Operational shadow pricing in back haul container shipping

Transportation Research Part E xxx (2016) xxx–xxx

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Transportation Research Part E journal homepage: www.elsevier.com/locate/tre

Operational shadow pricing in back haul container shipping Shao Hung Goh ⇑, Yuxian Chan SIM University, School of Business, 461 Clementi Rd, Singapore 599491, Singapore

a r t i c l e

i n f o

Article history: Received 24 September 2015 Received in revised form 2 March 2016 Accepted 12 March 2016 Available online xxxx Keywords: Shadow price Back haul shipping Container repositioning Spot market

a b s t r a c t Minimum acceptable rates for back haul cargo are difficult for carriers to establish in practice. They depend on complex factors such as availability of empty containers in the vicinity, cost of repositioning empties and container on-hiring decisions. A shadow pricing and ‘‘shadow credit” approach is proposed and applied to an inland network. Such a model can help carriers undertake yield management at the operational level to improve financial performance in a post-conference era. Results also suggest a positive relationship between variability in the imbalance situation of laden containers in a particular trade and volatility of short-term back haul freight rates. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction The back haul market for freight is an often neglected aspect of the container shipping business (Miller, 2010). The emergence of global markets, improved service of non-conference carriers, and deregulation have contributed to the restructuring of the liner shipping industry and led to a de-emphasis of traditional conferences (Federal Maritime Commission, 2001). At each IPI (inland point intermodal) location, which refers to a non-port that can be served by carriers on a through bill of lading, ocean carriers may compete fiercely in the spot market for export cargo from the hinterland, to minimize unused capacity on the return leg of the ocean journey. In a competitive market, although individual carriers may be price-takers, each indirectly exercises market influence by having the right to decline cargo that pay below the respective carrier’s marginal cost. A round trip in liner shipping can generally be divided into a head haul and a back haul, whereby the head haul is usually the demand intensive direction (Løfstedt et al., 2010). Vessel utilization is typically only around 50–70% in the Asia–Europe back haul trade lane (i.e. Europe to Asia) (Søndergaard et al., 2012). Likewise, half of containers entering the United States (US) are repositioned empty to foreign markets (Rodrigue et al., 2013). In other words, back haul trades are likely to have supply in excess of demand and thus face a surplus of empty containers. Negative trade imbalances tend to increase the rates for inbound flows and depress them for outbound flows, since the higher inbound rates are ‘‘subsidizing” the repositioning of empty containers (Rodrigue et al., 2013). Besides trade imbalance, dynamic operations and uncertainties are the other important factors that cause empty container movements (Song and Dong, 2015). In the US, more than 80% of cargo move under service contracts (Federal Maritime Commission, 2001). Contracts are commonly used for long hauls in thin back haul markets (Hubbard, 2001). Shippers are more likely to engage in spot pricing agreements when the cost of transactions is low, when there are several alternative sources of the commodity to be shipped, when multipurpose vessels can carry it, or when many shippers and carriers operate on a single trade (Pirrong, 1993).

⇑ Corresponding author. E-mail address: [email protected] (S.H. Goh). http://dx.doi.org/10.1016/j.tre.2016.03.008 1366-5545/Ó 2016 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Goh, S.H., Chan, Y. Operational shadow pricing in back haul container shipping. Transport. Res. Part E (2016), http://dx.doi.org/10.1016/j.tre.2016.03.008

