An approach for measuring the optimal fleet capacity: Evidence from the container shipping lines in Taiwan

ARTICLE IN PRESS Int. J. Production Economics 122 (2009) 118–126

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An approach for measuring the optimal fleet capacity: Evidence from the container shipping lines in Taiwan$ Wei-Ming Wu  Graduate Institute of Business and Management, National Kaohsiung First University of Science and Technology, 2 Juoyue Road, Nantz District, Kaohsiung City 811, Taiwan

a r t i c l e i n f o

abstract

Article history: Received 30 June 2008 Accepted 27 December 2008 Available online 14 May 2009

Excess capacity emerges as a persistent problem in the shipping industry and plays an essential role in determining the level of ocean freight. Consequently, the optimal fleet capacity has become a critical and frequently discussed issue within the container shipping industry. In practice, the designed capacity of a vessel is the most popular approach for measuring the fleet capacity for a shipping line. Despite this, it continues to lack the operational and economical reasonableness necessary to properly define or measure the capacity provided by a shipping line. This study has developed an economic model to find the optimal fleet capacity. In turn, the corresponding installation ratios have been computed to examine the level of excess capacity present and evaluate the performance of fleet development for three container shipping lines in Taiwan. The findings suggest that the shipping lines with deep-sea service routes are likely to deliberately hold excess capacity. Thus, the strategy of holding excess capacity to deter entry and maintain market power may have implicitly played a crucial role in determining the scale of fleet capacity for a container shipping line. & 2009 Elsevier B.V. All rights reserved.

Keywords: Excess capacity Container shipping Optimal fleet capacity

1. Introduction With the globalization in production and marketing activities, multi-national manufacturing companies are often faced with very difficult decisions regarding where and how to cost effectively manufacture products in a global setting (Taylor et al., 2008). In fact, the significant reduction of logistics cost, especially in ocean transportation segment, plays the key role on supporting trade globalization. As a result, the pressure on reducing the logistics cost has significantly changed the business

$ A previous version of this paper has been presented at International Forum on Shipping, Ports and Airports, Hong-Kong, May, 2008. This research was partially funded with grant from NSC (National Science Council of Taiwan): 95-2416-H-327-013.  Tel.: +886 7 6011000x3812; fax: +886 7 6011070. E-mail address: [email protected]

0925-5273/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2008.12.020

environment and greatly intensified the market competition in container shipping industry. It is well recognized that the container shipping industry has experienced a significant expansion in the size of containerships over the past decade (Imai et al., 2006). Initially, the driving force behind introducing large ships was to achieve greater economies of scale (Gilman, 1999; Cullinane and Khanna, 1999, 2000; Ircha, 2001). Despite deriving some expected benefit through economies of scale, ironically, the deployment of large ships has also resulted in the increase of excess capacity in the container shipping markets. Lim (1998) has stated that to add capacity in the form of large ships increases the risk of severe excess capacity. In particular, the major container shipping lines have uniformly delivered a substantial number of large containerships into the most competitive trade routes. As a consequence of aggressive competition among major container carriers to deliver both more and larger containerships into markets, the benefit of larger

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containership has been outweighed by detrimental effects including the deterioration of the loading factor and ocean freight level. Additionally, the strategic consideration of entry deterrence is also a reason for a shipping line to introduce larger containerships into markets. From the viewpoint of competitive strategy, many theoretical and empirical studies have verified that excess capacity may be utilized as a strategy to deter potential entrants into the market (Spence, 1977; Dixit, 1980; Osborne and Pitchik, 1987; von Ungern-Sternberg, 1988). Lim (1998) has pointed out that the strategy of preemption involving the introduction of mega-ships into markets has been exercised to avoid other competitors penetrating into specific service routes. Upon investigation of the excess capacity in the container shipping industry, Fusillo (2003) has also mentioned that the persistence of excess capacity may be partially motivated by the strategy of deterring entry. Alternatively, from an industry structure viewpoint, Telser (1987) has presented the notion of core emptiness to justify the motivation for holding excess capacity. Considering the characteristics of variable demand, fixed sailing schedules, lumpy capital and non-storable output, Sjostrom (1989, 2004) and Pirrong (1992) have shown that the core of the liner shipping market is indeed empty. To cope with the avoidable fixed costs and the integer problem, the cooperative arrangements among firms to fix prices and allocate output have been developed to solve the problem of an empty core. As a result, the longstanding shipping conference has been granted limited antitrust immunity by most governments. To some extent, core emptiness and strategically competitive behaviors have explained the occurrence of excess capacity in the container shipping industry. Additionally, some other non-market factors, such as nationally flagged ship fleets, direct and indirect subsidies from the government, and trade and shipping policies have also played important roles in determining the level of excess capacity. In practice, the existence of excess capacity in the container shipping industry has persisted for a long time. However, the level has varied over time. Most importantly, the Ocean Shipping Reform Act (OSRA) of 1998, which encourages long-term confidential contracts between shippers and carriers, has greatly relaxed the rigid conference pricing. Concurrently, the OSRA has also promoted the development of many global shipping alliances. By coordinating sailing schedules, marketing efforts and sharing slot space, a shipping alliance enables individual members to allocate capacity without purchasing or chartering entire vessels. Clearly, the emergence of shipping alliances has significantly reduced carrier equipment costs and financial risks, and therefore encourages deploying increasingly larger containerships on major trade routes. With the development of the shipping alliance and long-term contracts, the OSRA has greatly altered the operation of the conference system. Furthermore, most shipping lines have experienced this increase of capacity utilization in the post-OSRA period (Fusillo, 2004). Although the issue of capacity appears frequently in shipping studies, we still lack an operationally and economically meaningful approach to properly define or

