This study provides a cargo contribution yield management model to solve the ship capacity control problem for the container liner shipping industry. We propose a new objective to optimize cargo contribution to replace the focus on total revenue or average revenue in the current research. We reflect the special characteristics of yield management in container liner shipping, and all cost items were identified and calculated to develop a new cargo contribution evaluating system. We propose a mathematical model for service route segments’ allocation distribution based on cargo contribution. We use a genetic algorithm to solve the model further with comparative analysis with actual practice. The study cultivates new ground in the current literature with a wide range of innovative applications at a practical level.
Yield management (YM), alternatively known as revenue management (RM) is a practice that originated in the airline industry in the 1970s following the deregulation of the US airline market. The practice has been successfully applied to airlines, hotel management, and retail management. However, the research on YM for container liner shipping service is scant. There are few articles published in the last 50 years after filtering out irrelevant studies, and the unique features and usability of models developed for air transport remain unclear [
Meng et al. presented a summary of the YM problem for container liner shipping services and concluded that the YM problem is composed of ship capacity control and pricing for shipping services. This paper proposes an optimization model based on cargo contribution evaluation (here, we define the difference between cargo revenue and the apportioned cost calculated by cost logic as cargo contribution). The model maximizes the overall cargo contribution instead of total revenue, profit, or capacity utilization in the previous research studies.
The contribution of this study is threefold. First, the study reflects the special characteristics of YM in container liner shipping and proposes a new optimization model to solve the YM ship capacity control problem. The new research idea is based on the reconstruction of cargo contributions, which reflects both cargo revenue and cost. The cost-apportioned logic is established by the business process of the participative observation, which solves the problem of dealing with evaluating of empty container repositioning fee. Second, the study analyzes the complete shipping cycle and identifies all the cost items associated with container shipping and formulates an optimization problem of allocating container slots. The new idea based on cargo contribution evaluation provides a new direction for future research. Third, the optimization model reflects not only the contribution difference between long-term customer and spot market customers but also the difference caused by quantity discount, cargo flow direction, and cargo category. This has significant practical contribution through case study verification.
The remainder of the paper is organized as follows: Section
Yield management (YM) is a practice that originated in the airline industry; therefore, the earlier studies were focused on demand forecasting, overbooking control, dynamic pricing, and seat allocation in the airline industry. Littlewood, Lee and Hersh, and McGill studied the demand forecasting problem [
The research of yield management in container shipping began in the 1990s. Brooks and Button analysed the pricing structure and proposed a potential application of yield management in container shipping [
Previous literature report of YM for container shipping (source: summarized by the authors).
Literature reports | YM problems | Main contribution | Limitation |
---|---|---|---|
Brooks and Button | Dynamic pricing strategy | Analyzed the pricing structure and proposed a potential application of yield management in container shipping | Proposed an overall application suggestion, without clear solution |
Ha | Allocation control and pricing | Proposed an allocation control and pricing model | Evaluated revenue while cost was ignored, and the special characteristics of shipping were not reflected |
Maragos | Allocation control and pricing | Proposed an allocation control and pricing model | Evaluated revenue while cost was ignored, and the special characteristics of shipping were not reflected |
Ting and Tzeng | Allocation management | Proposed a conceptual model for liner shipping revenue management (LSRM) and recognized the special characteristics of empty container reposition of YM for container shipping | The empty container reposition fee, which is a variable cost, was calculated repeatedly in the objective function while cargo costs, transportation costs, equipment costs, vessel costs, and fuel cost were not reflected |