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Unlike in the airline industry, revenue management techniques used in the shipping industry are somewhat less wellestablished (Zurheide and Fischer, 2012). Even where they exist, the focus of tactical yield management is on slot allocation, i.e. rates are generally assumed fixed and capacity is allocated among particular trades (e.g. Karimi et al., 2005). However, in reality, in the short/immediate time frame, contracted rates may be fixed, but spot rates are still variable. Carriers can theoretically strive towards filling vessel capacity as much as possible in the short/immediate term by adjusting spot prices accordingly (as long as price is above marginal cost). Hummels et al. (2009)’s research suggests that the shipping industry exercises some market power, which helps to explain some portions of the variation in shipping prices. These can depend on cargo type, shippers’ urgency and any quasi-rents that carriers can capture from shippers. Fig. 1 shows the degree of flexibility of rates and capacity as the shipping cut-off (or cargo tender) date is approached in the planning horizon. At the strategic and tactical levels, the principal determinants of marginal costs and mark-ups in maritime shipping are distance, scale economies and policy barriers (Bertho et al., 2014). A low back haul rate is often cross-subsidized by charging a higher price on the head haul leg, and thus repositioning costs can be viewed as a recurring necessary cost. At the operational level, marginal costs are more complicated and have two components: the direct cost and the indirect cost (Koopmans, 1949). Direct costs are incurred when equipment is tied up at any time during loading, loaded movements and discharging. Indirect cost arises whenever there is a ‘‘departure from perfect balance in the program and a continual movement of empty equipment is required from points of equipment surplus to points where there is a deficit.” At the operational level, one challenge for carriers is thus in quoting rates that are greater than or equal to the short run marginal cost (SRMC) of accepting the export freight. In other words, it is a matter of establishing a ‘‘charging floor” consisting of the direct handling costs, but also charging as close as possible to the ‘‘charging ceiling” for each type of commodity, without ever exceeding it (Jansson and Schneerson, 1987). However, in a non-conference setting, each carrier would have different SRMC curves, due to different cost bases, trade strategies and states of container imbalance. Since the share of empty containers in hinterland transport ranges from 40% to 50% of all containers transported (Song and Dong, 2015), one of the largest components of marginal costs comes from the cost of regional repositioning of containers from IPIs with surplus containers, to where there are shortages. The discussion on marginal costs thus leads to the concept of shadow pricing. The use of the term ‘‘shadow price” in the context of shipping can probably be traced to Goss (1967), who described ‘‘shadow price” as the freight rate at which the net present value of using a ship becomes zero, taking into considering the investment cost of the ship, the opportunity cost of capital and port dwell time. However, in optimization problems, shadow price takes on a different meaning, in that the shadow price of a constraint is the ‘‘rate of change of the maximized objective with respect to a unit relaxation of the constraint” (Layard and Glaister, 1994). This shadow price concept has been used in the broader context of transportation and transport economics. For example, Satar and Peoples (2010) analyzed the US coal industry and the divergence between transportation prices charged to shippers and the shadow prices. Clyde and Reitzes (1998) studied the effect of conference sizes on shadow value and marginal cost of capacity. Bell et al. (2011) described how the dual variable for a maximum rate of container movements at a port provides a shadow price, or surcharge, for loading or unloading a container at a congested port. Talley (1994) presented a shadow price methodology in evaluating a hypothetical non-profit port with respect to its optimum economic throughput and proposed that the Lagrangian multiplier could be a single overall performance indicator of the port. Repositioning has a close link with yield management concepts. As Gardon´ et al. (2013) explained, ‘‘margin” refers to revenue subtracting costs, whereas ‘‘yield” is the ‘‘margin after the addition of the so-called flow adjustment linked to the empty containers evacuation”. Optimizing profitability at the operational level is challenging and requires not just good forecasts of revenue, but also of marginal costs. Marginal costs are difficult to determine due to the indirect cost components (Koopmans, 1949). Nonetheless, the operational planning level is characterized by a highly dynamic environment and the time factor plays an important role at this level (Braekers et al., 2011). Thus any optimization model at this level should not be too complex and should be solvable rapidly in almost real-time. Within a deregulated and highly competitive market, there is a propensity for carriers to enter in a price war (Bowman, 2013) and undercut not just competitors’ rates, but also the carrier’s own marginal costs. It would be of interest to pricing managers to understand how low a carrier should be prepared to quote to pursue the finite amount of freight in the back haul market. The motivation for this paper stemmed from a study at an Asia-based shipping line (Carrier X) that was seeking ways to improve its profitability in the US-export market. As a small/mid-sized carrier, Carrier X does not currently adopt a sophis-

Strategic planning (long term): Rates and capacity are all variable inputs in business plans

Tactical planning (medium term): Service contract rates are variable inputs (but highly subject to market conditions). Capacity is variable according to fleet deployment plan

Operational planning (short term): Capacity is fixed. Only spot rates are variable Sh Shipping Cut-off C Time

Fig. 1. Carrier’s ability to vary rates and capacity with time.

