can see that the volumes of imported containers to northern Taiwan via the ports of Keelung, Taichung and Kaohsiung are 376,622, 253,858, and 674,969 TEUs, respectively. The volumes of imported containers to central Tai-
wan via the ports of Keelung, Taichung and Kaohsiung are 209,163, 140,984, and 374,854 TEUs, respectively. The volumes of imported containers to southern Taiwan via the ports of Keelung, Taichung and Kaohsiung are 250,995, 169,180, and 449,825 TEUs, respectively. On the other hand, the volumes of exported containers from northern Taiwan via the ports of Keelung, Taichung and Kaohsiung are 261,039, 175,951, and 467,826 TEUs, respectively. The volumes of exported containers from central Taiwan via the ports of Keelung, Taichung and Kaohsiung are 191,276, 128,927, and 342,798 TEUs, respectively. The volumes of exported containers from southern Taiwan via the ports of Keelung, Taichung and Kaohsiung are 417,171, 281,189, and 747,640 TEUs, respectively. The result for the shipper’s port choice model proposed in this paper seems to be more promising than those for shipper’s port choice models proposed in previous studies. 5. Conclusion This paper proposes a combined fuzzy MCDM and optimization programming model for solving the container transportation demand split problem. There are two stages in this combined model: in stage one, we first compute the container transportation demand split rate by using fuzzy MCDM method; whereas
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in stage two, an optimization mathematical programming network model is proposed for determining the origin destination of imported/exported containers. There are two major differences between the model proposed in this paper and those models proposed in previous studies. The first one is that we formulate the decision making of carrier’s port choice by using a fuzzy MCDM model instead of using a mathematical programming model in stage one. The second one is that, in stage two, the mathematical programming model for formulating the decision making of shipper’s port choice takes into account the frequency of callings. Finally, the utilization of the proposed model is demonstrated with a case of Taiwanese ports. The results show that the proposed combined fuzzy MCDM and optimization programming model can be used to explain the container transportation demand split practice. References [1] Z. Yang, Analysis of container port policy by the reaction of an equilibrium shipping market, Maritime Policy and Management 26 (4) (1999) 369–381. [2] M.D. Dahlberg, J.H. May, Linear programming for sitting of energy facilities, Journal of Energy Engineering 106 (1980) 5–14. [3] J.A. Tompkins, J.A. White, Facilities Planning, John Wiley & Sons Company, New York, 1984. [4] G.A. Spohrer, T.R. Kmak, Qualitative analysis used in evaluating alternative plant location scenarios, Industrial Engineering 16 (1984) 52–56. [5] W.J. Stevenson, Production/Operation Management, Richard D. Irwin Inc., Illinois, 1993. [6] C.L. Hwang, K. Yoon, Multiple Attributes Decision Making Methods and Applications, Springer-Verlag, Berlin Heidelberg, 1981. [7] P. Rietveld, H. Ouwersloot, Ordinal data in multi-criteria decision making, a stochastic dominance approach to sitting nuclear power plants, European Journal of Operational Research 56 (1992) 249–262. [8] G.S. Liang, M.J. Wang, A fuzzy multiple criteria decision-making method for facilities site selection, International Journal of Production Research 29 (11) (1991) 2313–2330. [9] C.T. Chen, A fuzzy MCDM method based on interval analysis for solving plant location selection problem, Journal of the Chinese Institute of Industrial Engineers 17 (1) (2000) 111–120. [10] S.H. Chen, Representation, ranking, distance, and similarity of L-R type fuzzy number and application, Australian Journal of Intelligent Processing Systems 6 (4) (2000) 217–229. [11] R.E. Bellman, L.A. Zadeh, Decision-making in a fuzzy environment, Management Science 17 (4) (1970) 141–164. [12] H.M. Hsu, C.T. Chen, Fuzzy credibility relation method for multiple criteria decision-making problems, Information Sciences 96 (1997) 79–91. [13] L.A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning, Information Sciences 8 (1975) 199–249. [14] N. Chiadamrong, An integrated fuzzy multiple criteria decision making method for manufacturing strategies selection, Computers and Industrial Engineering 37 (1999) 433–436. [15] L.A. Zadeh, Fuzzy sets, Information and Control 8 (1965) 338–353. [16] H.J. Zimmermann, Fuzzy Set Theory and Its Applications, second ed., Kluwer Academic Publishers, Boston, 1991. [17] Y. Hayuth, Container traffic in ocean shipping policy, in: International Conference on Ports for Europe, Brugge, 1980.
