Stochastic Port Selection Under Correlated Arc Disruptions: Improving Defence Supply Lines in the Nordics

Introduction

The recent expansion of NATO in the Nordics has strengthened both the defence of the Nordic and Baltic Sea regions and the alliance as a whole (Gunter, 2022; Regjeringen.no, 2022). The degree of nonalignment within the Nordics, a severe limiting factor for defence integration (Dahl, 2021), is diminishing with Finland and Sweden as members.

Similar to NATO’s strategic deployment of Enhanced Forward Presence (eFP) in the Baltics and Poland in response to Russia’s actions in Ukraine (Jakobsen, 2022b), NATO is developing measures to strengthen its ability to deploy and apply military force in the Nordics. The expansion, therefore, has major implications for regional defence plans and preparations. Most notably, both the extension of NATO’s eastern border and Norway’s central role in the replenishment of allied forces in Sweden and Finland during crisis and conflict (Carlsen et al., 2023; Regjeringen.no, 2022) differ significantly from former planning scenarios (Lund, 1987).

Contemporary analyses of the war in Europe underscore that logistical sustainability is critical to modern military operations (Skoglund et al., 2022). NATO’s Nordic enlargement is expected to increase sea-to-road and sea-to-rail traffic across Nordic borders (Carlsen et al., 2023; Regjeringen.no, 2023; Samferdselsdepartementet, 2024), especially since conflict escalations may cause the Baltic Sea to become contested (Lucas & Crosbie, 2019). As a leading maritime nation (Tenold, 2019), Norway now plays a growing role in sustaining NATO’s northern flank through its ports and other maritime assets (Black et al., 2024; Edvardsen & Martinussen, 2024).

The transportation network in the Nordics, the Arctic region in particular, is subject to harsh weather with strong seasonal variations (Bardal, 2017). Railway lines are vulnerable to disruption (Nilsen, 2024; NRK.no, 2025), while poor driving conditions and closed roads arising from adverse weather affects network connectivity, particularly when access to alternative routes is limited (Bardal, 2018; Husdal & Brathen, 2010). The limitations are even higher for heavy vehicles due to road, bridge, and tunnel restrictions, which can also impact the military supply chain (Dovland, 2020). In addition, the ports and piers in the region are not all capable of handling large vessels and quantities due to limitations like water depth, storage capacity and terminal facilities, without further investment (Kystverket, 2022). This implies that port selection is a long term decision, and when deciding on which seaports are worthy of investment to facilitate regional defence plans the selection criteria should account for onward movement, meaning the inland infrastructure connecting the ports to assigned and potential assembly areas and all stages in between.

In the context of unit deployment, Longhorn et al. (2021) developed a seaport of embarkation (SPOE) selection criterion based on the shortest combined inland and oceanic transit time from the deploying installation to the military destination theatre. They call this the military port selection problem (MPSP), where the primary objective is the delivery speed of military units to respective destinations. Our paper considers the next stage of deployment, which is from the seaport of debarkation (SPOD) to the final destinations, specifically in the Nordics. Assuming the set of seaport alternatives either are, or can be, developed into adequate ports for military supply operations, the inland travel time between the seaport and destinations becomes a primary selection criterion.

This paper argues that it is important to consider the correlations in historical road conditions across both time and space and their impact on SPOD selection and vehicle allocation. We aim to provide insight into the trade-offs involved in selecting SPOD locations for supply operations. The insight can support decision-makers currently evaluating the military distribution concepts in the Nordic military theatre. Due to the adverse weather conditions in the Nordics, the approach in this paper incorporates road network disruptions including their inherent correlations, in both time and space. Additional factors like demand and distribution capacity are also incorporated. The context is to facilitate defence plans in the Nordics, specifically a supply route system, under the given transportation network, weather, and road conditions.

The paper is structured in the following way: The first section below reviews the literature. Next, the problem is formulated together with the approach for creating timetables, which forms the basis for SPOD selection. A stochastic mixed integer linear program (MILP) is then formulated, applied, and compared to selection based on various criteria. Afterward, the results, managerial insights and practical implications are discussed. The final section offers conclusions.