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ticated revenue management system, nor does it have any formal pricing guidelines based on internal measures of marginal break-even points in the Trans-Pacific Westbound (US export) market. The research questions are therefore as follows:
At the marginal level, given a specific state of container imbalance, what is the minimum acceptable rate that a carrier should set out of each IPI?
How would these minimum acceptable rates change throughout the year during the peak and off-peak shipping seasons? 2. Literature review This review briefly introduces selected relevant literature on optimizing empty repositioning, but focuses on back haul pricing in the ocean transportation industry. There is an extensive wealth of recent literature on the repositioning of empty containers and the reader is referred to Theofanis and Boile (2009), Khakbaz and Bhattacharjya (2014) as well as Song and Dong (2015)’s papers for more comprehensive syntheses of the key developments and issues in empty container repositioning. Braekers et al. (2011)’s paper also described the decisions to be taken at each planning level (strategic, tactical and operational) of the empty container management problem. Several researchers have considered the joint fleet-sizing and empty-allocation problem. Dong and Song (2009) studied the joint container fleet sizing and empty repositioning problem for a liner shipping system via a simulation-based optimization tool. Karimi et al. (2005) developed a deterministic linear programming formulation for tank containers, with an extended variant that incorporates yield management to identify containers which would be seemingly non-profitable but have positive profit contribution when repositioning is taken into account. Erera et al. (2005) formulated an operational tank container management model that integrates container routing and repositioning decisions. They proposed a 2-phase strategy, in which repositioning decisions are first made once per week using estimates of weekly inflows and outflows of containers at depots, before routing decisions are determined based on booking demands. Dong et al. (2013) compared the performance between time-dependent origin–destination matrices with control policies consisting of dynamic decisionmaking rules and found that parameterized state-feedback control policies are more cost-effective than other repositioning policies if threshold values are designed properly. Bell et al. (2013) presented a cost-based container assignment model, which assumes that the routes, service frequencies and ship sizes are given, so the ship operating and voyage costs are approximately fixed. Full and empty containers are assigned to routes to minimize container handling costs, container rental and container inventory costs. The Lagrangian equation to the container assignment model can then be applied such that when a route (or port) constraint is exceeded, the shipping line (or port) can impose a surcharge on each overloaded link sufficient to bring demand into line with capacity. However, inland costs are not considered in this model and the variable cost of repositioning an empty container is modeled as an average. From a cost allocation perspective, round trips can be viewed as ‘‘joint products” whose production incurs ‘‘joint costs”, some of which are not allocable (Felton, 1981). Under competitive circumstances, all the joint costs will be borne by the head haul shippers, while back haul shippers will pay only the separable marginal loaded back-haul costs. Jansson and Schneerson (1987) presented theoretical perspectives concerning shadow pricing and marginal cost pricing for shipping conferences. They pointed out that the scarcity value of holding capacity on the ‘‘fat leg” (i.e. head haul) is greater than the scarcity value on the ‘‘meagre leg” (i.e. back haul) unless they are both equal to zero, and that associated capacity shadow price in the back haul is necessarily equal to zero. Yet, the authors also found that in reality, conferences at that time departed from the marginal cost structure. Averaging of freight rates implied that there was cross-subsidization for cargoes with respect to port of loading/unloading and imbalance between head haul and back haul, leading to ‘‘a large volume of low-rated cargo. . .not paying its way”. Rónai (2003) summarized the arguments for and against price setting equal to marginal costs and discussed how the practice of price discrimination within the transport sector might cover average costs. Similarly, Demirel et al. (2010) studied the back haul pricing phenomenon in inland navigation shipping and found that back haul prices are not necessarily equal to marginal costs (which is zero in that situation), as carriers are compensated for the time they spend searching for customers. Relatively few researchers have considered pricing and empty positioning collectively. Gustafsson (2006) analyzed the breakeven points for reefer and dry containers in the Caribbean-Europe back haul market and found that back haul freight rates fully pay for the cost of container repositioning in that market. Zhou and Lee (2009) developed a model to study the pricing strategy in the transportation industry with a duopoly. They studied how the profit of a firm is affected by potential imbalance, unit loaded equipment movement cost, unit empty equipment repositioning cost, price sensitivity and competition intensity. In that study, unit costs of transportation (and therefore marginal costs of head hauls and back hauls) were assumed constant. Gorman (2001) developed an Intermodal Pricing Model (IPM) at Burlington Northern and Santa Fe Railway (BNSF), which helped identify a 3.5% improvement in net profitability through a 61% reduction in empty repositioning. A bonus-or benefit mechanism was proposed to allocate costs of repositioning empties back to markets that caused them and credit the markets that reduced them. This was however not implemented due to resistance from pricing managers. Fan et al. (2014) analyzed the relationship between freight rates for head hauls and back hauls under different levels of imbalance. They found that when trade is balanced, front and back haul freight rates are closely related and combine to cover fixed round trip costs and respective marginal costs. When trade is imbalanced, the rates are ‘‘disintegrated”, i.e. front haul prices changes according to freight demand while back haul pricing reverts to marginal cost. Xu et al. (2015) built a mathPlease cite this article in press as: Goh, S.H., Chan, Y. Operational shadow pricing in back haul container shipping. Transport. Res. Part E (2016), http://dx.doi.org/10.1016/j.tre.2016.03.008