[18] S. Brian, Containerization: inter-port competition and port selection, Maritime Policy and Management 12 (4) (1985) 293–303. [19] J.O. Jansson, D. Shneers, Liner Shipping Economics, Chapman and Hall Ltd., New York, 1987. [20] B. James, B. Gail, The perception of route competition via seaports in the European communities, Maritime Policy and Management 15 (1) (1988) 35–55. [21] B.J. Thomson, Structure changes in the maritime industry’s impact on the interport competition in container trade, in: International Conference on Shipping Development and Port Management, 1998. [22] R.W. Sternberg, The successful factors of one ocean transshipment center, the case study of one Italian port, The Journal of Chinese Ports 29 (2) (2000) 13–18. [23] B. Mary, Sea Change in Liner Shipping Regulation and Management Decisionmaking in a Global Industry, Elserier Science Ltd., Oxford, UK, 2000. [24] G.F. Ernst, Economics of transportation in container shipping logistics, in: International Conference on Port and Maritime R&D and Technology, Singapore, 2001. [25] T.C. Kuo, C.W. Chu, A decision-making model for the selection of calling container port, in: The 5th Symposium on Transportation Network, Taiwan, 2000. [26] C.C. Chou, C.W. Chu, G.S. Liang, A transportation demand split model for international ports, Journal of the Eastern Asia Society for Transportation Studies 5 (2003) 625–637. [27] C.C. Chou, C.W. Chu, G.S. Liang, Comparison of two models for port choice, Maritime Quarterly 12 (3) (2003) 45–62. [28] C.C. Chou, Application of FMCDM model to select the hub location in the marine transportation: a case study in southeastern Asia, Mathematical and Computer Modelling 51 (2010) 791–801. [29] C.C. Chou, A fuzzy MCDM method for solving marine transshipment container port selection problems, Applied Mathematics and Computation 186 (2007) 435–444. [30] M. Mizumoto, K. Tanaka, The four operations of arithmetic on fuzzy numbers, Systems Computers Controls 7 (5) (1976) 73–81. [31] D. Dubois, H. Prade, Operations on fuzzy numbers, International Journal of Systems Sciences 9 (1978) 613–626. [32] S. Nahmias, Fuzzy variables, Fuzzy Sets and Systems 1 (2) (1978) 97–111. [33] J.M. Adamo, Fuzzy decision trees, Fuzzy Sets and Systems 4 (1980) 207–219. [34] S.H. Chen, Operations on fuzzy numbers with function principle, Tamkang Journal of Management Sciences 6 (1) (1985) 13–26. [35] L. Campos, J.L. Verdegay, Linear programming problems and ranking of fuzzy numbers, Fuzzy Sets and Systems 32 (1989) 1–11. [36] A. Kaufmann, M.M. Gupta, Introduction to Fuzzy Arithmetic Theory and Applications, Van Nostrand, Reinhold, 1991. [37] T.S. Liou, M.J. Wang, Ranking fuzzy numbers with integral values, Fuzzy Sets and Systems 50 (1992) 247–255. [38] S. Heilpern, Representation and application of fuzzy numbers, Fuzzy Sets and Systems 91 (1997) 259–268. [39] M. Delgado, M.A. Vila, W. Voxman, On a canonical representation of fuzzy numbers, Fuzzy Sets and Systems 93 (1998) 125–135. [40] M. Ma, M. Friedman, A. Kandel, A new fuzzy arithmetic, Fuzzy Sets and Systems 108 (1) (1999) 83–90. [41] R.J. Li, Fuzzy method in group decision making, Computers and Mathematics with Applications 38 (1) (1999) 91–101. [42] C.C. Chou, The canonical representation of multiplication operation on triangular fuzzy numbers, Computers and Mathematics with Applications 45 (2003) 1601–1610. [43] C.C. Chou, The representation of multiplication operation on fuzzy numbers and application to solving fuzzy multiple criteria decision making problems, Lecture Notes in Artificial Intelligence 4099 (2006) 161–169. [44] C.C. Chou, An empirical study on port choice behaviors of shippers in a multipleport region, Marine Technology Society Journal 43 (3) (2009) 71–77.
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Applied Soft Computing journal homepage: www.elsevier.com/locate/asoc
Application of a combined fuzzy multiple criteria decision making and optimization programming model to the container transportation demand split Chien-Chang Chou ∗ , Fu-Tsuan Kuo, Rong-Hua Gou, Chaur-Luh Tsai, Chun-Pong Wong, Ming-Cheng Tsou Department of Shipping Technology, National Kaohsiung Marine University Kaohsiung, Taiwan, ROC
a r t i c l e
i n f o
Article history: Received 30 April 2008 Received in revised form 22 May 2010 Accepted 25 May 2010 Available online 8 June 2010 Keywords: Optimization Decision making Fuzzy sets theory Mathematical programming Containerization Marine transportation
a b s t r a c t The container transportation demand split is one of the most important decision issues for government transportation departments and port organizations. In previous studies, many researchers assumed that the shipping carrier would aim to minimize the total operation cost by selecting an appropriate port as the most favorable one to call, and the shipper would aim to minimize the inland freight cost by selecting the nearest port as the most favorable one to import and export international trade containers. Thus, a number of mathematical programming models have been developed. But in practice, the shipping carrier not only aims to minimize the total operation cost but also takes into account other criteria such as the volume of containers and port facility conditions when choosing an appropriate port as the most favorable one to call. The shipper not only aims to minimize the inland freight cost but also takes into account the frequency of ship callings when choosing an appropriate port as the most favorable one to import and export international trade containers. Thus, the purpose of this paper is to formulate a combined fuzzy multiple criteria decision making and optimization programming model for solving the container transportation demand split problem. There are two stages in this combined model: in stage one, we first compute the container transportation demand split rate by using fuzzy multiple criteria decision making (MCDM) method; whereas in stage two, an optimization mathematical programming network model is proposed for determining the inland origin destination (O-D) of import/export containers. The utilization of the proposed model is demonstrated with a case of Taiwanese ports. The results show that the proposed combined fuzzy MCDM and optimization programming model can be used to explain the container transportation demand split practice. © 2010 Elsevier B.V. All rights reserved.