Literature Review

The function of a seaport of debarkation (SPOD) includes reception, processing, staging, transit, storage, marshalling, and trans-shipment. To determine a seaport’s suitability for defence purposes, NATO highlights general considerations such as time, risk, distance, financial factors, as well as enabling capabilities like mobility, infrastructure, and supporting functions (NATO, 2022b). U.S. Joint Chiefs of Staff (2013b) point to factors for evaluating a seaport’s adequacy, including navigability, depth, berths, port equipment, explosive handling limitations, and throughput capabilities. Additional holistic factors, such as diversification, movement corridors, asset pools, and border mobility, are discussed in ongoing work by U.S. Transportation Command and the U.S. Army to optimize the distribution network across Europe, specifically for military deterrence (Ray & Chapman, 2023; US ARMY, 2024).

Although NATO doctrine is most relevant to the Nordic theatre, this paper also draws on U.S. military terminology, as the majority of existing military operations research in the field of logistics and distribution is rooted in U.S. doctrinal frameworks.

Port selection problems in the literature are closely related to general network optimization problems. Tran and Haasis (2015) explore the significance of network decisions in container liner shipping, including network design, which addresses the selection and combination of ports to establish the shipping operation’s infrastructure. Steven and Corsi (2012) examine factors affecting port attractiveness for containerized shipments based on shipper size, suggesting that larger shippers prioritize delivery speed over freight charges, implying the need for investments in port development for optimal returns. Parola et al. (2016) conducted a literature review on port competitiveness for the years 1983 to 2014, identifying key drivers like costs, infrastructure, location, as well as hinterland proximity and connectivity, finding that significant industry transformations alter the relative importance of traditional drivers. Similarly, Moya and Valero’s (2017) literature review on port choice identifies key criteria for both shipping lines and land decision-makers, emphasizing the impact of port authorities on competitiveness through infrastructure investment, efficiency improvements and hinterland accessibility.

Nagy and Salhi (2007), Drexl and Schneider (2013), and Schneider and Drexl (2017) offer extensive and referenced surveys of location-routing (LRP) literature. More recent research and additional variations are classified by Mara et al. (2021). Research with similar methodologies in adjacent contexts includes network problem formulations related to disaster relief and emergency response.

Notable surveys include Boonmee et al. (2017) on facility location problems related to emergency humanitarian logistics, Ahmadi-Javid et al. (2017) on healthcare facility location, the reviews of Dönmez et al. (2021) on humanitarian facility location problems under uncertainty, and Liu et al. (2021) on emergency response facility location in transportation networks.

Military theatre distribution is described by the U.S. Joint Chiefs of Staff (2000, 2017) as the processes of synchronizing all elements of the logistics system to deliver the “right things” to the “right place” at the “right time” to support the combatant commander. The term is embedded in NATO’s broader definition of logistics, where “logistic sustainment” refers to supplying a force and replacing losses and equipment attrition across the theatre to sustain combat power (NATO, 2020).

Similar to NATO’s Joint Logistics Support Network (2018), the U.S. Joint Chiefs of Staff (2000) outline that the physical components of the theatre distribution network include facilities in support of distribution operations, the transportation network (air, sea, rail, road) with ports and hubs, warehouses, supply depots, and pipelines. More specifically, theatre distribution is the flow of personnel, equipment, and materiel within the geographic theatre to meet the combatant commander’s mission.

Lykke (1989) emphasized that a successful military strategy requires a balance between ends, ways, and means (objectives, concepts and resources). In our context, military theatre distribution is a key element for providing the means (that is, the facilitation of logistics) to achieve the desired ends. Building on Lykke’s influential work, Jakobsen (2022a) applied causal theory to formulate military strategies, and discussed competing combinations of ways and means in order to achieve NATO’s objective of deterrence in the Baltics. The same logic informing NATO’s response in the Baltics can be extended to the Nordics. Moreover, enhancing NATO’s distribution capability in the Nordic theatre will likely increase operational and tactical freedom to address threats and opportunities, including in the Baltic theatre.