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ematical model to investigate the use of pricing policies to balance the cargo demands as well as how the empty equipment repositioning costs may be shared between a carrier and forwarders. While the literature review to this point has focused on costs, carriers may also seek to minimize lead times to shippers and/or inventories of empty containers in inland locations. Shipping lines may be constrained by the limited time within which they must bring an empty container to the shipper. An example of a multi-objective model with cost and lead time considerations is the research by Min (1991) who developed a chance-constrained goal programming (GP) model that best combines different modes of transportation and best maintains a continuous flow of products during intermodal transfer. On the other hand, Yun et al. (2011) considered an inventory control problem of empty containers in an inland transportation system, though container lead time was assumed to be fixed in that study. Other researchers (e.g. Cheung and Chen, 1998; Long et al., 2012; Dang et al., 2012) addressed the stochastic demand of empty containers. These studies attempted to minimize expected total cost of empty container repositioning, but as the planning horizon narrows at the operational level planning, the two-stage stochastic model assumes that the future is known at the end of the first stage (Long et al., 2012). Similarly, Choong et al. (2002) observed that the majority of models in the literature assume the number of empty containers left from the previous planning horizon at a container pool is known. To round up, review of literature has found that some researchers considered the combined joint fleet sizing and empty allocation problem. Others focused on back haul pricing strategies under trade imbalance situations. With the exceptions noted above, past studies seldom considered the joint empty allocation and back haul pricing problem, especially in the context of the container shipping industry. Moreover, studies in these areas tended to focus on planning at the strategic and tactical levels (medium to long term) rather than at the operational level (which is more relevant to rate-making in the spot market or for short-term contracts). While time and inventory levels may be important factors in container repositioning, the literature on repositioning (e.g. Choong et al., 2002; Coslovich et al., 2006; Dong and Song, 2009) has largely focused on minimizing repositioning costs with a given time horizon rather than repositioning lead times (which are usually modeled as constraints rather than as objectives). Some researchers assumed marginal costs are constant (e.g. Zhou and Lee, 2009; Fan et al., 2014). However, this is almost always not the case, since carriers have different cost bases and operate IPI networks of varying complexities and containers need to be repositioned from depots of various distances from customers’ locations. These mean that in a market with multiple sellers, there exist multiple marginal costs. Other researchers assumed in repositioning studies that carriers have no control over volumes. Yet, the reality is that carriers do have some control in the volume of freight accepted in the spot market, using quoted rates as a lever. There is a thus a gap between academic research and industry needs in this area, which this paper aims to address. 3. Methodology Minimum acceptable rates for back haul cargo (at inland points especially) are difficult to establish in practice, since they depend on a complex interplay of factors. The availability of empty containers in the vicinity which can be repositioned to shippers’ locations is probably one of the most important direct considerations for a carrier when accepting back haul cargo. The further the nearest available empty container is, the lower the carrier’s ability to deliver the empty to the shipper in a cost-effective and timely manner. The carrier might simply just find it more worthwhile to immediately circulate the empty containers back to the head haul trade. Depending on seasonal factors, smaller carriers may also not accept freight to/from all IPI points throughout the year. Even if empty containers are available in close proximity to where export freight demand exists, the cost of repositioning these empty containers may vary considerably, for it would depend on not just distance but also the availability of rail and trucking services between IPI locations. On-hiring refers to the leasing of empty containers from equipment owners or other carriers. A common assumption in the literature is that under a master lease arrangement, containers can be leased from lessors whenever owned containers are out of stock to meet customer demands (Song and Dong, 2015). Furthermore, in reality, due to the container imbalance in the Trans-Pacific trade, the cost to lease a container at US East Coast and Mid-West IPI locations is actually negative (i.e. lessees are provided with a cash incentive) if the container is returned to the lessor at major ports in Asia. On the other hand, since ship operating costs are largely fixed, the incremental cost of transporting a laden (versus an otherwise empty) container on the ocean leg is low and can be neglected. 3.1. A three-node network Consider a simple 3-node network with two IPI locations and a port (Fig. 2). The carrier faces a surplus of empty containers at one IPI location, but the demand for export containers can be found at another IPI location. Should the carrier be unable to find (or choose not to accept) export cargo, an empty container would be sent along Leg A, from a source IPI point (with a surplus) directly to the port for export. The direct cost incurred would be:

CostEmpty ¼ TPTA þ HCEmpty

ð1Þ

If the export cargo is accepted (and on-hiring is not applicable), the direct cost incurred is:

CostLaden ¼ TPTB þ TPTC þ HCLaden

ð2Þ

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Shipper’s location (Deficit IPI point) Repositioning Leg B (empty)

Intermodal Leg C (laden)

Surplus IPI point Repositioning Leg A (empty)

Port

Fig. 2. Inland costs for export of containers in a three-node network.

where
TPTA: Cost of inland movement of empty container from source IPI to port (Leg A).
TPTB: Cost of inland movement of empty container from source IPI to shipper (Leg B).
TPTC: Cost of inland movement of laden container from shipper to port (Leg C).
HCLaden: Handling fees for a laden container.
HCEmpty: Handling fees for an empty container. For simplicity, it is assumed that every inland movement is via a single most economical mode (i.e. either by truck or rail), regardless of lead time. Further assuming similar handling costs (e.g. at port and rail terminals) for laden and empty containers, the marginal cost of accepting the export cargo can be simplified to:

CostLaden  CostEmpty ¼ ðTPTB þ TPTC þ HCLaden Þ  ðTPTA þ HCEmpty Þ ¼ TPTB þ TPTC  TPTA

ð3Þ

The key insight from the 3-node network is that the carrier would be willing to ‘‘subsidize” or provide a ‘‘credit” to the back haul export shipper (up to the cost that would otherwise be incurred in handling and hauling an empty container from the source IPI back to the port). In a more realistic network with many more than 3 nodes, the challenge of computing this ‘‘subsidy” increases significantly due to the numerous possible permutations on how an empty container can be routed within the network, depending on the repositioning plan. Accepting one unit of export container at one IPI may also upset the balance at another IPI in the regional network. 3.2. Conceptual shadow pricing model formulation In this context, the term ‘‘shadow credit” (rather than ‘‘subsidy”) is used to denote the decrease in regional empty repositioning cost from the acceptance of one more unit of export container at an IPI. From the pricing perspective, the shadow credit is the maximum incentive that a carrier would be willing to pass on to the export shipper due to the cost avoidance in shipping an empty container back to port. The shadow price (or effective marginal cost) can then be derived based on the shadow credit, such that:

Shadow Price ¼ Direct Marginal Cost  Shadow Credit

ð4Þ

Consider a set of inland terminals (IPI) N = {1, 2, . . . , n}. A virtual node, which may represent a leasing pool for empty containers or a port from which surplus containers are injected or drained from the inland network, is denoted as {0}. The carrier shuttles containers (both empty and laden) between these IPI locations and the port. The set of arcs is thus defined as A ¼ fð0; iÞ; ði; 0Þ; i 2 Ng [ fði; jÞ [ ðj; iÞ; i 2 N; j 2 N; i–jg (see Fig. 3). Following the findings of Dong et al. (2013) on the superior performance of state-feedback control policies, a linear programming model based upon dynamic decision-making rules is used to determine the optimal repositioning plan over several time periods, at the end of each the entire network’s containers are rebalanced. The formulation is thus that of a linear program for a classic transportation problem (considering only empty repositioning and not laden). Although more sophisticated models can be built, one purpose of this paper is to compute shadow prices,

0

1

IPI node 1

2

IPI node 2

…

Leasing pool or port (node 0)

n-1

IPI node n-1

n

IPI node n

Fig. 3. Generalized inland network of IPI and port nodes.