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measure the capacity for a shipping line. Intuitively, the excess capacity is the unused capacity in production. Generally, the engineering approach which employs the designed slot capacity of a vessel, measured in terms of Twenty Equivalent Unit (TEU) in container shipping practice, is the most popular approach to measure the capacity provided by a vessel. Accordingly, the corresponding capacity utilization of a vessel could be easily obtained by computing the loading factor in a sailing voyage. Superficially, the designed slot capacity appears to be a straightforward way to measure the capacity provided by a vessel. However, it merely reveals the maximum capacity in operating a vessel, and does not reflect the economic conditions faced by a shipping line. In a simplified case that a vessel is deployed to ship between two ports, the annual capacity provided by this vessel could be easily computed by multiplying the designed slot capacity by the sailing voyages in a year. However, in reality the computation of annual capacity is more complex. Practically speaking, the arrangements of port callings, sailing frequency and the number of containers loaded and unloaded on a given service route are much more complicated than in the simplified case. For example, the true capacity installed for a 2500 TEUs containership dispatched to serve the trans-Pacific route will vastly differ from one which serves the Asia/Europe route. If the engineering approach is applied to measure capacity, in fact, the installed capacity in the above example is totally dependent on the number of sailing voyages on each service route in any given year. Due to the complexity caused by the arrangements mentioned above, it is evident that the engineering approach of utilizing the designed slot capacity is unable to correctly measure the amount of slot capacity provided by a container shipping line during a year. Theoretically, a meaningful measure of capacity should consider factors such as market competition and cost structure simultaneously (Coelli et al., 2002). Accordingly, the measure of fleet capacity should not only allow for operating a containership fleet efficiently, but also satisfy the requirements of competitive strategy. The aim of this paper is to present an economic approach to the computation of the optimal fleet capacity for a container shipping line. Once the measure of optimal fleet capacity is feasible, the derived installation ratio of the optimal fleet capacity may be used to investigate cost efficiency when running a given fleet of containerships. This paper is organized as follows. Section 2 includes an economic model developed to find the optimal fleet capacity for a container shipping line. In Section 3, an empirical application is performed to investigate the cost efficiency and the level of excess capacity of fleet deployment for the three container shipping lines in Taiwan. Finally, some conclusions are drawn in Section 4.