Since World War II, military operations research has tackled a wide range of problems, eventually becoming integral to logistics and resource-allocation planning (Fortun & Schweber, 1993). Theater distribution problems (TDPs) in the military (Burks et al., 2010; Craig et al., 2015; Crino, 2002; Crino et al., 2004; Hicks IV, 2019) are, in essence, the same type of problem as the one formulated in our paper. Related research within the TDP framework addresses network design (Lai & Tseng, 2022; Longhorn & Muckensturm, 2019; Ren et al., 2014; Toyoglu et al., 2011), deployment planning (Longhorn et al., 2022; Salmerón et al., 2009; Singgih & Lee, 2014), vehicle fleet sizing (Longhorn & Stobbs, 2021), ship loading (Longhorn et al., 2022), tactical distribution (Sebbah et al., 2013), forecasting (Lobo et al., 2019), and supply chain resilience (Zhao et al., 2011). The work on assessing the vulnerability of the routes in a TDP (Muckensturm & Longhorn, 2019) and port selection (Longhorn et al., 2021) have been the main inspiration for the approach in our paper.

For military facility location problems in particular, Karatas et al. (2018) argue for incorporating the stochastic and dynamic aspects of military operations more extensively and accurately to improve model realism, thereby providing better support for decision-makers. In our paper, we include uncertainty similar to approaches within stochastic programming, as described by Kall and Wallace (1994) and King and Wallace (2024).

Lium et al. (2009) investigated the significance of incorporating uncertain demand in a freight service network. While we adopt a similar approach by using the second stage as an evaluation mechanism for the strategic first stage decision (in our case, port selection), our handling of uncertainty does not include probabilistic scenarios, as will be explained below.

There is a discrepancy between military (NATO, 2018, 2022a; US Joint Chiefs of Staff 2013a) and operations research/management frameworks (Anthony, 1965) with regards to definitions of the “operational” and “tactical” planning levels. To avoid ambiguity, we will therefore refer to the tactical/operational decision-maker as the vehicle “dispatcher” and the strategic decision-maker as “DM”.

Problem Description and Model Formulation

The purpose of this paper is to provide DMs with insight into the trade-offs in selecting SPOD locations while taking the regional road and weather conditions into account. We seek to achieve this by addressing a military theatre distribution problem as a multi-depot location-routing problem with arc disruptions. The goal is to provide the DM with the best depot locations to achieve their objective. In our problem, the depots are a set of potential SPODs, with daily distribution of supplies via the inland transportation network to a set of final destinations, that is, area of operations.

We consider a state of heightened readiness setting where the main bodies of reinforcements and equipment have either arrived or are being moved to their respective destinations by other means, for instance rail, while the SPODs we now select will be part of a road-based main and alternate supply route (MSR/ASR) system.

Each destination is requesting supplies every day, with a limited safety stock of supplies that can be used between deliveries. The safety stock is limited due to capacity and security concerns. SPODs can be used interchangeably to supply the different destinations, with a limited number of vehicles for distribution.

Disruptions (road closures) can occur, blocking arcs in the network, which can lead to the need for vehicles be re-routed, and a SPOD cannot supply a destination in time periods where no path exists between them. In the latter case, vehicles must already be present at other SPODs and be dispatched from there if demand is to be met. Therefore, all vehicles must be assigned to a SPOD as a home base where they return after supplying any of the destinations. Assigning home bases in advance ensures that vehicles are more likely to be available at the respective SPODs when disruptions occur at the other SPODs. Similarly, vehicles that are already on route when disruptions occur cannot return to their home SPOD until connection is reestablished. The primary assumptions of the transportation problem description are summarized in Table 1 and discussed in the relevant section below.