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which would not be as easily achieved using mixed integer programming (MIP) formulations that may be required of more complex models. Notation:








cij = cost of repositioning an empty container from node i to node j xij = decision variables for number of empty containers to be repositioned from node i to j Si = inflow of laden containers at source node i Dj = outflow of laden containers at sink node j Bk = projected net surplus (shortfall if negative) of empty containers at IPI k Xij = dual variables ak = Lagrangian multipliers Objective function:

C 0 ðxÞ ¼ Min cost ¼

n X n X ðcij xij Þ

ð5Þ

i¼0 j¼0

Subject to: n X ðxij Þ ¼ Si ;

8i

ð6Þ

8j

ð7Þ

8k

ð8Þ

for i ¼ j

ð9Þ

j¼0 n X ðxij Þ ¼ Dj ; i¼0

Sk  Dk ¼ Bk ; xij ¼ 0; xij P 0

ð10Þ

If given that costs of repositioning trips originating and ending at the same node are positive, the constraint in (9) is redundant in an optimal solution and can be neglected. Combining (6)–(8): n n X X ðxkj Þ  ðxik Þ ¼ Bk ; 8k j¼0

ð11Þ

i¼0

The dual variable for the constraint in Eq. (11) provides the ‘‘shadow credit” of a unit change of the imbalance at each IPI (i.e. the marginal change in rebalancing cost of accepting the last unit of cargo). The Lagrangian equation for C0 is:

LðX; aÞ ¼

n X n X

ðC ij X ij Þ 

i¼0 j¼0

" # n n n X X X ðak Þ ðX kj Þ  ðX ik Þ  Bk k¼0

j¼0

ð12Þ

i¼0

The first order conditions are:

@L ¼ 0; @X ij

8i; j

ð13aÞ

@L ¼ 0; @ ak

8k

ð13bÞ

Using the Kuhn–Tucker conditions,

ak UIS; 8 k

ð14aÞ

" # n n X X   ðX kj Þ  ðX ik Þ  Bk P 0; j¼0

"

ak

# n n X X ðX kj Þ  ðX ik Þ  Bk ¼ 0; j¼0

8k

ð14bÞ

i¼0

8k

ð14cÞ

i¼0

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Hence ak (under the optimum repositioning plan) can be solved and would represent the shadow credit (i.e. impact to the rebalancing plan) from accepting the last unit of export container at IPI location k. In this single-period model, container imbalance at the operational level is assumed deterministic, i.e. the numbers of inbound and outbound containers at each IPI are known. It is also assumed that there are no constraints on the maximum number of empty equipment that can be on-hired from container lessors. In practice, shadow credit and therefore shadow price are usually only applicable for small changes in the number of export containers accepted. If the allowable range from the sensitivity analysis is exceeded, the projected surplus/deficit should be adjusted by the required amount and the model be resolved. In problems with successive planning periods, this model can then be reapplied in the next time period (t + 1) by resolving the LP model based on an updated set of imbalance projections from the preceding time period (t). 4. Results and discussion 4.1. Numerical example The Trans-Pacific container trade is highly imbalanced, with more laden containers on the Eastbound (Asia–North America) than on Westbound routes. This imbalance is most acute during peak season months (from August to November each year), in which imports are the highest just prior to the year-end holidays. This surge in imports leads to a large surplus of empty containers that have to be subsequently repositioned out of the United States. Since Carrier X does not operate on the Trans-Atlantic trades, empty containers often have to be sent back to Asia without any cargo. Off-hiring of surplus containers is generally not viable as other carriers also face a surplus situation. Besides, import containers used in the network are generally carrier-branded and therefore have low-interoperability with other carriers. If there is a deficit of containers at any IPI, empty containers are sourced from nearby IPIs. Empty containers may be on-hired (as a last resort) from a leasing company that provides a US$300/container incentive for the carrier to return the empty container at a major port in Asia. As will be illustrated later, this incentive usually falls short of the benefit of using an empty container (if available) from within the carrier’s own network. Carrier X operates in the US Mid-West and US East Coast with 12 IPI locations (Fig. 4). Chicago (CHI) and Houston (HOU) are Carrier X’s most important markets for import containers. Chicago is also by far the largest source of export containers in the region with about 50% share by volume. New York (NYC) and Atlanta (ATL) are seasonal IPIs that are only open to accept export cargo in Quarter 3 (to alleviate the container surplus situation in Chicago). Data (on costs to reposition containers between IPIs, as well as historical imbalance figures at each IPI for 2013 and 2014) were made available by Carrier X for this study.

New York

Minneapolis

Cleveland Chicago Omaha

Columbus

Kansas City St Louis Memphis Atlanta Dallas Houston

Fig. 4. IPI locations in Carrier X’s US Mid-West and East Coast network.