2. Model Conceptually, the action of selecting fleet capacity for a shipping line can be analogized to the process of

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determining a fixed stock of capital for a firm. Therefore, the properties of the cost function would be utilized to demonstrate how a container carrier can find the optimal fleet capacity. In theory, operating under the condition of a U-shaped average cost curve, a firm could achieve increased cost efficiency by raising the output level, provided that the actual output level is less than the output level at minimum cost (the output level at minimum efficient scale, MES). During the operation of container shipping, this condition implies that a shipping line could continuously enjoy more cost efficiency by shipping more containers, if the fleet capacity utilized has not reached the MES level. Consequently, it will impose a huge cost burden to the shipping line, while the installed fleet capacity is not efficiently utilized. In fact, the short-run cost function has only described the relationship between cost and output, conditional on a given stock of capital. In practice, firms have frequently changed the stock of capital to reach the optimal situation of production in the long-run. With reference to the envelope theorem in economics, it has been shown that the long-run cost function is the loci of output associated with the lowest cost for all the different potential stock of capital invested. For a point that is neither an optimal point in the short-run situation nor in the long-run situation, theoretically, there are two feasible ways to reach an optimal point, which is located at the point of tangency between the long-run average cost curve (LRAC) and short-run average cost curve (SRAC). One is to move along the original short-run average cost curve to a tangent point with different potential output. The other is to hold the output level constant and change the stock of capital to a tangent point between LRAC and SRAC. During the process of adjustments from non-optimal point to optimal point, in shipping industry, the path of the first way indicates the approach by varying the amount of containers shipped and holding the existing fleet capacity constant. However, the path of the second way represents the approach that a shipping line reaches an optimal point through adjustments of the fleet capacity, conditional on a given amount of containers shipped. In order to reach the ultimate goal of finding the optimal fleet capacity, the approach of changing the stock of capital will be selected to develop an economic model to seek the optimal fleet capacity in this study. Assume a shipping line possesses a production function as Q ¼ f ðL; F; M; K; TÞ

(1)

where L, F, M and K represent the quantities of labor, fuel, intermediate materials inputs and stock of capital invested, respectively, and T is an index of technology which is included to express the influence of sailing distance on the output level, measured by TEUs carried during any given year. Following Lau (1976), if the shipping line minimizes the variable cost of producing a given output, subject to a given level of fleet capacity, there exists a variable cost function as follows: VC ¼ f ðQ ; P; K; TÞ

(2)

where P is the price vector of factor inputs. This variable cost function represents the minimum variable cost of producing a given output, Q, conditional on a given set of input prices, the stock of capital, and a technological parameter. In the following study, it is noteworthy that the stock of capital invested in Eq. (2) will be considered as the level of fleet capacity installed by a shipping line. In regards to the specification of the functional form, Viton (1981) has utilized the translog variable cost function to estimate the relevant level of capacity output to investigate the cost efficiency of firms in the transportation industry. With reference to Christensen et al. (1975) and Christensen and Greene (1976), the translog variable cost function of Eq. (2) may be specified as X X XX d f Df þ ai ln Pi þ 0:5 aij ln Pi ln Pj ln VC ¼ a0 þ i

f

þ bQ ln Q þ 0:5bQQ ðln Q Þ2 þ

X

i

j

bQi ln Q ln Pi

i

þ gK ln K þ 0:5gKK ðln KÞ2 þ

X

gKi ln K ln Pi

i

þ gKQ ln K ln Q þ dT T þ 0:5dTT T 2 X þ dTi T ln Pi þ dTK T ln K þ dTQ T ln Q

(3)

i

where i, j ¼ F, L, M, and Df appears in this variable cost equation to represent the dummy variables that are set to account for the immeasurable attributes of a shipping line’s operation that remain constant over time. Given the translog variable cost as shown in Eq. (3), the following restrictions on the parameters should be imposed: X X X ai ¼ 1 aij ¼ aij ¼ 0 i

X i

i

bQi ¼ 0

X

j

dTi ¼ 0

i

X

gKi ¼ 0

(4)

i

Following economics theory, conditions in Eq. (4) are imposed to ensure that the variable cost is homogeneous of degree one with respect to factor prices and that the Hessian matrix, qVC2/qPiqPj, is symmetrical. Furthermore, the short-run total cost (SRTC) may be defined as SRTC ¼ VC þ rK

(5)

where r is the price of capital. Following Klein’s (1960) definition, the potential output associated with the optimal stock of capital is the point at which the SRAC and the LRAC are at a tangency. Accordingly, each point on the LRAC is tangent to a specific SRAC, which also implies a minimized SRAC with respect to a given stock of capital. Mathematically, this statement can be expressed as @SRAC @ðSRTC=Q Þ @SRTC 1 ¼ ¼ ¼0 @K @K @K Q

(6)

In terms of the short-run total cost, the above result requires: @SRAC @SRTC @VC ¼ ¼ þr ¼0 @K @K @K

(7)

In order to measure the unobservable term, qVC/qK, the logarithmic derivative of VC with respect to K may be used to solve this equation. The term may be expressed as

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qlnVC/qlnK ¼ (qVC/qK)  (K/VC), while the unobservable term, qVC/qK, can be derived as following: qVC/ qK ¼ (qlnVC/qlnK)  (VC/K). As a consequence, Eq. (7) has become countable and can be rewritten as @SRAC @VC @ ln VC VC ¼ þr ¼  þr ¼0 @K @K @ ln K K