Timetable creation with preserved correlations

The model in this paper requires timetables containing the quickest round trip travel times, meaning the time it takes to drive from a SPOD to a destination and back to the same SPOD. To incorporate disruptions, we apply historical traffic and road data for the region’s transportation network from 2016 to 2023 with the assumption that this data will continue to be relevant. The data contains instances of weather conditions (storm, avalanche, landslide, flood) that have led to roads being untraversable for some period on a given day. Once a road is disrupted, we assume it remains closed for the entire day (Table 1, assumption T8). The data spans a period long enough to capture correlations among the road disruptions. The data is kept in chronological order to preserve the dependence between all arc disruptions in both time and space. This dataset will be referred to as the “correlated” set, exemplified in Table 2.

Table 2

Correlated Set: Historical Data. Each row represents a day of the transportation network. Each column contains the status of an arc in the set of all arcs.

DAY	ROAD 1	ROAD 2	ROAD 3	ROAD 4
1
2			Closed
3	Closed			Closed
4	Closed	Closed	Closed	Closed
5		Closed
Sum	2	2	2	2

Let F be the set of all days between 2016 and 2023. For every day f ∈ F, let the directed road network graph G, which contains the set of all arcs A, be updated with travel times of every arc (i, j) ∈ A. The round trip travel time along the quickest path is then recorded. The process is illustrated in Figure 1. Table 3 shows an example of the recorded data.

Table 3

Round Trip Travel Timetable (Hours) Between SPODs (S1, S2) and Destinations (D1, D2). An infinite travel time means no path exists between the SPOD and the destination in the given day (of 24 hours).

DAY	S1–D1	S1–D2	S2–D1	S2–D2
1	19	22	23	21
2	19	22	27	21
3	19	∞	23	∞
4	∞	∞	∞	∞
5	24	22	23	21

Figure 1

Table 3 contains the data needed to create the input for our optimization model, as will be explained in the relevant section below. The table is also kept in chronological order to preserve correlations in disruptions across the network.

To assess the value of preserving correlations in disruptions, we generate an additional set of network states from the same road condition data, where each arc (i, j) ∈ A is treated independently. Consider a case where historical road condition data only contains the number of days each arc has been disrupted over a given timeframe, without details regarding timing or if disruptions coincide with other arc disruptions. We create a new dataset under this assumption, conducting random sampling without replacement in each column of the correlated set (Table 2). Table 4 shows the difference between the two sets. The columns in both sets contain the same number of disruptions, and the difference is that the disruptions have been randomly distributed across the new columns. This new dataset will be referred to as the “randomized” set.

Table 4

Since weather conditions are a major cause of road disruptions, the historical data shows a higher concentration of disruptions during seasons with harsh weather, while milder seasons exhibit few or none. The randomized set will lack this seasonal clustering, meaning that simultaneous closers, such as those on Day 4 in Table 4 are less likely to occur. Consequently, the randomized set tends to be less impactful compared to the correlated set, as disruptions are less concurrent and more evenly dispersed across the seasons.

Stochastic mixed integer linear program formulation

We formulate a stochastic MILP to select the optimal set of SPODs that facilitate the sustainment of supply levels at every destination over all time periods, given limited distribution resources and a limited safety stock at each destination. The stochastic MILP uses timetables as input and selects SPODs based on sustainment aspects.

Once the strategic decision of opening SPODs (x) has been made, distribution of supplies has to be handled by a finite number of vehicles hν that can be assigned to an open SPOD as a home base (w). Next, the dispatcher runs the supply operation over an extended time horizon, detailed after the stochastic MILP definitions in Table 6.

The model does not rely on probabilistic scenarios, as is common in stochastic programs. Instead, it deterministically selects SPODs to minimize the total supply operation cost over a time horizon spanning multiple years, effectively treating it as infinite. This approach also preserves disruption correlations across the network in both time and space, which would be difficult to achieve through traditional scenario generation.

Each destination d ∈ D is requesting supply deliveries every time period k ∈ K, measured in number of vehicles q_k,d. The number of vehicles dispatched from s ∈ S to d ∈ D in time period k ∈ K is denoted y_k,s,d.