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Table 1 shows the projected equipment surplus or shortfall arising from service contracts in four quarterly time periods, before the acceptance of cargo from the spot market. Due to the sensitive nature of the data, actual volume figures are not revealed in this paper, only the projected surplus or shortfall figures at each IPI. This analysis is also restricted to 40-foot high-cube containers and figures are thus in forty-foot equivalent units (FEUs). Chicago is a major consumption center that has a large surplus of empty container equipment throughout the year, most notably in the third quarter, during which import containers outnumber export ones by 490 FEUs. On the other hand, IPIs such as Dallas (DAL), Kansas City (KCK) and Minneapolis (MSP) typically face a deficit of empty containers, due to the strong exports of petrochemical, wheat and soya bean products respectively. Despite these broad trends, the container imbalance situation is seasonal and varies throughout the year. By aggregating imbalance at quarterly level, it is assumed that the carrier adopts a quarterly rebalancing plan (i.e. an empty container may wait no more than 3 months in the US for export cargo, before it must be repositioned back to Asia). It is possible to set a shorter horizon for the repositioning plan, though movement costs would increase (offset slightly by the lower costs of maintaining a smaller pool of container equipment inventory). Fig. 5 illustrates the repositioning plan for the projected imbalance scenario and rebalancing plan in Quarters 3 and 4. In this numerical example, the loading terminals for export containers (whether laden or empty) are generally the West Coast ports of Los Angeles and Long Beach. However, containers from IPIs that are located near the East Coast (e.g. NYC, ATL, HOU) are loaded at the nearest East Coast ports (e.g. Newark, Savannah, Houston). In either case, the cost of each individual leg to an East or West Coast load port is taken into account in the model. Excel Solver was used for this example. In Quarter 3, Chicago (being the IPI with the largest surplus) provides empty equipment to meet the shortfall in neighboring IPIs such as St. Louis and Minneapolis. 341 containers are required to be repositioned empty back to West Coast ports. Due to distance, Dallas and Houston are isolated from other IPIs in the repositioning plan. In Quarter 4, the overall network still faces a surplus of empty containers. However, the optimal repositioning plan has shifted such that Kansa City now serves as the primary source of empty containers. The optimal repositioning plan can therefore vary greatly under a dynamic decision rule. Fig. 6 plots shadow credit for the marginal laden container accepted for export to Asia at various IPIs. For example, if direct land-side rail, local trucking and handling costs of $4000 (assumed) would be incurred to ship a laden container from Cleveland to Asia in Quarter 2, the carrier could provide to the shipper a maximum incentive (or shadow credit) of $676. The marginal cost of providing the service would be $3324 (which is $4000 less $676). In Quarter 3, this maximum incentive would rise to $1410 due to the acute surplus of containers that would have to be repositioned empty to the port if no export cargo can be found. This large fluctuation of shadow prices (and marginal costs) throughout the year is one reason for the volatility of TransPacific Westbound rates which is prevalent in the container shipping industry. For example, actual historical data from Carrier X shows that in 2014, Trans-Pacific Eastbound rates have a standard deviation of $616/FEU compared to $1125/FEU in the Westbound trade. As might be expected, when the equipment imbalance situation is more severe (i.e. in the second half of the year), shadow credit tends to be high (and consequently shadow price low). Furthermore, it is also worth noting that the incentive ($300) provided by the leasing company is probably but a fraction of the potential profit from providing the service. The shadow pricing approach can further be used to determine the effective marginal cost curve as more containers of export cargo are accepted at each IPI. For illustration, Fig. 7 shows the marginal costs for every unit of export container shipment accepted on the spot market in Cleveland. The shadow credit of positioning an empty container at Cleveland is a constant $676/unit for the first 11 units in Quarter 2. Assuming a direct variable cost of $4000/unit for export containers, the marginal cost of accepting the first 11 units of spot cargo is $3324 (i.e. $4000 subtracted by $676). Should the carrier choose to accept an additional 43 units of export cargo, the shadow credit to the repositioning plan decreases to $650/unit and marginal cost of accepting the export cargo increases to

Table 1 Projected quarterly surplus or shortfall of empty containers at IPI level. IPI

Projected equipment surplus (+ve) or shortfall (ve) Quarter 1

Atlanta (ATL) Chicago (CHI) Cleveland (CLE) Columbus (CMH) Dallas (DAL) Houston (HOU) Kansas City (KCK) Memphis (MEM) Minneapolis (MSP) New York City (NYC) Omaha (OMA) St Louis (STL) Total

Quarter 2

Quarter 3

7 27 43 46 50 40 24 19

188 68 51 78 12 22 37 59

9 8

43 15

40 490 34 46 23 55 76 23 16 80 58 8

143

173

385

Quarter 4 137 27 25 30 34 103 43 1 4 0 198

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S.H. Goh, Y. Chan / Transportation Research Part E xxx (2016) xxx–xxx

Minneapolis -16 Chicago -58

Cleveland

46 St Louis

Omaha 76

-80

-34

490

New York

Columbus

-8

Kansas City -23 -40

Memphis -23

Atlanta

Dallas 55 Houston

Quarter 3

Minneapolis -1 27

137 -4

Omaha

- 25

Chicago 103

Cleveland

NA New York

Columbus 0

St Louis

Kansas City -43 NA

Memphis -30

Atlanta

Dallas 34

Quarter 4

Houston

Fig. 5. Optimal repositioning plan for Quarters 3 and 4.