1. Introduction In Taiwan, almost 37.37% (2,210,265 TEUs) of the total volume of imported and exported international trade containers is to/from northern Taiwan, with 23.47% (1,388,000 TEUs) to/from central Taiwan, and 39.16% (2,316,000 TEUs) to/from southern Taiwan, respectively. On the other hand, there are three major international container ports in Taiwan. They are the Port of Keelung in northern Taiwan, the Port of Taichung in central Taiwan and the Port of Kaohsiung in southern Taiwan, respectively. The container throughput splits for the Port of Keelung, the Port of Taichung and the Port of Kaohsiung are 28.64% (1,693,589 TEUs), 13.52% (799,817 TEUs) and 57.84% (3,420,859 TEUs), respectively. That is, many of the international trade containers to/from northern Taiwan and cen-
∗ Corresponding author. E-mail address: [email protected] (C.-C. Chou). 1568-4946/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.asoc.2010.05.021
tral Taiwan were imported/exported via the Port of Kaohsiung in southern Taiwan. In previous studies, many researchers assumed that the shipping carrier would aim to minimize the total operation cost by selecting an appropriate port as the most favorable one to call. Thus, a number of mathematical programming models have been developed. But in practice, the shipping carrier not only aims to minimize the total operation cost but also takes into account other criteria such as the volume of containers, port facility, port location, port operation efficiency and other conditions. The port choice behavior of the carrier is a multiple criteria decision making (MCDM) problem. The MCDM is an appropriate method for solving the port choice problem of the carrier. On the other hand, since 1990s Taiwanese government actively pushed the Port of Kaohsiung to become the transshipment center for the Far Eastern region by improving computer hardware and software, the inland transportation system, the Customs clearance operation and reducing the container handling charges. Therefore the Port of Kaohsiung attracted a lot of liners to call. As a result, the
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Fig. 1. Relationship between port administrators, carriers and shippers. Fig. 2. Structure of Stackerlberg model for port choice.
frequency of callings of the Port of Kaohsiung is larger than that of the Port of Keelung and the Port of Taichung. In previous studies researchers assumed that the shippers would aim to minimize the inland freight costs by selecting the nearest port as the most favorable one to import and export international trade containers. These researchers developed some container transportation demand split models by using mathematical programming. In other words, in those models the shippers in northern Taiwan would choose the Port of Keelung for importing/exporting international trade containers, the shippers in central Taiwan would choose the Port of Taichung for importing/exporting international trade containers, and the shippers in southern Taiwan would choose the Port of Kaohsiung for importing/exporting international trade containers. But in fact, many of the shippers in the northern Taiwan area decided to export and import their containers via the Port of Kaohsiung in southern Taiwan because they attached a great deal of importance to the frequency of liner calls when making port choice decision even though it meant added time and additional freight costs. That is why many of the international trade containers to/from northern Taiwan are imported/exported via the Port of Kaohsiung in southern Taiwan. Those models proposed in previous studies neglect that shippers not only aim to minimize the inland freight costs but also take into account the frequency of ship callings when making port choice decision in the real world. Those model proposed in previous studies cannot be used to fully explain the actual port choice behaviors of shippers in Taiwan area. Thus, the purpose of this paper is to formulate a combined fuzzy MCDM and optimization programming model for solving the container transportation demand split problem in Taiwan. There are two stages in this combined model: in stage one, we first compute the container transportation demand split rate by using fuzzy MCDM method; whereas in stage two, an optimization mathematical programming network model is proposed for determining the inland origin destination (O-D) of import/export containers. 2. Literature review 2.1. Port choice Yang [1] discussed that the international trade container transportation market could be regarded as a Stackerlberg market. That is, three players including port administrators, carriers and domestic shippers, can be considered in the international container transportation market. Port administrators can be regarded as the superior players, because they have complete information about the optimal behaviors of both carriers and domestic shippers under a given port management policy. Carriers, on the contrary, can be regarded as superiors and leaders to domestic shippers who are followers in the market, because carriers have complete informa-