(8)

The derivation of qlnVC/qlnK can be obtained by logarithmically differentiating Eq. (3) with respect to the stock of capital, K. In turn, multiplying qlnVC/qlnK by the observable term, VC/K, and substituting the resulting expression into Eq. (8) yields the following result:

VC þr ¼0 K

(9)

In contrast to Eqs. (7) and (8), Eq. (9) provides an observable and countable method to express the necessary condition of satisfying the optimal stock of capital. Since Eq. (9) is exactly derived from Eq. (3), the parameters in Eq. (9) could easily be found by estimating the corresponding coefficients in Eq. (3). With regard to computing the optimal level of K, intuitively, it seems quite straightforward and involves applying the corresponding estimated coefficients from Eq. (3) into (9). The optimal K may not be obtained by using analytical methods; however, K and lnK appear in Eq. (9) simultaneously. For this reason, an iterative method will be employed to search for the optimal K after defining some required conditions, such as the starting point, ending condition and interval of iteration. In estimating the parameters shown in Eq. (3), econometrically, the appropriate approach based on past research related to the evaluation of cost efficiency of firms, is Zellner’s seemingly unrelated regression (SUR) technique by treating the cost function and the associated cost share function as a multivariate regression system to estimate the parameters of the cost function (Christensen and Greene, 1976; Caves et al., 1981; Nelson, 1989; Azeez, 2001; Rodrı´guez-A´lvarez et al., 2007). Following economics theory, the factor demand function for a variable input can be obtained by applying Shephard’s Lemma: Xi ¼

@VC ; @P i

i ¼ F; L; M

(10)

where Xi is the demand for factor i. Furthermore, the cost share function for a specific factor i might be derived through the factor demand function: Si ¼

does introduce additional statistical information into the regression system. Statistically, efficiency in estimation can be enhanced by simultaneously estimating the translog variable function and the associated cost share equations as a system, constraining the corresponding estimated coefficients to equality across equations. Moreover, the estimation of the variable cost function along with the associated cost share functions has increased the degrees of freedom.

3. Empirical application 3.1. Data description

ðgK þ gKK ln K þ gLK ln P L þ gFK ln P F þ gMK ln P M þ dKT T þ gKQ ln Q Þ 

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X i Pi @VC P i @ ln VC ¼ ¼ VC @P i VC @ ln Pi

(11)

Thus, the corresponding cost share equation could be calculated by taking the derivative of Eq. (3) with respect to the price of factor i: @ ln VC @ ln P i X ¼ ai þ aij ln Pj þ bQi ln Q þ gKi ln K þ dTi T

Si ¼

(12)

j

Whilst simultaneously estimating the parameters with Eq. (3), Eq. (12) actually reveals that the cost share function does not introduce any additional parameters. Nevertheless, it

The purpose of the current empirical study is to measure the optimal fleet capacity for a container shipping line. The data used in this study was taken from a sample of three container shipping lines in Taiwan over the period spanning 1992–2006. The variable cost of a shipping line is defined as the total operating cost. Although the operating cost includes many cost items, such as cargo handling expenses, port charges, fuel expenses, and container stevedoring charges, most of the items are all related to expenditure on manpower, fuel consumption and some intermediate materials required to support the sailing and stevedoring operations. Therefore, all the variable factors in the production process have been categorized as three input items: labor, fuel, and intermediate materials in this empirical study. The price of labor is denoted by the average compensation per employee. The fuel price is obtained by dividing the total fuel expenditure by the amount of fuel consumed. Due to the absence of fuel consumption reporting in a company’s financial statement, it is necessary to create some regression equations estimating the fuel consumption for the three shipping lines. These regression equations are developed to incorporate the relationships between actual fuel price, fuel market price, fuel consumption, sailing distance, and ocean freight rate. Detailed discussion for the calculation described above is presented in Appendix A. Once we have ascertained the fuel and labor costs, the evaluation of the cost of intermediate materials input can be completed relatively easily by subtracting the labor and fuel costs from the total operating cost. Since the items of intermediate materials are fairly diversified, it is not an easy task to find a common unit to compute the unit cost of intermediate materials input. However, the cost of intermediate materials is closely related to activities in the operations of moving containers. Therefore, the cost of intermediate materials adjusts in proportion to the amount of containers shipped. Accordingly, the unit cost of intermediate materials input per TEU shipped is computed by dividing the cost of intermediate materials by the total TEUs of containers carried in a year. In practice, it is quite common for a shipping line to charter containerships in or out to allow for expected and unexpected variations in market demand. In order to accurately count the installed capacity for running a fleet of containerships, it is more appropriate to use the slot capacity of the owned and chartered containerships to