If the total number of vehicles dispatched to a destination is less than demanded, safety stock can be used, creating a backlog. The variable i_k,d is the backlog at destination d at the end of time period k, measured in number of vehicles. Backlog is limited to $h_d^i$ at destination d. All safety stocks are full in the first time period, and it is beneficial to keep the inventories filled up. Therefore, a time penalty cⁱ is given for every vehicle in backlog per time period. If it is impossible to provide enough supply with the dispatched vehicles, and safety stock runs out, variable u_k,d records the difference between supply and demand at each destination, so the model is always feasible. The penalty for not meeting demand is c^u per vehicle.

The stochastic MILP uses parameters derived from the timetable example described in Table 5. For constraint (10) and (12), the binary parameter b_k,s,d,n is 1 only if a vehicle dispatched in time period k will spend n time periods to drive from SPOD s to destination d and back to the same SPOD. This parameter also contains waiting time, meaning we add 24 hours for every subsequent day with infinite travel time (when no paths exist). Consider an example from Table 3, where a dispatched vehicle from S1 to D2 in Day 3 would spend 24 + 24 + 22 = 70 hours before returning to its SPOD because no path exists for two subsequent days. This means b_k,s,d,n = 1 between s = S1 and d = D1 for all four time periods of Day 3. Since n is a whole number, we round it up to 18 time periods.

Table 5

Table 6

Stochastic Mixed Integer Linear Program.

SYMBOL	DESCRIPTION
Sets
S	Set of SPODs indexed by s
D	Set of destinations indexed by d
F	Set of all days indexed by f (later split into time periods)
K	Set of time periods of equal time duration indexed by k
N	Set of whole numbers {0, …, |N|} indexed by n
Parameters
tk,s,d	Round trip travel time between s and d at time k excluding waiting time
bk,s,d,n	$\{\begin{array}{cc}1,& \mathrm{\text{if }}n=\mathrm{\text{time}} \mathrm{\text{periods }}\mathrm{\text{are }}\mathrm{\text{required }}\mathrm{\text{from }}s \mathrm{\text{to }}d \mathrm{\text{to}} s \mathrm{\text{at }}\mathrm{\text{time }}k\\ 0,& \mathrm{\text{otherwise}}\hfill \end{array}$
ek,s,d	$\{\begin{array}{cc}1,& \mathrm{\text{if }}\mathrm{\text{a }}\mathrm{\text{path }}\mathrm{\text{exists }}\mathrm{\text{between }}s \mathrm{\text{and }}d \mathrm{\text{at }}\mathrm{\text{time }}k\\ 0,& \mathrm{\text{otherwise}}\hfill \end{array}$
ci	Time penalty for safety stock backlog (per vehicle per time period)
cw	Time cost of assigning a vehicle to a SPOD
cu	Time penalty for not meeting demand (per vehicle)
$h_d^i$	Maximum safety stock capacity at destination d
hx	Maximum number of SPODs allowed to be opened
hν	Maximum number of vehicles available for assignment
M	Arbitrarily large value ≥ hν (for binary constraints)
qk,d	Number of vehicles requested at destination d at time k (demand)
Variables for the Strategic Decision-Maker
xs	$\{\begin{array}{c}1, \mathrm{\text{if }}\mathrm{\text{SPOD}} s \mathrm{\text{is}} \mathrm{\text{opened}}\\ 0, \mathrm{\text{otherwise}} \hfill \end{array}$
ws	Number of vehicles assigned to SPOD s as home base (integer)
Variables for the Dispatcher
yk,s,d	Number of vehicles dispatched from SPOD s to destination d at time k
vk,s,d,n	Number of vehicles returning to s from d with n periods remaining at time k
ik,d	Safety stock backlog at destination d at time k
uk,d	Unmet demand (vehicles) at destination d at time k

Parameter t_k,s,d is used in the model objective function, where all cases of infinite travel time in Table 5 are replaced with the travel time of the first subsequent day where a path is available. We exclude waiting time in the objective function because we assume our vehicle dispatcher only cares about the actual driving times as long as demand is met. The only drawback of waiting times is that vehicles are unavailable for dispatch for an extended time.

