Logistical rivalries and port competition for container flows to US markets: Impacts of changes in Canada's logistics system and expansion of the Panama Canal

Abstract

Shipments of container imports are heavily concentrated in a number of ports, which has resulted in pressures on logistics networks. Partly in response to such pressures, several new routes are being developed to gain access to US markets. One involves the port of Prince Rupert; the other is the expansion of the Panama Canal. The purpose of this article is to estimate prospective traffic flows through these logistics channels for container shipments to US markets. An optimization model is developed that accounts for congestion and demand uncertainty. It determines the optimal route, ship size, port and hinterland shipping channels based on cost minimization. Our results show that inter-port competition is very intense. Prince Rupert can become an important rival of US ports and routes and the expansion of the Panama Canal can have similar impacts.

Appendix

Model details

Sets:

F :

=set of origin of container imports

P ^u :

=set of container ports in Unite States

P ^c :

=set of container ports in Canada

E :

=set of oceans carriers

V(e):

=set of vessel type belonging to ocean carrier e∈E

B :

=set of border crossings between Canada and the United States

R ^u :

=set of US Class-I primary railways

R ^c :

=set of Canadian railways

Π _E ^F:

=set of strings (routes), that is selected sequence of ports (i, j, k, … n) over specified trade lane; , served by ocean carrier e∈E

L^F(π _e ^f):

=set of lags (i, j) within string π _e ^f∈π _E ^F

Π _E ^A:

=set of strings (routes) on trade lane via Panama Canal, Π _E ^A⊂Π _E ^F, served by ocean carrier e∈E

D:

=set of BEAs located in interior areas of United States

O :

=set of BEAs located in coastal areas of United states

^o :

=set of container flow arcs (j, o) from US seaport j to coastal BEA o; ^o⊆{j∈P^u, o∈O}

Γ ^r :

=set of container flow arcs (j, o, r, d) from US seaport j at coastal BEA o via railway r to destination BEA d;

Γ ^t :

=set of container flow arcs (j ,o, r, t, d) from US seaport j at coastal BEA o via railway r transit to railway t and to destination BEA d;

Γ ^rl :

=set of railway corridors (o,r,d) from US coastal BEA o via railway r to destination BEA d ;

Γ ^tl :

=set of railway corridors (o, r, t, d) from US coastal BEA o via railway r transit to railway t and to destination BEA d;

Γ ^c :

=set of container flow arcs (j, r, b, d) from Canadian port j by Canadian railway r through border crossing b and to destination US BEA d;

H:

=the set of container trade lanes (f, j) between import origin f and North American sea port

S :

=set of probability of each scenario for uncertainty parameters

Parameters:

Dem _d ^fs :

=demand for TEU at BEA d∈D∪O with import origin from f∈F in scenario s

VCap _v :

=the maximum of TEU that can be handled by a vessel of type v∈V(e)

HCap _j :

=the throughput capacity for container imports (TEUs) at North American ports j∈P^u∪P^c

VCapF _j :

=the maximum TEU of a container ship that can be handled at North American ports j∈P^u∪P^c

VCapM _j :

=the largest vessel type that can be handled at North American ports j∈P^u∪P^c

:

=the largest vessel type that can go through Panama Canal

PNCap :

=the maximum number of cruises (schedules) through Panama Canal

VNCap _v :

=the available number of cruises (schedules) of vessel type v∈V(e) of ocean carrier e∈E

:

=operating cost (at sea) of a vessel of type v∈V(e) over strings π _e ^f∈Π _E ^F

:

=operating cost (in port) of a vessel of type v∈V(e) over strings π _e ^f∈Π _E ^F

BCap _b :

=the throughput of railway capacity for container imports at border crossing between Canada and the United States b∈B

RCapO _o :

=the throughput capacity of railway for container imports at coastal BEA, o∈O

RCapC _j :

=the throughput capacity of railway for container imports at Canadian ports, j∈P^c

URCapR _ord :

=the throughput capacity for container imports over US railway routes (o, r, d)∈Γ^rl

URCapT _ortd :

=the throughput capacity for container imports over US railway routes (o, r, t, d)∈Γ^tl

CRCap _jrbd :

=the throughput capacity for container imports over Canadian railway routes (j, r, b, d)∈Γ^c

URCostR _jord :

=the shipping cost per TEU for container imports over US railway routes (j, o, r, d)∈Γ^r

URCostT _jortd :

=the shipping cost per TEU for container imports over US railway routes (j, o, r, t, d)∈Γ^t

CRCost _jrbd :

=the shipping cost per TEU for container imports over Canadian railway routes (j, r, b, d)∈Γ^c

N _fj :

=the number of pieces over trade arc (f, j)∈H

QCost _fj ⁿ :

=queuing costs per TEU in corresponding piece n∈(1…N _fj ) over trade arc (f, j)∈H

QCost _fj ⁿ⩾:

if n=1 then 0 else QCost _fj ⁿ⁻¹

QLim _fj ⁿ :