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measure the capacity installed. Therefore, in this study, the total slots provided by owned and chartered-in containerships are utilized to measure the capacity actually installed for a shipping line. As the total slot capacity is set as the proxy variable of stock capital in this study, the unit cost of capital is the corresponding capital cost per slot installed. For calculating the unit cost of capital, this study initially estimates the total cost of capital by subtracting the accumulated depreciation from the book value of owned containerships. In turn, the derived net value is multiplied by the average annual interest rate to measure the opportunity cost of operating the owned ships. Given that the depletion of the ship has to be incurred during the ship operation, the annual depreciation expense is used to approximate the cost of depletion of operating the owned ships. In addition to the opportunity cost and depreciation expense of holding owned containerships, the hire expenditure paid for chartering vessels in has also been included in the calculation of the total cost of capital. Finally, the unit cost of capital may be computed by dividing the total cost of capital by the slot capacity actually installed. In this study, the setting of the technology parameter in the variable cost function will involve defining the output. On account of the output level being defined as the total TEUs of containers carried in a year, the influence of sailing distance has been neglected completely. In order to allow for the influence of the sailing distance on the measure of the output level, an index called the TEU-mile index will be constructed as a proxy variable for the technology parameter. In fact, the derived fuel consumption per TEU carried, as the Oit term presented in Appendix A, could be employed to construct the index of technology. The rationale for applying fuel consumption per TEU carried to represent the TEU-mile index (technology index) is to reflect the significant relationship between fuel consumption and sailing distance. Therefore, the fuel

consumption per TEU carried estimated in Appendix A will be borrowed to represent the TEU-mile index. The data required for computing the three categories of inputs and fuel consumption are all collected from the carriers’ annual financial statements. In this study, the financial statements of the three container shipping lines are required by government to report in public and available at the website of Taiwan Stock Exchange Incorporation (http://newmops.tse.com.tw/). The data regarding the total slot capacity of the owned and chartered containerships for each shipping line is collected from the relevant issue of the Containerisation International Yearbook.

3.2. Computation of optimal fleet capacity As a result of the optimal fleet capacity being computed through an economics analysis of the cost function, understanding the variations of cost composition among different factor inputs would be of immense benefit. The annual cost shares of the three input categories for the three shipping lines are summarized in Table 1. Unsurprisingly, since the year 2000, the cost shares of fuel input display significant increases, reflecting the uprising trend of prices in the oil market. The growing shares of fuel input demonstrate that the fuel expenditure cost has gradually occupied a larger portion of the operational cost for a shipping line. In addition, Table 1 also shows that, on average, the summation of the cost shares of fuel and intermediate materials inputs over the period studied, accounts for 87%, 94% and 95% of total variable cost for Carriers A, B and C, respectively. This finding illustrates that the operation of container shipping is extremely dependent on the capital invested, given that the expenditures on fuel and intermediate materials inputs has a substantially positive relationship with the scale of containership fleet deployed. Therefore, a study

Table 1 Cost share of fuel and intermediate materials inputs for the three container shipping lines. Carrier A