1

$min{\displaystyle \sum _{s\in S}}{c}^w\cdot w_s + {\displaystyle \sum _{k\in K}}{\displaystyle \sum _{s\in S }}{\displaystyle \sum _{d\in D}}{t}_{k,s,d} \cdot y_{k,s,d} + {\displaystyle \sum _{k\in K}}{\displaystyle \sum _{d\in D}}[c^u\cdot u_{k,d} + c^i \cdot i_{k,d}]$

Subject to:

2

${\displaystyle \sum _{d\in D}}{\displaystyle \sum _{n\in N}}{v}_{k,s,d,n} \le w_{\mathrm{\text{s}}} \forall k\in K, s\in S$

3

${\displaystyle \sum _{s\in S}}{w}_s \le h^v$

4

${\displaystyle \sum _{d\in D}}{y}_{k,s,d} \le {\displaystyle \sum _{d\in D}}{v}_{k,s,d,n} \forall k\in K, s\in S, n = 0$

5

${\displaystyle \sum _{\mathrm{\text{s}}\in \mathrm{\text{S}}}}{y}_{k,s,d} \ge q_{k,d} + i_{d,k-1} - i_{k,d} - u_{k,d} \forall k\in K|k \ne 0, d\in D$

6

${\displaystyle \sum _{\mathrm{\text{s}}\in \mathrm{\text{S}}}}{y}_{k,s,d} \ge q_{k,d} - i_{k,d} - u_{k,d} k = 0,\forall d\in D$

7

$x_s \le w_s \forall s\in S$

8

$w_s \le M\cdot x_s \forall s\in S$

9

${\displaystyle \sum _{s\in S}}{x}_s \le h^x$

10

$v_{k,s,d,n} = v_{k-1,s,d,n+1} + y_{k,s,d}\cdot b_{k,s,d,n} \begin{array}{c}\forall k\in K|k \ne 0,s\in S,\\ d\in D,n\in N|n \ne \left|N\right|\end{array}$

11

${\displaystyle \sum _{d\in D}}{v}_{k,s,d,n} = w_s - {\displaystyle \sum _{d\in D}}{y}_{k,s,d} k = 0,\forall s\in S, n = 0$

12

$y_{k,s,d} \cdot b_{k,s,d,n} \le v_{k+1,s,d,n-1} \begin{array}{c}\forall k\in K|k \ne \left|K\right|, s\in S,\\ d\in D, n\in N|n \ne 0\end{array}$

13

$i_{k,d} \le h_d^i \forall k\in K, d\in D$

14

$y_{k,s,d} \le M\cdot ({\mathrm{\text{e}}}_{k-1,s,d}+e_{k,s,d}) \forall k\in K|k \ne 0, s\in S, d\in D$

15

$v_{k,s,d,n} = 0 \forall k\in K, s\in S, d\in D, n = \left|N\right|$

16

$u_{k,d},v_{k,s,d,n},w_s,y_{k,s,d} \ge 0 \forall k\in K, s\in S, n\in N, d\in D$

The stochastic MILP objective (1) seeks both to minimize the cost of assigning vehicles to SPODs, which inherently determines which SPODs are opened (at no additional cost), and includes the total travel time for all dispatched vehicles between SPODs and destinations across all time periods, along with penalties for unmet demand and for not replenishing safety stock. These elements serve as an approximation of expected future costs. The constraints are explained in Table 7.

Table 7

Stochastic Mixed Integer Linear Constraint Explanations.