Gordon et al. | Allocation management | Analyzed the weakness of the existing revenue measure and concluded that factors such as cost and utilization should be incorporated | The proposed new yield optimization measure still focuses on the increase in revenue per capacity unit |
Zurheide and Fischer [ | Allocation management | Proposed a slot allocation model to maximize expected profits through booking limits to different demand segments | The empty container reposition cost, container leasing, and storage costs were reflected in the slot allocation without distribution in the whole service network |
Zurheide and Fischer [ | Booking order control | Presented a booking limit strategy, nested booking limit strategy, and bid-price strategy based on the booking class defined by combined segmentation | The slot allocation model was evaluated by the average price and average cost without considering cost logic |
Wang et al. [ | Seasonal revenue problem | Proposed multitype container selection, routing, assignment, and sailing speed in each shipping leg of the service network | The model focused on maximizing seasonal profit; however, only operating cost was evaluated without considering cost logic. |
Feng and Chang [ | Allocation management | Optimized the space allocation model so that the same model is applicable to the complex port-to-port slot distribution networks of Asian port | Costs were not fully evaluated and empty container reposition cost was simply apportioned in the network without considering cost logic |
Lee et al. [ | Allocation management | Proposed control model for allocation distribution and recognized the special characteristics of empty container reposition of YM for container shipping | Costs were not fully evaluated and empty container reposition cost was simply apportioned in the network without considering cost logic |
Lu and Mu [ | Slot reallocation planning | Proposed an allocation control model under the circumstances of vessel delay and port operation restriction and recognized the special characteristics of empty container reposition of YM for container shipping | Available only under specific circumstances, and empty container reposition cost was simply apportioned in the network without considering cost logic |
Liu and Yang [ | Allocation management specially for sea-rail intermodal transportation | Proposed a two-stage slot control optimization mode to maximize expected revenue | Costs were not clearly identified and calculated for cargo contribution analysis, and the YM objective was not well reflected in the objective function |
Given the above, the existing literature already well reflected the constraints of the objectives, which include limitations on total capacity, vessel deadweight, and the number of plugs for reefers. The existing literature also addresses demand segmentation. The special characteristics of demand segmentation include the container types (e.g., dry or reefer), container sizes (e.g., 20 ft or 40 ft), and freight contracts (i.e., long-term or spot). Most of the current studies achieved consistency in this point. However, the objectives showed great differences in the study of ship capacity control in YM. We found the following limitation in the current research on the practice of container liner shipping. First, the definition of objective function is unreasonable. The objectives were mostly based on the optimization of average revenue or total revenue while the corresponding costs were not reflected. Second, the characteristics of yield management for container shipping which distinguish from other industry are not systematically identified. The ignorance of cost and its apportioned logic may cause deviation. The incomplete evaluation of related factors (such as quantity discount, cargo flow direction, and cargo category) may affect applicability in practice. Third, most of the existing literature focuses on the overall allocation strategy, but few research studies focus on service route segment allocation management (here, we define the path between different nodes in the service network as “service route segment”). This is what this paper intends to contribute to the current literature.
The container liner service route is composed of various loading ports and discharging ports on a weekly service frequency. Correspondingly, the service route can be divided into several different segments according to the loading port and discharging port. Taking a service route of AEU3 from COSCO Shipping Lines as an example, as shown in Figure
The AEU3 service route from COSCO Shipping Lines (source:
The service route can be divided into 24 westbound segments and 24 eastbound segments, as shown in Table
Westbound and eastbound segments of the service route AEU3 (source: summarized by the authors).