Carrier B

Carrier C

Cost share of fuel input

Cost share of intermediate materials

Cost share of fuel input

Cost share of intermediate materials

Cost share of fuel input

Cost share of intermediate materials

1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006

0.05 0.04 0.04 0.05 0.05 0.05 0.04 0.06 0.09 0.10 0.10 0.10 0.08 0.11 0.12

0.88 0.87 0.86 0.85 0.83 0.81 0.81 0.76 0.71 0.68 0.74 0.81 0.83 0.80 0.80

0.05 0.05 0.05 0.06 0.07 0.07 0.05 0.05 0.08 0.07 0.07 0.08 0.08 0.11 0.14

0.84 0.86 0.87 0.87 0.87 0.87 0.91 0.92 0.89 0.89 0.90 0.88 0.88 0.82 0.81

0.04 0.03 0.03 0.04 0.04 0.05 0.04 0.05 0.07 0.08 0.08 0.10 0.10 0.12 0.17

0.90 0.91 0.92 0.92 0.91 0.90 0.91 0.89 0.87 0.87 0.87 0.85 0.84 0.82 0.79

Average

0.07

0.80

0.07

0.87

0.07

0.88

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investigating capital utilization will be more effective at revealing the cost efficiency of a container shipping line. Consistent with the theoretical derivation shown in the preceding section, the first step for finding the optimal fleet capacity is to estimate the coefficients in Eq. (3). This study gives a system of four equations, one variable cost and three cost share equations which constitute a SUR model for estimating the parameters. Since by definition the cost share functions must sum to unity, only two equations should be considered amongst the three cost share functions in order to avoid introducing linear dependence in the data set. Actually, the resulting estimates are asymptotically equivalent to maximum likelihood estimates, as well as being invariant to which equation is deleted. The following empirical study is carried out by only considering the cost share functions of fuel and intermediate materials whilst applying the SUR technique to estimate the coefficients of the cost function in Eq. (3). In reference to Eq. (12), the corresponding cost share equations for fuel and intermediate materials inputs could be formulated as SF ¼

SM ¼

@ ln VC ¼ aF þ aFF ln P F þ aLF ln P L þ aMF ln PM @ ln P F þ bQF ln Q þ gKF ln K þ dTF T

(13)

@ ln VC ¼ aM þ aMM ln P M þ aLM ln PL þ aFM ln PF @ ln P M þ bQM ln Q þ gKM ln K þ dTM T (14)

Upon methodological application of Zellner’s SUR technique, Eqs. (3), (13) and (14) should be jointly estimated to obtain estimates of the parameters for the variable cost function. Meanwhile, the degrees of freedom in coefficients estimation have been greatly increased due to the stacked panel data while involving pooling equations (3), (13) and (14). Theoretically, a cost function is well-behaved only if it is concave in input prices (that is, the Hessian matrix is negative semi-definite) and if its input share functions are positive. However, when inputting these observations into the translog variable function, the empirical study indicates that the conditions shown above are not completely satisfied. By investigating the first order and the second order conditions at each point of observation, this study found that the estimated cost share functions are positive at all observation points and thereby satisfying the first-order condition globally. In contrast, the second-order condition is satisfied on 63% of the observations. The estimated coefficients for the variable cost function, together with their t-ratio, are reported in Table 2. From the 30 parameters in the variable cost function, there are 18 estimated coefficients that are statistically different from zero at the 10% significance level. The R2s for the variable cost function and the cost share functions of fuel and intermediate materials inputs are 0.99, 0.94 and 0.62, respectively. Meanwhile, the estimated coefficients reported in Table 2 also reveal that the linear homogeneity condition has been satisfied due to the restrictions imposed during the estimation process.

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Table 2 Estimated coefficients of translog variable cost function. Variable

Est. coef.

t-ratio

a0

3.33 0.13 0.15 0.287 0.127 0.587 0.028 0.068 0.076 0.01 0.017 0.058 1.21 0.066 0.103 0.019 0.083 0.533 0.069 0.093 0.009 0.084 0.057 2.65 1.022 0.037 0.046 0.084 0.171 0.091

1.08 4.24a 5.29a 1.63 2.12a 3.48a 1.35 16.7a 4.02a 1.97a 0.95 9.97a 1.22 0.42 3.31a 2.42a 2.84a 0.69 0.94 3.96a 1.64 3.83a 0.053 5.56a 9.51a 1.27 5.36a 2.93a 2.08a 1.01

d1 d2

aL aF aM aLL aFF aMM aLF aLM aMF bQ bQQ bQL bQF bQM

gK gKK gKL gKF gKM gKQ dT dTT dTL dTF dTM dTK dTQ

a Indicates that the estimated coefficient is statistically significant at the 10% level.

Once the coefficients in Eq. (3) have been estimated, the corresponding parameters in Eq. (9) become available. Since a closed form solution is not feasible, the iterative procedure is utilized for solving Eq. (9). In this empirical study, the initial value for K is set to be 2000 TEUs. The maximum loop calculation is set to 800,000 times, with an interval of 2 TEUs each time. The iterative process will be truncated if the sign of the value of objective function is changed. Then, the truncated value of K will be defined as the optimal fleet capacity. Finally, a ratio may be computed by dividing the total slot capacity installed by the optimal fleet capacity. In this study, this ratio is defined as the installation ratio of the optimal fleet capacity, used to reveal the extent of fleet capacity deployment under or over the optimal level for a container shipping line. A ratio higher than one is indicative of the shipping line having introduced a level of fleet capacity into markets, where it is actually unnecessary to ship the given number of containers in that year. In other words, the shipping line has encountered excess capacity in developing fleet capacity. Conversely, if the ratio is less than one, this implies that the shipping line has suffered a shortage of fleet capacity to optimally ship the given number of containers during that year. In this situation, the shipping line should have shipped fewer containers to efficiently operate the installed fleet capacity.