=the break point of pieces; (f, j)∈H, n∈{(1…N _fj )−1}

QLim _fj ⁿ⩾:

if n=1 then 0 else QLim _fj ⁿ⁻¹

PCost _d ^f :

=the penalty cost per TEU due to failure in meeting demand d∈D∪O with import origin from f∈F

P ^s :

=the probability of each scenario s∈S

Decision variables:

:

=the number of TEUs shipped over leg(i, j)∈L^F(π _e ^f) by vessel type v∈V(e), in scenario s

:

=the unused capacity on leg(i, j)∈L^F(π _e ^f) by vessel type v∈V(e), in scenario s

:

=the number of cruises (schedules) on string π _e ^f∈Π _E ^F by vessel type v∈V(e), in scenario s

suo _jo ^fs :

=the number of TEUs delivered over flow arcs (j, o)∈И^o with import origin f∈F in scenario s

sut_R _jord ^fs :

=the number of TEUs delivered over US rail routes (j, o, r, d)∈Γ^r with import origin f∈F in scenario s

sut_T _jortd ^fs:

=the number of TEUs delivered over US rail routes (j, o, r, t, d)∈Γ^t with import origin from f∈F in scenario s

sct_R _jrbd ^fs:

=the number of TEUs delivered over Canadian rail routes (j, r, b, d)∈Γ^c with import origin f∈F in scenario s

sp _j ^fs :

=the number of TEUs shipped from foreign port origin to North American ports (f, j)∈H in scenario s

d_U _d ^fs:

=logical variable to represent number of TEU failing to meet demand d∈D∪O with import origin f∈F in scenario s

Objective function:

The objective function (A1) is to minimize the total transportation, congestion and related logistical costs. The first term is the containership cost at sea and the in-port cost for unloading. The Panama Canal fee applies to routes from Northeast Asia to the Gulf/Atlantic. The second, third and fourth terms represent total costs for container shipment from US and Canada ports to US BEA markets by railways. The fifth term defines total cost due to congestion at US ports. We employ the piecewise-linearity's technique to represent the nonlinear congestion cost function. As there is no standard way to describe piecewise-linear functions in algebraic notation, we use notation specified in AMPL to represent piecewise-linearities in the model. The last terms corresponds to the penalty cost incurred for elastic or undelivered containers.

Subject to:

Constraint descriptions

Constraint (A2) takes into account the maximum TEU of a loaded containership that can be accommodated by North American seaports. This constraint considers the scenario that some ports have difficulty handling full-loaded large ships (8000+TEU) as first-inbound calls, because of relatively small terminals, inefficient rail/transit infrastructure to handle high volume container inflow, or not enough channel depth to allow fully loaded large containerships to access. Large ships are allowed to access at second or third call and so forth.

The Panama Canal constraint (A3) ensures that the ship size cannot exceed Canal restriction. This constraint will only apply to the strings from Northeast Asia to Gulf/Atlantic Coast trade lane. The current vessel size that Panama Canal can handle is Panamax with approximately 4400 TEU. Constraint (A4) defines the largest container ship type that can be handled by North American seaports. Most North American ports cannot handle large containerships due to water depth restrictions. This constraint differs from constraint (A2), which specifies the restriction for maximum TEU number of a loaded vessel that can be handled. Constraint (A5) takes into account the number of schedules of each type of container vessel available to ocean carriers. Constraint (A6) considers the maximum number of container vessels allowed through the Panama Canal. Constraint (A7) states that the delivered TEU number plus unused capacity of vessel v on each leg(i, j)∈L^F(π _e ^f) equals the specified TEU capacity of vessel type v∈V(e). Constraint (A8) specifies total annual TEU flow rate (sum of containers originated from Northeast Asia and Europe) via North American ports. Congestion is expected to occur when the flow rate of import containers approaches the port handling rate.

The set of constraints (A9) and (A10) represent equilibrium of container flow at US and Canadian seaports. Given that it may be impossible to meet certain realization of the uncertain parameters or some constraints may be violated, constraint (A11) specifies that in each scenario s the TEUs consumed by coastal BEA o equals the inflow TEU by water mode and rail mode from other coasts plus the elastic or undelivered TEUs. This constraint will ensure a feasible solution.

Equation (A12) presents throughput restriction for import containers at border crossing between Canada and the United States. This constraint only applies to Canadian railroads. Equation (A13) represents rail capacity through coastal BEA of United States. Constraint (A14) states the rail capacity to serve Canadian seaports. The set of equations (A15), (A16) and (A17) specify railway capacity for container shipment on each individual railway route. Constraint (A18) ensures that in each scenario s the TEUs needed by inland US market BEA d equal the total inflow TEUs plus the elastic or undelivered TEUs. Similar as indicated in constraint (A11), this will ensure a feasible solution. The last equation (A19) states that the total TEU flow rate via US ports cannot exceed desired volume.