Westbound segment | Eastbound segment | ||
---|---|---|---|
Loading port | Discharging port | Loading port | Discharging port |
Tianjin | Piraeus | Piraeus | Tianjin |
Rotterdam | Dalian | ||
Hamburg | Qingdao | ||
Antwerp | Shanghai | ||
Dalian | Piraeus | Ningbo | |
Rotterdam | Singapore | ||
Hamburg | Rotterdam | Tianjin | |
Antwerp | Dalian | ||
Qingdao | Piraeus | Qingdao | |
Rotterdam | Shanghai | ||
Hamburg | Ningbo | ||
Antwerp | Singapore | ||
Shanghai | Piraeus | Hamburg | Tianjin |
Rotterdam | Dalian | ||
Hamburg | Qingdao | ||
Antwerp | Shanghai | ||
Ningbo | Piraeus | Ningbo | |
Rotterdam | Singapore | ||
Hamburg | Antwerp | Tianjin | |
Antwerp | Dalian | ||
Singapore | Piraeus | Qingdao | |
Rotterdam | Shanghai | ||
Hamburg | Ningbo | ||
Antwerp | Singapore |
There is a trade imbalance between the westbound and eastbound segments. For example, in 2008, 17.7 million TEUs (twenty feet equivalent units) were transported from Asia to Europe, and only 10 million TEUs were transported from Europe to Asia (UNCTAD 2008) [
It is common practice to allocate slots to each loading port with relatively fixed numbers, and the local office on container liners is responsible for local slot control. The main advantage of this practice lies in clear responsibility and easy management; however, the weakness is prominent as dynamic allocation management cannot be applied to improve the cargo contribution. The cargo contribution shows substantial difference in each service route segment in terms of five aspects. First, the cargo flow (for example, port pair and destination) has a significant impact on the contribution by calculating the empty container reposition cost and the drop-off cost due to a significant difference in the surplus or shortage areas. Second, the cargo structure (for example, cargo owners or forwarders) has a significant impact on the contribution due to the different customer pricing policies. Third, the freight rate contract types (for example, long term or spot) have a significant influence on the contribution due to the rate difference between a long-term deal and the spot market. Neither long-term deals nor the spot rate is always at a low level, and both change dynamically with market fluctuations. Fourth, the proportion of overweight cargo and light cargo in different segments also has a significant influence on contribution. YM in the container liner shipping is restricted by both total capacity and vessel deadweight; the overweight cargo should be balanced with light cargo to improve utilization. Fifth, container liner’s strategy and product competitiveness (for example, delivery time, on-time performance, and uniqueness) lead to difference of pricing strategies, which have a substantial influence on cargo contribution. In short, the contribution difference in each service route segment allows the container liners to allocate the slot according to the cargo contribution evaluation to carry out YM management in the industry.
In addition, wide fluctuations and short freight rate floating cycles make YM necessary in container liner shipping. Figure
CCFI and SCFI indexes from 2009 to 2018 (source: Alphaliner weekly newsletter 2019, issue 1).
Therefore, we propose a new optimization model through cargo contribution evaluation. We identify all cost items associated with container shipping and formulate an optimization problem of allocating container slots. We present the cargo contribution YM model in Section
Figure
The shipment cycle in container transportation (source: COSCO Shipping Liners Company Limited).
In many of these links, calculating the costs for the container liners is a complex process. Some costs are directly associated with shipments. These costs should be directly related to the shipments generating the costs. Some costs, however, must be apportioned in the service route network as these costs are generated as public investments by the container liners to provide network services and products. In addition, some costs must be distributed according to the operated zone (for example, the empty container reposition fee). This is because the imbalances both inbound and outbound are caused by the interaction of several different areas. Therefore, it is only reasonable to combine this area as an operated zone and apportion of the empty container reposition fee to the whole operated zone.
Following this logic, we identified 36 subdivision costs that can be classified into seven categories as shown in Table
Cost details in the container liner transportation (source: summarized by the authors).