0

Q1

Q2

Q3

Q4 ATL Net

Shadow Incenves

-500

CHI Net CLE Net CMH Net

-1000

DAL Net HOU Net KCK Net

-1500

MEM Net MSP Net NYC Net

-2000

OMA Net STL Net

-2500

Quarterly Period Fig. 6. Quarterly shadow credit for various IPIs.

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S.H. Goh, Y. Chan / Transportation Research Part E xxx (2016) xxx–xxx

3800

Marginal Cost

3700 3600 3500 3400 3300 3200 3100

1

6

11

16

21

26

31

36

41

46

51

56

Quantity Fig. 7. Effective marginal cost of accepting spot containers at Cleveland.

$3350. Subsequent units of cargo accepted will yield only $300/unit of shadow credit (which is the on-hiring incentive from the leasing company) and marginal cost therefore rises to $3700. The marginal cost function is upward-sloping as more units of export cargo are accepted. Initially, shadow credit is high as Cleveland absorbs the surplus equipment at nearby IPIs. Subsequently, empty containers have to be brought in from IPIs located further away. Eventually, it becomes infeasible (or not cost-effective) to procure equipment from within the network and these have to be leased (on-hired). Fig. 8 shows the volatility of shadow price versus imbalance. There is a generally positive relationship between an IPI’s standard deviation of imbalance and the standard deviation of shadow price, e.g. in CHI and KCK. The main exceptions are CMH and CLE which are in close proximity to CHI (an IPI with a large surplus of empty equipment that can be repositioned cost effectively to CMH and CLE). At these two IPIs, variability of rates is therefore lower than what the imbalance situation might suggest.

4.2. Managerial implications Carriers often play a delicate balancing act in managing mismatches between inbound and outbound containers. They all likely face slight differences in their container imbalance situations and as such marginal costs can vary widely. When the imbalance situation is uneven across IPIs, short-term rates are also likely to have high variances across these IPIs, even if the inbound and outbound trades are in balance on aggregate. Secondly, even though the shipping industry is highly competitive in the post-conference era, it is probably closest to a monopolistic competition with non-uniform underlying cost structures. Freight rates in the container trade are not synchronized through international indices but are instead set at the discretion of the liner companies (Meenaksi, 2009). Carriers may attempt to compete for spot freight through under-cutting of prices, but ultimately, each carrier would likely end up

Standard Deviaonof Imbalance (FEU)

160 KCK

140 120 CHI

100 80

R² = 0.2124

60

HOU

40 DAL

20 -

STL

-

100

200

MSP

300

CLE

OMA

MEM

CMH

NYC ATL

400

500

600

700

800

900

1,000

Standard Deviaon of Shadow Price (US$) Fig. 8. Standard deviation of imbalance vs standard deviation of shadow price.

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S.H. Goh, Y. Chan / Transportation Research Part E xxx (2016) xxx–xxx Table 2 Marginal profit example. IPI

Direct separable costs (assumed)

Q3 shadow credit

Q3 shadow price

Marginal revenue (market spot rate)

Marginal profit (yield)

CHI DAL KCK

4000 4000 4000

2000 300 1530

2000 3700 2470

2300 3500 2500

300 200 30

with very similar market shares compared to when they first started, since other carriers would often match price drops. Should all carriers attempt to match the lowest rates in the back haul spot-market, most would likely to have to quote rates at below profit-contributing levels. For instance, the analysis in this study reveals that in the network studied, the historical rates out of at least 3 IPI locations may have been inadvertently under-quoted by Carrier X, resulting in negative yields. Visibility of rate floors can thus help carriers reduce the risk of undercutting rates to below profit contributing levels and better understand the financial cost of price wars to gain or defend market share. Thirdly, even if the risk of under-quoting rates (that are below shadow prices) is low in a particular trade, there exists an opportunity for carriers to carry out yield management at the operational level, without the need for a costly optimization procedure. In the short/immediate term, the available volume of freight is essentially fixed, as is the available ocean vessel slot capacity. One potential application of the shadow pricing model is in identifying the IPIs in which a carrier has minimum acceptable rates that are below market rates (i.e. where the carrier has a comparative cost advantage). The carrier can then prioritize sales efforts accordingly towards these IPIs locations that have the highest yields. For example, a trade manager may be faced with the following decision scenarios in Table 2. The carrier would incur an assumed $4000 in direct separable costs to accept one additional unit of export cargo to Asia from each of these IPIs. On the other hand, the current spot rates vary considerably across these 3 IPIs in Quarter 3. With the output from the shadow pricing model, it would be clear that despite the spot rate at DAL being the highest, the yield is negative. As such, accepting cargo from DAL would be less preferred to repositioning an empty container back to Asia. Although the spot rate at CHI is lower than that at KCK, the carrier is much better off with accepting the last unit of export freight booking from CHI rather than that from KCK. The same principle can be adopted in developing countries such as India and Vietnam that (similar to the US) have a trade deficit of physical goods and a large inland containerized freight market. Hence, the export markets for freight in these countries can also generally be classified as back haul and the shadow pricing model would be applicable.