tion about the optimal behaviors of shippers under given carriers’ services. This leads to a bi-level Stackerlberg problem. The relationship between port administrators, carriers, and shippers is shown in Fig. 1. In the Stackerlberg model for port choice, the carrier aims to maximize his net revenue by using his strategies of routing, vessel type, call port and frequency of call on each route. While making these strategies, the carriers should take into account all information concerning the behaviors of shippers. For example, carriers first investigate the origin destination of foreign trade containers, then make an estimation of flows of containers, and finally decide the services and declare it. So carriers have complete information about domestic shippers. For this reason carriers can be regarded as leaders and domestic shippers can be regarded as followers in the foreign trade container transportation market. Domestic shippers may choose their port to minimize the total inland transportation cost under a given liner service. They also consider the port access time. However, the port access time is often neglected when modeling. According to the above analysis, the structure of Stackerlberg model for port choice can be constructed in Fig. 2. In Fig. 2, we note that there are two stages in the model. In stage one, the shipping carrier aims to maximize the revenue and choose an appropriate port to call. In stage two, the shipper aims to minimize the inland transportation cost and choose an appropriate port to import/export international trade containers. 2.2. Fuzzy MCDM The location selection is one of the most important decision issues for business organizations. Many precision-based methods for location selection have been developed [2–5]. The MCDM methods were provided to deal with the problem of ranking and selecting locations under multiple criteria [6,7]. In general, the selection of a best location for business organizations from two or more alternatives locations on the basis of two or more factors is a MCDM problem. Under many situations, the values for the qualitative criteria are often imprecisely defined for the decision maker. It is not easy to precisely quantify the ratings of each alternative location, and the precision-based methods as stated above are not adequate to deal with the location selection problem [8–10]. Since human judgments including preference are often vague and can not estimate his preference with an exact numerical value. It is more realistic to use linguistic terms to describe the desired value and important weight of criteria, e.g. “very low”, “low”, “fair”, “high”, “very high”, etc. [11,12]. Due to this type of existing fuzziness in the location selection process, fuzzy set theory is an appropriate method for dealing with uncertainty, and the
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subjective evaluation data can be more adequately expressed in fuzzy linguistic variables [8–10,13,14]. Fuzzy set theory was developed exactly based on the premise that the key elements in human thinking are not numbers, but linguistic terms or labels of fuzzy sets [11,15,16]. Based on the literature review in Sections 2.1 and 2.2, we note that there are two stages in the decision making of transportation demand split, including the decision making of carrier’s port choice in stage one and the decision making of shipper’s port choice in stage two. Furthermore, carrier’s port choice is a MCDM problem. Thus, this paper proposes a mixed fuzzy MCDM and mathematical programming model for solving the container transportation demand split problem.
3. Fuzzy MCDM model for carrier’s port choice 3.1. Hierarchical analysis structure for carrier’s port choice Hayuth [17] proposed the most common characteristics of a transshipment port are related to: (a) location, (b) operation, (c) infrastructure and (d) degree of integration (EDI). Brian [18] thinks that the transshipment port decision makers are influenced more by price, service considerations of land and ocean carriers than by perceived differences in the ports of entry and exit. Port infrastructures do not appear to play an important role in the routing decisions. Brian uses the following 11 criteria for port selection: (a) port security, (b) size of port, (c) inland freight rates, (d) port charges, (e) quality of Customs handling, (f) free time, (g) congestion, (h) port equipment (i) number of sailings, (j) proximity of port, (k) possibility of inter-modal links. Jansson and Shneers [19] conclude that a shuttle-service/seafeeder transportation seems worthwhile only in exceptional cases where these rout characteristics co-exist: (a) a very low trade density which require a very wide service range relative to the coast-to-coast distance, (b) a large proportion of the total cargo is generated in the hinterland of the base port, (c) the ports are situated deep into the country along a much-indented coast or on scattered islands