Cost category | Subdivision cost | Cost calculating logic |
---|---|---|
Cargo cost | Loading and discharging cost | Calculated to corresponding shipments |
Tally cost | ||
Overtime cost | ||
Receiving and delivery cost | ||
Storage cost | ||
On dock rail handling cost | ||
Tonnage assessment fees | ||
Gate in fees | ||
Gate out fees | ||
Reefer power and monitoring fees | ||
Laden container agency fees | ||
Depot costs | ||
Transportation cost | Transportation cost by feeder | Calculated to the transportation shipments |
Transportation cost by rail | ||
Transportation cost by truck | ||
Port cost | Canal fees | Apportioned by all shipments in the port pairs |
Berthing cost | ||
Tonnage dues | ||
Tug and towage fees | ||
Pilotage fees | ||
Harbour dues | ||
Escort boat fees | ||
Vessel agency fees | ||
Equipment variable cost | Empty container reposition fees | Calculated by the operated zone creating the imbalance |
Empty container storage fees | ||
Container agency fees | ||
Equipment fixed cost | Container rental fees | Apportioned in the service route network |
Container maintenance and repair fees | ||
Hanger container fees | ||
Chassis and reposition fees | ||
Demurrage and detention cost | ||
Vessel cost | Vessel construction cost | Apportioned in the service route network |
Vessel rental cost | ||
Vessel maintenance cost | ||
Fuel cost | Fuel cost | Calculated by vessel and apportioned by all shipments in the vessel |
CMTX1: contribution I CMTX2: contribution II CMTX3: contribution III CMTX4: contribution IV
S: a
The different contribution levels are introduced to evaluate how cargo revenue compensates for different costs. Figure
Comparisons of different contribution levels (source: summarized by the authors).
Constraint (
According to the actual statistical analysis, we assume that demand
Since
In the formula,
Equation (
Genetic algorithm is a very widely used heuristic algorithm, which has the characteristics of high efficiency and stability when solving large-scale complex optimization problems. It is suitable for solving the mathematical model established in this paper. Therefore, the genetic algorithm is in search for the optimal solution, and the number of booking requirements for each customer is determined to maximize the contribution of the entire route. The main steps of the genetic algorithm are designed as follows:
Chromosome coding (source: summarized by authors).
GENE 1 | GENE 2 | GENE 3 | GENE 4 | ... | GENE | |
---|---|---|---|---|---|---|
Customer number | ... | |||||
Customer ID | ... |
We take the service of AEU3 from COSCO Shipping Lines as an example. The service route rotation is shown in Figure
Contribution and demand of ODF (source: summarized by the authors).
Loading port | Discharging port | CTW4 | Average demand | Standard deviation | Average weight |
---|---|---|---|---|---|
Tianjin | Piraeus | $230 | 420 TEU | 5 | 15Ton/TEU |
Rotterdam | $160 | 630 TEU | 4 | 14Ton/TEU | |
Hamburg | $260 | 520 TEU | 6 | 15Ton/TEU | |
Antwerp | $220 | 350 TEU | 3 | 13Ton/TEU | |
Dalian | Piraeus | $220 | 120 TEU | 5 | 14Ton/TEU |
Rotterdam | $145 | 150 TEU | 4 | 13Ton/TEU | |
Hamburg | $198 | 250 TEU | 7 | 15Ton/TEU | |
Antwerp | $176 | 160 TEU | 4 | 14Ton/TEU | |
Qingdao | Piraeus | $265 | 460 TEU | 3 | 13Ton/TEU |
Rotterdam | $154 | 750 TEU | 6 | 12Ton/TEU | |
Hamburg | $198 | 1340 TEU | 2 | 14Ton/TEU | |
Antwerp | $182 | 1650 TEU | 6 | 13Ton/TEU | |
Shanghai | Piraeus | $275 | 1230 TEU | 3 | 10Ton/TEU |
Rotterdam | $212 | 2450 TEU | 5 | 9Ton/TEU | |
Hamburg | $264 | 1980 TEU | 4 | 11Ton/TEU | |
Antwerp | $238 | 1940 TEU | 6 | 10Ton/TEU | |
Ningbo | Piraeus | $263 | 920 TEU | 5 | 11Ton/TEU |
Rotterdam | $207 | 1650 TEU | 4 | 8Ton/TEU | |
Hamburg | $258 | 1430 TEU | 3 | 9Ton/TEU | |
Antwerp | $236 | 1120 TEU | 7 | 10Ton/TEU | |
Singapore | Piraeus | $164 | 360 TEU | 2 | 9Ton/TEU |
Rotterdam | $152 | 540 TEU | 4 | 11Ton/TEU | |
Hamburg | $185 | 210 TEU | 2 | 10Ton/TEU | |
Antwerp | $176 | 120 TEU | 3 | 10Ton/TEU |
Use the fitness functions
Convergence velocity of algorithm (source: drawn by the authors).