5. Conclusion The purpose of this paper is not to suggest an alternative to optimization models for the repositioning of containers, but to describe an approach that takes into consideration the complex factors affecting the marginal costs in the back haul market from inland locations. Uncertainties and dynamic operations are some of the most important factors in empty container movements (Song and Dong, 2015) and shadow prices can help carriers determine minimum acceptable rates for the spot market. In particular, this paper focuses on the operational planning level and the spot rate-making process. Although the model is formulated as a regional (rather than global) problem, this is arguably representative of the problem at the operational level. There is also the benefit of working with a reduced subset of regional nodes, which would make it possible for minimum acceptable rates to be continuously recalculated in real-time. Our research has contributed to the literature in two ways. First, it has demonstrated a novel shadow pricing and ‘‘shadow credit” approach to the back haul pricing problem. While the shadow pricing method has been proposed for scenarios such as transport economic efficiency (Satar and Peoples, 2010), shipping conferences (Clyde and Reitzes, 1998), port performance (Talley, 1994; Bell et al., 2011) and container assignment (Bell et al., 2013), this paper is the first to have proposed applying shadow pricing in a competitive inland back haul shipping environment. Our research builds on the theoretical work on marginal pricing in a conference system by Jansson and Schneerson (1987) and has developed an industry application of shadow pricing in the post-conference era in which multiple carriers set prices independently. Secondly, results have suggested that there is a positive relationship between variability in the imbalance situation of laden containers in a particular trade and the standard deviation of back haul freight rates. This finding helps explain why shippers in the back haul trades might experience a much larger variability of freight rates, even though average back haul rates are much lower compared to those in the head haul. A key limitation of this study is that it is based on the perspective of just one carrier. Data from multiple carriers can further validate the shadow pricing approach. This study also does not address routing, scheduling or fleet mix, which are problems in the tactical horizon. Moreover, a shadow price is applicable for the last or incremental unit of container accepted at each IPI. It is calculated independently of acceptances at other IPIs and is not applicable for large volumes of spot cargo. Besides, the imbalance situation at each IPI is assumed deterministic at each point in time. This is not unrealistic, since up to 1–2 weeks before a shipping cut-off date, the number of inbound and outbound containers under contract rates at each IPI can be projected with reasonable accuracy. The problem can be broken into successive planning periods and at the end of each planning period, imbalance is assumed deterministic. The proposed methodology is therefore practical for adoption by Please cite this article in press as: Goh, S.H., Chan, Y. Operational shadow pricing in back haul container shipping. Transport. Res. Part E (2016), http://dx.doi.org/10.1016/j.tre.2016.03.008

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S.H. Goh, Y. Chan / Transportation Research Part E xxx (2016) xxx–xxx

carriers and its implementation would be similar to the 2-stage container repositioning and routing method proposed by Erera et al. (2005). As a proof-of-concept study, this paper has modeled the repositioning problem as a transportation problem with limited decision variables and constraints. The model can certainly be extended as necessary (e.g. to take into account container substitution, consider multiple carriers or be incorporated into a global revenue management system). In addition, this study does not consider the multi-criteria problem or the trade-off between time and cost. However, we argue that in a back haul trade with an abundance of empty containers, cost is the most important consideration and lead time less so, especially if the on-hiring option is available. In a local geography with an efficient system of roadways, the cost of the execution of a pairing is usually proportional to the length of the route or to the time necessary to complete it (Coslovich et al., 2006), such that by minimizing cost, we are also minimizing lead time. An exception would be in the case of multiple possible transport modes used in repositioning operations over greater distances, such as truck, rail and barge (Choong et al., 2002), which is not considered in this study. Furthermore, should empty positioning lead time govern (e.g. when the inventory of empty containers is low), the guidelines provided by the shadow pricing model would be a lowerbound floor rate that carriers must not undercut (since a time-constrained repositioning operation would be more costly). That a shadow price acts as a ‘‘charging floor” (Jansson and Schneerson, 1987) means it does not necessarily correspond to the actual price charged or the spot rate. In a profit maximizing environment, carriers would aim to charge as high as possible above this floor rate, depending on their ability to search for better paying customers (Demirel et al., 2010), exploit shippers’ urgency or capture any quasi-rents from shippers (Hummels et al., 2009). If shadow pricing guidance is adopted by all carriers in a highly competitive market, spot rates out of a particular IPI would in theory be driven down to just under the marginal cost of the second most competitive carrier. Yet, such a regime does not imply that the problem becomes stochastic. Rather, a carrier would have a captive market at an IPI in which that carrier has the lowest shadow price among all carriers, until a new repositioning plan is defined in the next planning period or a large unexpected disruption to the imbalance situation occurs in the market. Minimum acceptable rates are often independently set by major ocean carriers via proprietary methods that are not transparent or well-understood by the market. Smaller carriers (such as the one in this study) may not even be fully cognizant of their effective marginal costs of operating in the back haul market, since marginal costs are seldom constant (either over time or as more back haul cargo is accepted). Many researchers have described back haul freight rates to be ‘‘subsidized” by their head haul counterparts, which only reinforces the misconception that back haul planning is somehow unimportant. While carriers have traditionally concentrated on optimizing head haul volumes and routes to drive profitability, there are clearly opportunities to improve financial performance in the back haul direction via operational pricing strategies. 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