of an archipelago. James and Gail [20] voice the widespread belief that frequency of shipping services is a main reason for choice of seaport in cargo movement. Time on the route and labor problems at ports is major concerns of freight forwarders. Thomson [21] found that the key successful factors of the transshipment port including: (a) the length of berthing time at port, (b) the loading/discharge rate, (c) the available number of berths, (d) the quantity of containerized cargo, (e) the port facility, (f) the links of port to major consumers market, (g) the working hours of ports. Sternberg [22] stated that the port’s key successful factors are as follows: (a) superior geographical location, (b) the knowledge of market of marine container operators, (c) the flexible operation process, (d) continuous investment in the infrastructure and facility, (e) the operation of related business. Mary [23] suggested that cost and coverage are not the only drivers of the network configuration decision. A carrier’s optimal port call structure is not only a function of voyage distance, steaming time, or port time, but also a complicated interplay of these operational factors with shippers’ needs for transit time, service frequency, special equipment, or other service elements. Ernst [24] found that to achieve large scale transshipment requires: (a) increase in service frequency, (b) build up of shipping and intermodal alliance, and (c) sharing of space on each other’s ships, inland depots, feeders, container terminals, and container inventories. Kuo and Chu [25] construct a decision-making model for the selection of calling container port by using mathematics programming method. Chou et al. [26] discussed some important factors
Table 1 Linguistic variables for the importance weight of criteria. Very low Low Medium low Fair Medium high High Very high
(0.0,0.025,0.075,0.1) (0.0,0.1,0.2,0.3) (0.05,0.15,0.25,0.35) (0.1,0.2,0.3,0.4) (0.15,0.25,0.35,0.45) (0.2,0.3,0.4,0.5) (0.25,0.35,0.45,0.55)
that influent the container port choice and developed a transportation demand split model by using mathematic programming. Chou et al. [27] discussed some important factors that influent the container port choice then compared the Stackerlberg port choice model with the Equilibrium port choice model. They found out factors that influent the port choices of carriers in the Asia-America oceangoing route are different from factors that influent the port choices of carriers in the Intra-Asia coasting route. Chou [28] developed a fuzzy MCDM model for the hub port choice in southeastern Asia. The hub ports include the ports of Hong Kong, Kaohsiung and Shanghai. A sensitivity analysis is performed in the study. Based on the literature review of port choice, Chou [29] summarized and constructed the hierarchical analysis structure for port selection in Fig. 3. 3.2. Solution procedure The concept of linguistic variable is very useful to describe the human judgments or preference in many situations. Terms of linguistic variables could be called “very poor”, “poor”, “medium poor”, “medium”, “medium good”, “good”, “very good”, and so on. These linguistic variables can be also expressed in fuzzy numbers. Owing to the fuzziness of the container port selection problem, the importance weight of various criteria and the preference of each candidate container port are considered as linguistic variables in this paper. These linguistic variables can be expressed in trapezoidal fuzzy numbers. In general, the decision making of the port selection is not made by a committee of many decision makers, but by one top decision maker of the shipping company. Thus the author interviewed the top decision makers of five major shipping companies in Taiwan. And then we obtained the important weight of each criterion in Table 1, the preference for each candidate container port in Table 2, and put the important weight and the preference in Fig. 3. Chou [29] proposed a fuzzy MCDM method for the port choice. In this paper we use Chou’s solution procedure to solve the fuzzy MCDM problem of the carrier’s port choice. The solution procedure is shown as follows. Assume there are M shipping companies (S1 , S2 , Sm . . ., SM ), N container ports (A1 , A2 , An . . ., AN ), I evaluation criteria (C1 , C2 , Ci . . ., CI ) and J sub-criteria (Ci1 , Ci2 , Cij . . ., CiJ ) under criteria i. Let P(Sm,An,Ci,Cij) be the mth shipping company’s fuzzy preference assigned to the nth container port by the top decision maker under criteria Ci and sub-criteria Cij . Wmi and Wmij are the mth shipping company’s importance weights assigned to Ci and Cij , respectively. Let Pmnij = P(Wmi ⊗ Wmij ⊗ P(Sm,An,Ci,Cj) ) be the representation of Wmi ⊗ Wmij ⊗ P(Sm,An,Ci,Cij) , where 1 ≤ n ≤ N, 1 ≤ i ≤ I, 1 ≤ j ≤ J. And Table 2 Linguistic variables for the preference of port. Very poor Poor Medium poor Fair Medium good Good Very good
(0,0,1,2) (1,2,2,3) (2,3,4,5) (4,5,5,6) (5,6,7,8) (7,8,8,9) (8,9,10,10)
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let TPmn =
J I j=1