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3.3. Results and discussion The actual installation ratios of optimal fleet capacity for the three container shipping lines in Taiwan have been computed and plotted in Fig. 1. Firstly, it shows that the variations of the installation ratios are quite different among the three shipping lines. In particular, carrier B has experienced a wider range of variations in installation ratios, whereas the variations for carrier C are relatively more stable. However, even if the variations of installation ratios among the three carriers are considerably differentiated and unstable over the period studied, the trends present a fairly steady path towards the optimal level, which is a ratio equal to one. Overall, it suggests that the performances of fleet deployment among the three shipping lines have been significantly improved over the past decade. In fact, the improvements in the performance of fleet development towards the optimal level for the three shipping lines studied have completely reflected the development of containership fleets in the container shipping industry over the last decade. In practice, almost all the major container carriers have introduced a number of bigger containerships into markets since 1995. Additionally, the uncontrolled expansion of containership capacity has led to increasing levels of excess capacity and more intensive price wars in the shipping markets. Based on strategic considerations, the major carriers began to form global shipping alliances by pooling and allocating capacity without purchasing or chartering entire ships. As a result, the utilizations of fleet capacity among the major carriers have been improved globally. Clearly, the result of these improvements among the three container shipping lines is a direct consequence of improving fleet utilization in the container shipping industry. In addition, carrier C has performed relatively better than the other two shipping lines in regards to the utilization of fleet capacity. With reference to the historical development of service routes, carrier C which was formerly focused on the regional service routes in Asia for almost 30 years, has since the year 2000 begun

4

Carrier A

Installation Ratios

3.5

penetrating the North American and European markets. This finding suggests that a regional carrier may find it unaffordable to leave fleet capacity idle and thus require improved performance with regard to the utilization of fleet capacity. Regardless of improvements in the installation ratios for the three shipping lines in the past decade, Fig. 1 also indicates that the two deep-sea shipping lines, carriers A and B have persistently held excess capacity in the longrun. In contrast, before the year 2000, the fleet capacity deployed by carrier C maintained capacity below the optimal level. However, since 2002, the installation ratios for carrier C have become gradually higher than the optimal level. Evidently, carrier C has faced the same situation as the other two deep-sea carriers and thus found it necessary to install excess capacity in the development of the containership fleet. After aggressively penetrating into the deep-sea markets and thus ultimately building its own worldwide service network in the past several years, the emergence of excess capacity for carrier C implies that holding excess capacity seems to be a competitive strategy for a shipping line with deep-sea service routes. 4. Conclusion During the past decade, the major container shipping lines have all aggressively expanded their fleets by introducing both more and larger containerships into markets. Clearly, the traditional studies that have only accounted for the optimal ship size may not exactly reflect the real considerations that shipping lines should factor in when making the decision of fleet deployment. In contrast, the concept of optimal fleet capacity would be a more appropriate approach for reflecting the prevailing market activities in the container shipping industry. Instead of the engineering approach usually used in shipping-related studies, this paper presents an economics approach to estimate the optimal fleet capacity for a shipping line. Conceptually, this paper has extended the traditional viewpoint in an attempt to determine the

Carrier B

Carrier C

3 2.5 2 1.5 1 0.5 0 1992

1994

1996

1998

2000

2002

2004

2006

Year Fig. 1. Installation ratios of optimal fleet capacity for three container shipping lines in Taiwan.

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optimal ship size to seek the optimal level of containership fleet deployed. The results of the empirical study indicate that the fleet development of the three container shipping lines in Taiwan has improved significantly in the past decade. The patterns of fleet development for the shipping lines with varying scales of service networks are quite different. Reference to the variations of installation ratios for the three shipping lines suggests that the shipping lines with deep-sea service routes are likely to deliberately hold excess capacity. In addition, the strategy of holding excess capacity to deter entry and maintain market power may have implicitly played a crucial role in determining the scale of fleet capacity for a container shipping line. Moreover, in the application of the optimal fleet capacity, the installation ratio may be a good indicator for a shipping line to use when monitoring the performance of fleet development. Finally, the approach developed in this paper could be used as the foundations for further studies related to the dynamic path of fleet development. By developing an isocost function to demonstrate the relationship among operating cost, ship size and number of ships, the optimal fleet capacity derived in this paper could be decomposed into two parts: the optimal ship size and the optimal number of ships deployed. Furthermore, the analysis could be extended to investigate the optimal fleet combinations, which includes the right size and number of ships deployed by a shipping line. The dynamic analysis for examining the path of fleet adjustment in the long-run might also provide some insights into clarifying the strategy of fleet expansion exercised by a shipping line. From the viewpoint of practical operation, the results would actually be both meaningful and feasible. This paper presented fundamental techniques on which further studies could be based. Appendix A Usually, the fuel price actually paid by a carrier is not exactly equal to the market price. The relationship between the two prices can be expressed as f it ¼ f t eyit a