According to the genetic algorithm, the maximum payoff of the service route is $4,139,400. Under this approximate optimal solution, Table
Segment allocation proposed by MATLAB (source: summarized by the authors).
Loading port | Discharging port | Route number | Average demand | Standard deviation | Average weight | Allocation proposed | |
---|---|---|---|---|---|---|---|
Tianjin | Piraeus | 1 | 230.00 | 420 | 5 | 15 | |
Rotterdam | 2 | 160.00 | 630 | 4 | 14 | ||
Hamburg | 3 | 260.00 | 520 | 6 | 15 | ||
Antwerp | 4 | 220.00 | 350 | 3 | 13 | ||
Dalian | Piraeus | 5 | 220.00 | 120 | 5 | 14 | |
Rotterdam | 6 | 145.00 | 150 | 4 | 13 | ||
Hamburg | 7 | 198.00 | 250 | 7 | 15 | ||
Antwerp | 8 | 176.00 | 160 | 4 | 14 | ||
Qingdao | Piraeus | 9 | 265.00 | 460 | 3 | 13 | |
Rotterdam | 10 | 154.00 | 750 | 6 | 12 | ||
Hamburg | 11 | 198.00 | 1340 | 2 | 14 | ||
Antwerp | 12 | 182.00 | 1650 | 6 | 13 | ||
Shanghai | Piraeus | 13 | 275.00 | 1230 | 3 | 10 | |
Rotterdam | 14 | 212.00 | 2450 | 5 | 9 | ||
Hamburg | 15 | 264.00 | 1980 | 4 | 11 | ||
Antwerp | 16 | 238.00 | 1940 | 6 | 10 | ||
Ningbo | Piraeus | 17 | 263.00 | 920 | 5 | 11 | |
Rotterdam | 18 | 207.00 | 1650 | 4 | 8 | ||
Hamburg | 19 | 258.00 | 1430 | 5 | 9 | ||
Antwerp | 20 | 236.00 | 1120 | 7 | 10 | ||
Singapore | Piraeus | 21 | 164.00 | 360 | 2 | 9 | |
Rotterdam | 22 | 152.00 | 540 | 4 | 11 | ||
Hamburg | 23 | 185.00 | 210 | 2 | 10 | ||
Antwerp | 24 | 176.00 | 120 | 3 | 10 |
The above model solution shows that the rate of utilization of the entire service route reaches 100% while the rate of weight utilization reaches 99%. That is, the allocation distribution seems to best meet the requirements between the light and overweight cargo in different segments. The contribution for the whole service route is maximized by giving priority to high-contribution segments and high-contribution cargos. Thus, this seems to be an excellent solution to the container liner’s YM. Thus, how is it possible to make an evaluation of the optimum solution in actual practice?
First, from the model solutions proposed by the genetic algorithm, one of the problems is the ignorance of the potential loss that will result from not satisfying the current customers’ allocation requirements. The above solution might cause unexpected losses due to customer complaints. This could produce significant potential losses and significantly influence (in a negative way) the stability of the service route. Using the model solution, for example, looking at route numbers 2, 6, 8, 10, 21, 22, 23, and 24 under the approximate optimal solution of distribution strategy, only 2%, 5%, 55%, 0.4%, 2%, 1%, 40%, and 8%, respectively, of the average allocation demand have been matched. Such results could lead to severe customer complaints along with the potential loss of both customers and market share. These results, in turn, could cause unexpected losses that are not considered in the models and solution. A further solution in future research would be to add additional constraints (such as a deviation index) to ensure that maintenance and service stability are not affected. Another solution could be to conduct an evaluation of customers and divide them into different groups (such as global key accounts, regional key accounts, trade key accounts, big cargo owners, small and medium-size cargo owners, and spot-forwarding businesses) with further subdivision based on the average allocation demand in each segment. This can be done by calculating the different groups of customer requirements to determine the reasonable section of allocation distributed in each segment and adding the result into the mathematical model constraints.