P i=1 mnij
be the mth shipping company’s total
N
fuzzy preference for the nth container port. Rmn = TPmn / n=1 TPmn be the mth shipping company’s transportation demand split rate M M N for the nth container port. Rn = R / m=1 n=1 Rmn be all m=1 mn shipping companies’ transportation demand split rate for the nth container port. For example, the 1st shipping company’s total preference for the Port of Keelung is
TP11 =
J I
P11ij =
j=1 i=1
J I
P(W1i ⊗ W1ij ⊗ P(S1,A1,Ci,Cij) )
j=1 i=1
= P[(0.05, 0.15, 0.25, 0.35) ⊗ (0.2, 0.3, 0.4, 0.5) ⊗ (8, 9, 10, 10)] +P[(0.05, 0.15, 0.25, 0.35) ⊗ (0.15, 0.25, 0.35, 0.45) ⊗ (5, 6, 7, 8)] +P[(0.05, 0.15, 0.25, 0.35) ⊗ (0.15, 0.25, 0.35, 0.45) ⊗ (5, 6, 7, 8)] +P[(0.2, 0.3, 0.4, 0.5) ⊗ (0.25, 0.35, 0.45, 0.55) ⊗ (5, 6, 7, 8)] +P[(0.2, 0.3, 0.4, 0.5) ⊗ (0.2, 0.3, 0.4, 0.5) ⊗ (4, 5, 5, 6)] +P[(0.2, 0.3, 0.4, 0.5) ⊗ (0.25, 0.35, 0.45, 0.55) ⊗ (5, 6, 7, 8)] +P[(0.1, 0.2, 0.3, 0.4) ⊗ (0.15, 0.25, 0.35, 0.45) ⊗ (5, 6, 7, 8)] +P[(0.1, 0.2, 0.3, 0.4) ⊗ (0.15, 0.25, 0.35, 0.45) ⊗ (5, 6, 7, 8)] +P[(0.1, 0.2, 0.3, 0.4) ⊗ (0.25, 0.35, 0.45, 0.55) ⊗ (7, 8, 8, 9)] +P[(0.15, 0.25, 0.35, 0.45) ⊗ (0.2, 0.3, 0.4, 0.5) ⊗ (5, 6, 7, 8)] +P[(0.15, 0.25, 0.35, 0.45) ⊗ (0.05, 0.15, 0.25, 0.35) ⊗ (7, 8, 8, 9)] +P[(0.15, 0.25, 0.35, 0.45) ⊗ (0.15, 0.25, 0.35, 0.45) ⊗ (7, 8, 8, 9)] +P[(0.15, 0.25, 0.35, 0.45) ⊗ 0.15, 0.25, 0.35, 0.45) ⊗ (7, 8, 8, 9)] +P[(0.15, 0.25, 0.35, 0.45) ⊗ (0.25, 0.35, 0.45, 0.55) ⊗ (5, 6, 7, 8)] +P[(0.15, 0.25, 0.35, 0.45) ⊗ (0.2, 0.3, 0.4, 0.5) ⊗ (8, 9, 10, 10)] +P[(0.0, 0.1, 0.2, 0.3) ⊗ (0.1, 0.2, 0.3, 0.4) ⊗ (7, 8, 8, 9)] +P[(0.0, 0.1, 0.2, 0.3) ⊗ (0.05, 0.15, 0.25, 0.35) ⊗ (5, 6, 7, 8)] +P[(0.0, 0.1, 0.2, 0.3) ⊗ (0.00, 0.025, 0.075, 0.1) ⊗ (2, 3, 4, 5)] The basic fuzzy arithmetic operations on fuzzy numbers have been proposed in previous literature [9,10,12,14,30–43]. This paper calculates the total preference for the port by using the canonical representation of multiplication operation on fuzzy numbers proposed by Chou [42].
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4. Mathematical programming model for shipper’s port choice In this section, a mathematical programming model for the port choice of the shipper is presented. Chou [44] took into account the frequency of ship callings and developed a mathematical programming model for the port choice of the shipper. We applied the model proposed by Chou [44] to solve the problem of shipper’s port choice. First of all, decision variables and deterministic parameters are introduced and then the model for port choice of shipper is presented as follows. Decision variables Xkijk : the volume of foreign trade containers assigned by shippers, origin zone is k, departure port is port i, discharge port is port j, and destination zone is k . Deterministic parameters • • • • •
k: origin zone of foreign trade container, k = 1, 2, . . .., K. k : destination zone of foreign trade container, k = 1, 2, . . .., K . CIki : inland transportation cost from zone k to port i. CIjk : inland transportation cost from port j to zone k . Q: the total volume of exported/imported trade containers from/to Taiwan. • Ri : the share rate of the capacities of vessels assigned by carriers to visit port i. • Qk : the volume of foreign trade containers from origin zone k.
4.1. Model for shipper’s port choice As previously mentioned, domestic shippers not only aim to minimize their inland freight costs under a given marine transportation service presented by carriers, but also to take into account the frequency of callings. Thus the shippers’ objective function is formulated in Eq. (1) and constraints are formulated in Eqs. (2)–(7). Objective function
Min
k
i
(CIki + CIjk )Xkijk
(1)
k
j
Subject to P(A1 ⊗ A2 ⊗ A3 ) =
1 1 (c1 + 2a1 + 2b1 + d1 ) × (c2 + 2a2 + 2b2 + d2 ) 6 6 ×
1 (c3 + 2a3 + 2b3 + d3 ) 6
Xkijk ≥ 0,
k
Thus, we can obtain quickly the total preference for the Port of Keelung TP11 = 10.52. Similarly, we can obtain easily the 1st shipping company’s total preference for the Port of Taichung TP12 = 8.80 and the total preference for the Port of Kaohsiung TP13 = 12.08. Thus the 1st shipping company’s transportation demand split rates for the Port of Keelung, the Port of Taichung and the Port of Kaohsiung are
∀k, i, j, k
i
j
k
j
k
k
j
k
(3)
k
Xkijk = Ri Q
(4)
Xkijk = Qk
(5)
=
Ri Ri+1
k= / i, i + 1
(6)
=
Ri Ri+2
k= / i, i + 2
(7)
Xkijk
Xkijk = Q
(2)
R11 = 10.52/(10.52 + 8.80 + 12.08) = 0.3350 R12 = 8.80/(10.52 + 8.80 + 12.08) = 0.2803 R13 = 12.08/(10.52 + 8.80 + 12.08) = 0.3847
Xk(i+1)jk
Similarly, we can obtain easily the other 4 shipping companies’ transportation demand split rates for the Port of Keelung, the Port of Taichung and the Port of Kaohsiung are R21 = 0.2785, R22 = 0.1675, R23 = 0.5540, R31 = 0.2873, R32 = 0.1766, R33 = 0.5361, R41 = 0.2628, R42 = 0.1945, R43 = 0.5427, R51 = 0.2789, R52 = 0.1534, R53 = 0.5677. Finally, we can compute all shipping companies’ transportation demand split rates for the Port of Keelung, the Port of Taichung and the Port of Kaohsiung are R1 = 0.2885, R2 = 0.1945, R3 = 0.5170, respectively.