(A1)

a f it

where is the fuel price actually paid (per barrel) by carrier i at time t. f¯t is the market fuel price (per barrel) at time t, and yit represents the deviations in percentage a between the two prices, f it and f¯t. For a carrier, the total fuel expenditure cost per TEU carried may be formulated as a

F it ¼ f it Oit

(A2)

where Fit and Oit are the fuel expenditure cost per TEU carried and the fuel consumption (in barrels) per TEU carried for carrier i at time t, respectively. Furthermore, Eqs. (A1) and (A2) imply: f t eyit Oit ¼ F it

(A3)

Although the data of fuel consumption, Oit, is unavailable, a fuel consumption function, stating the relationship

125

between sailing distance and fuel consumption may be formulated as g

Oit ¼ a1 Dit1

(A4)

where Dit is the average sailing distance per TEU carried for carrier i at time t. By taking a logarithmic transformation of the resulting expression by substituting Eq. (A4) into Eq. (A3), a relationship between fuel expenditure cost, fuel market price, and sailing distance for carrier i at time t could be formulated as ln F it ¼ ln a1 þ ln f t þ g1 ln Dit þ yit

(A5)

In Eq. (A5), the data for the distance variable, Dit, is also unavailable. Similarly, this paper has also developed an ocean freight function to solve this problem. The ocean freight function is supposed to reflect the relationship between fuel price and sailing distance. As a consequence, the ocean freight function could be directly formulated in a logarithmic form as ln Pit ¼ ln a2 þ b ln f t þ g2 ln Dit

(A6)

where Pit is the ocean freight rate per TEU charged by carrier i at time t. In order to cancel the unavailable term, Dit, Eq. (A5) could be reformulated by substituting Eq. (A6) into Eq. (A5). After doing some mathematical manipulation, the yit term could be regarded as a residual term in a regression equation. Thus, it could be estimated by running the following regression model: ln F it ¼ W 0 þ W 1 ln f t þ W 2 ln P it þ yit

(A7)

Once the yit term is estimated by Eq. (A7), the actual a fuel price (f it ) can be computed by Eq. (A1). By referring to Eq. (A2), the fuel consumption (Oit) can be computed by dividing the fuel expenditure cost (Fit) by the derived a actual fuel price (f it ). References Azeez, A., 2001. Utilization of optimal capacity in Indian manufacturing 1974–1996. Applied Economics Letters 8, 623–628. Caves, D., Christensen, L., Swanson, J., 1981. Productivity growth, scale economics, and capacity utilization in US railroads, 1955–74. American Economic Review 71, 994–1002. Christensen, L., Greene, W., 1976. Economies of scale in US electrical power generation. Journal of Political Economy 84, 655–676. Christensen, L., Jorgenson, D., Lau, L., 1975. Transcendental logarithmic utility function. American Economic Review 65, 367–383. Coelli, T., Grifell-Tatje, E., Perelman, S., 2002. Capacity utilization and profitability: a decomposition of short-run profit efficiency. International Journal of Production Economics 79, 261–278. Containerisation International Yearbook, 1992–2007. Informa, UK Limited, London. Cullinane, K., Khanna, M., 1999. Economies of scale in large container ships. Journal of Transport Economics and Policy 33, 185–208. Cullinane, K., Khanna, M., 2000. Economies of scale in large containerships: optimal size and geographical implications. Journal of Transport Geography 8, 181–195. Dixit, A., 1980. The role of investment in entry-deterrence. The Economic Journal 90, 95–106. Fusillo, M., 2003. Excess capacity and entry deterrence: the case of ocean liner shipping markets. Maritime Economics and Logistics 5, 100–115. Fusillo, M., 2004. Is liner shipping supply fixed. Maritime Economics and Logistics 6, 220–235.

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