Second, the model solution is based on the average demand of each segment and the segment’s contribution analysis. This can be the benchmark when shipping carriers make decisions regarding each segment’s allocation. However, the limitation with this strategy is the ignorance of each segment’s allocation demand between the peak and slack seasons. These variations might significantly affect the contribution and the conclusion. For example, even when a certain segment’s contribution is lower compared to others, the majority of the cargos remain in the slack season, and that segment’s contribution cannot be simply evaluated by numbers. One possible solution is to add each segment’s ratio between the average allocation demand to both slack and peak seasons. The ranking from high to low of such ratios should be considered when making decisions on the allocation distribution strategy (together with the contribution evaluation) and added as the mathematical model constraint.
Third, the model solution is based on the reconstruction of the contribution by maximizing the contribution of the service route. This can serve as the optimized strategy to achieve YM management objectives under a specific container liner’s current customer structure and existing service route network. However, in actual YM practice, when container liners make decisions regarding their allocation strategies, all service routes in the network should be considered together with their competitors’ service profile, both in general and in specific segments. This requirement relates to specific marketing strategies in specific areas and is an important factor in establishing competitiveness by virtue of a larger market share, better delivery times in certain markets, and superior service differentiation. This can be further studied through the game theory and by adding a segment competitiveness index in the mathematical model when deciding on a segment strategy.
Finally, the allocation distributed to each segment by the model solutions should be assigned to specific target customers. Because the different orders of some customers are often inseparable, no possibility exists to simply and strictly meet each segment’s allocation. Doing so might cause potential losses due to booking shut outs that, in turn, could result if only a portion of the allocation is satisfied for different customers. How to adjust the allocations distributed in each segment and how to distribute allocations to each customer under contribution reconstruction using customer evaluations and allocation promises for long-term contracts should be studied further.
YM refers to the management of allocation and pricing to maximize the payoff in a stochastic environment. However, how to define the objectives is a matter worth discussing. The majority of the current research attributed the objective to maximizing revenue (e.g., total revenue and average revenue) without considering the generated relational cost. Other studies attributed the objective to profit maximization while costs were selected without considering how the costs were generated and calculated, or they were calculated repeatedly. The special characteristics of container liner shipping compared to air transport, hotel arrangements, or retail management must be reflected in the traditional YM models. This study proposes a new solution to evaluate the YM payoff by considering the special characteristics in container liner shipping. The idea is to reflect both cargo revenue and cost and to maximize the cargo contribution. All costs were identified and calculated according to the logic cost generated to allow evaluation of the cargo contribution. Although the number of plugs for reefers was not considered in the constraint, this will not affect the conclusions. It is common practice that container liners give priority to reefer containers and reserve allocation for reefer containers in advance. The reservation can be deducted from the whole capacity and will not lead to a different conclusion.
The emphasis of this study is to maximize the payoff though capacity management in different service route segments. Future proposed research directions would be the slot allocated to different customers in each segment and the pricing strategy and model solution based on the cargo contribution.
The datasets used during the current study are available from the corresponding author upon reasonable request.
The authors declare that they have no conflicts of interest.
Yisong Lin conceived and designed the analytic framework. Xuefeng Wang and Jian Gang Jin analysed the data. Yisong Lin wrote the paper. All the authors read and approved the final manuscript.
The author J. G. Jin is sponsored by the Shanghai Rising-Star Program.