Eq. (2) ensures that decision variable Xkijk is a positive number. Eq. (3) means that the total volume of foreign trade containers assigned by shippers equals to the actual total volume of foreign trade containers to/from the Taiwan area. Eq. (4) guarantees that the volume of foreign trade containers assigned by shippers to departure from port i equals to the number of capacities of vessels assigned by carriers to call port i. Eq. (5) means that the total volume of foreign trade containers assigned by shippers in origin zone k equals to the actual volume of foreign trade containers from/to
Xkijk Xk(i+2)jk
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Fig. 3. Hierarchical analysis structure for port choice.
Table 3 The volumes of containers from/to northern/central/southern Taiwan. Northern Taiwan Import Export Total
1,305,449 (45%) 904,816 (30%) 2,210,265 (37.37%)
Central Taiwan 725,000 (25%) 663,000 (22%) 1,388,000 (23.47%)
Southern Taiwan
Total
870,000 (30%) 1,446,000 (48%) 2,316,000 (39.16%)
2,900,449 (100%) 3,013,816 (100%) 5,914,265 (100%)
Source: Annual statistical reports of Ministry of Transportation and Communications, Taiwan, Republic of China. (Unit: TEU).
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Table 4 The inland transportation distance and freight in Taiwan. Origin (Keelung) → Destination (as follows)
Distance
Freight (Taiwan dollar)
Origin (Kaohsiung) → Destination (as follows)
Basic freight Taipei city Taipei county Taoyuan city Chungli city Taoyuan county Hsinchu city Hsinchu county Miaoli county Taichung county Taichung city Changhua county Nantou county Chiayi county Tainan county Tainan city Kaohsiung city Ilan county
Within 12 km 100 km 120 km 140 km 160 km 180 km 230 km 260 km 300 km 360 km 400 km 440 km 520 km 560 km 600 km 680 km 760 km 240 km
3,500 5,000 6,000 6,300 6,800 7,200 8,000 8,500 9,000 10,000 11,000 12,000 14,000 15,000 16,000 17,000 19,000 9,000
Basic freight Kaohsiung county Tainan city Tainan county Hsining city Chiayi city Chiayi county Yunlin county Nantou county Changhua county Taichung city Taichung county Hsinchu county Taoyuan county Chungli city Taoyuan city Keelung city
Source: Association for Truck Container Transportation, Taiwan, Republic of China.
Table 5 The results for the shipper’s port choice model. Imported containers to northern Taiwan Keelung Port Taichung Port Kaohsiung Port Total
376,622 253,858 674,969 1,305,449 Exported containers to northern Taiwan
Keelung Port Taichung Port Kaohsiung Port Total
Keelung Port Taichung Port Kaohsiung Port Total
261,039 175,951 467,826 904,816
Imported containers to central Taiwan 209,163 140,984 374,854 725,000
Imported containers to southern Taiwan 250,995 169,180 449,825 870,000
Exported containers to central Taiwan 191,276 128,927 342,798 663,000
Total 836,780 564,021 1,499,648 2,900,449
Exported containers to southern Taiwan
Total
417,171 281,189 747,640 1,446,000
869,486 586,067 1,558,263 3,013,816
Imported/Exported containers to/from northern Taiwan
Imported/Exported containers to/from central Taiwan
Imported/Exported containers to/from southern Taiwan
Total
637,661 429,808 1,142,795 2,210,265
400,438 269,910 717,652 1,388,000
668,166 450,369 1,197,465 2,316,000
1,706,265 1,150,088 3,057,912 5,914,265
(Unit: TEU).
origin zone k. Eqs. (6) and (7) mean that there is a positive relationship between the preference for port choice of shipper and the frequency of ship callings. 4.2. Data and results for shipper’s port choice model The data required for the port choice models are shown in Tables 3 and 4. Table 3 is the volumes of import/export international trade containers to/from northern Taiwan, central Taiwan and southern Taiwan. Table 4 presents the distances and the freights among all major cities and counties in Taiwan. By the way, according to the report from the Ministry of Transportation and Communications of Taiwan, Keelung city, Taipei city, Taipei county, Taoyuan city, Chungli city, Taoyuan county, Hsinchu city and Hsinchu county belong to the northern Taiwan area, and Miaoli county, Taichung county, Taichung city, Changhua county, Nantou county, and Chiayi county belong to the central Taiwan area, and Tainan county, Tainan city, Kaohsiung city and Kaohsiung county belong to the southern Taiwan area. The results for the shipper’s port choice model proposed in this paper are shown in Table 5. In Table 5, we can see that the volumes of imported containers to northern Taiwan via the ports of Keelung, Taichung and Kaohsiung are 376,622, 253,858, and 674,969 TEUs, respectively. The volumes of imported containers to central Tai-
wan via the ports of Keelung, Taichung and Kaohsiung are 209,163, 140,984, and 374,854 TEUs, respectively. The volumes of imported containers to southern Taiwan via the ports of Keelung, Taichung and Kaohsiung are 250,995, 169,180, and 449,825 TEUs, respectively. On the other hand, the volumes of exported containers from northern Taiwan via the ports of Keelung, Taichung and Kaohsiung are 261,039, 175,951, and 467,826 TEUs, respectively. The volumes of exported containers from central Taiwan via the ports of Keelung, Taichung and Kaohsiung are 191,276, 128,927, and 342,798 TEUs, respectively. The volumes of exported containers from southern Taiwan via the ports of Keelung, Taichung and Kaohsiung are 417,171, 281,189, and 747,640 TEUs, respectively. The result for the shipper’s port choice model proposed in this paper seems to be more promising than those for shipper’s port choice models proposed in previous studies. 5. Conclusion This paper proposes a combined fuzzy MCDM and optimization programming model for solving the container transportation demand split problem. There are two stages in this combined model: in stage one, we first compute the container transportation demand split rate by using fuzzy MCDM method; whereas
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in stage two, an optimization mathematical programming network model is proposed for determining the origin destination of imported/exported containers. There are two major differences between the model proposed in this paper and those models proposed in previous studies. The first one is that we formulate the decision making of carrier’s port choice by using a fuzzy MCDM model instead of using a mathematical programming model in stage one. The second one is that, in stage two, the mathematical programming model for formulating the decision making of shipper’s port choice takes into account the frequency of callings. Finally, the utilization of the proposed model is demonstrated with a case of Taiwanese ports. The results show that the proposed combined fuzzy MCDM and optimization programming model can be used to explain the container transportation demand split practice. References [1] Z. Yang, Analysis of container port policy by the reaction of an equilibrium shipping market, Maritime Policy and Management 26 (4) (1999) 369–381. [2] M.D. Dahlberg, J.H. May, Linear programming for sitting of energy facilities, Journal of Energy Engineering 106 (1980) 5–14. [3] J.A. Tompkins, J.A. White, Facilities Planning, John Wiley & Sons Company, New York, 1984. [4] G.A. Spohrer, T.R. Kmak, Qualitative analysis used in evaluating alternative plant location scenarios, Industrial Engineering 16 (1984) 52–56. [5] W.J. Stevenson, Production/Operation Management, Richard D. Irwin Inc., Illinois, 1993. [6] C.L. Hwang, K. Yoon, Multiple Attributes Decision Making Methods and Applications, Springer-Verlag, Berlin Heidelberg, 1981. [7] P. Rietveld, H. Ouwersloot, Ordinal data in multi-criteria decision making, a stochastic dominance approach to sitting nuclear power plants, European Journal of Operational Research 56 (1992) 249–262. [8] G.S. Liang, M.J. Wang, A fuzzy multiple criteria decision-making method for facilities site selection, International Journal of Production Research 29 (11) (1991) 2313–2330. [9] C.T. Chen, A fuzzy MCDM method based on interval analysis for solving plant location selection problem, Journal of the Chinese Institute of Industrial Engineers 17 (1) (2000) 111–120. [10] S.H. Chen, Representation, ranking, distance, and similarity of L-R type fuzzy number and application, Australian Journal of Intelligent Processing Systems 6 (4) (2000) 217–229. [11] R.E. Bellman, L.A. Zadeh, Decision-making in a fuzzy environment, Management Science 17 (4) (1970) 141–164. [12] H.M. Hsu, C.T. Chen, Fuzzy credibility relation method for multiple criteria decision-making problems, Information Sciences 96 (1997) 79–91. [13] L.A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning, Information Sciences 8 (1975) 199–249. [14] N. Chiadamrong, An integrated fuzzy multiple criteria decision making method for manufacturing strategies selection, Computers and Industrial Engineering 37 (1999) 433–436. [15] L.A. Zadeh, Fuzzy sets, Information and Control 8 (1965) 338–353. [16] H.J. Zimmermann, Fuzzy Set Theory and Its Applications, second ed., Kluwer Academic Publishers, Boston, 1991. [17] Y. Hayuth, Container traffic in ocean shipping policy, in: International Conference on Ports for Europe, Brugge, 1980.
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