(2)	The sum of vehicles in transit between SPOD s and any destination d in either direction at any time period cannot exceed the number of vehicles assigned to SPOD s as a home base ws.
(3)	The sum of assigned vehicles cannot exceed the number of vehicles available for assignment.
(4)	Vehicles dispatched from SPOD s to any destination d in time period k cannot exceed the available vehicles present at SPOD s (vehicles with n = 0).
(5)	The number of vehicles dispatched to destination d in time period k must be sufficient to meet demand. Any deficit will add to the backlog, while any excess will replenish the safety stock. If dispatched vehicles and safety stock are insufficient, the unmet demand is recorded and penalized in the objective.
(6)	Constraint 5 is also valid in the first time period and there is no backlog at the start of the first time period.
(7)	Vehicles can only be assigned to SPODs that are open.
(8)	Unused SPODs remain closed.
(9)	The number of SPODs opened cannot exceed the number of SPODs allowed.
(10)	For each time period k, we keep track of the number of vehicles in transit between SPOD s and destination d as well as the number of remaining time periods n each vehicle has until returning to their home SPOD s. If vehicles are dispatched in time period k the parameter b add the vehicles to the correct vehicle tracking variable ν.
(11)	Vehicles available at SPOD s in the first time period k = 0 are all vehicles assigned to SPOD s except vehicles dispatched from SPOD s in the first time period.
(12)	Ensures that no vehicles are on route in the first time period, except those being dispatched.
(13)	The safety stock backlog (use) cannot exceed the safety stock capacity.
(14)	Whenever SPOD s becomes isolated from destination d, it can be beneficial to dispatch vehicles even though they cannot return to SPOD s without waiting for a path to open. Therefore, if SPOD s becomes isolated from destination d in time period k, and there was a path in k–1, we assume vehicles are still able to reach the destination, however, they have to wait for the path to open in order to return to the SPOD. If there is no path for multiple time periods in a row, vehicles cannot reach the destination other than in the first time period of the sequence. In other words, vehicles can only be dispatched from s to d if a path exist in time period k or in k–1. Vehicles need n time periods to return to SPOD s (where bk,s,d,n = 1).
(15)	Technical constraint to stop vehicles from appearing in |N|.
(16)	Non-negativity constraints

Data

This section describes the input data used to optimize SPOD selection. We extracted the road networks of Finland, Norway, and Sweden from OpenStreetMap (Boeing, 2017; OSM, 2017). Historical road-condition data from the Norwegian Public Roads Administration, the Swedish Transport Administration, and Fintraffic (2016–2023) were used to generate travel timetables. The final data set F covers 2,683 days and includes approximately 40,000 disruption cases on 1,454 distinct arcs, as shown in Figure 2. Due to inherent limitations and inconsistencies in the source datasets, manual filtering was necessary to extract disruption data, and as a result, the set may contain some inaccuracies.

Figure 2

Figure 3 shows potential SPODs located along the Norwegian and Swedish coasts facing the Norwegian and North Sea, based on the extensive mapping work by Viste and Birkemo (2023). Destinations are arbitrarily chosen nodes in Finland and Northern Norway.

Figure 3

Ofotfjorden, the fjord on which the Norwegian city of Narvik is located, and Trondheimsfjorden (the fjord on which the Norwegian city of Trondheim is located), and Göteborg in Sweden have been marked as key areas for defence logistics in the region (Johnsen & Kristiansen, 2022). This set of SPODs will be used as a benchmark for comparing SPOD selections in the computational results. Table 9 summarizes network assumptions.

Correlations in the travel timetables are shown in Figure 4, using the destinations Alta and Lappeenranta as examples. The correlations occur due to network sparsity resulting in shared arcs, and correlations in road conditions between arcs in geographical proximity. Increases in travel times primarily occur due to disruptions in proximity of the SPOD or the destination, but rarely in between, likely due to missing data relating to central Sweden, as seen in Figure 2.

Figure 4

In Figure 4, a correlation of one between Oslo and Göteborg means that almost all days in the dataset that have an increased travel time between Oslo and Alta coincide with an increase between Göteborg and Alta. Positive correlations are most prominent, and the results imply that geographical proximity of a SPOD increases positive correlations in travel times. Exceptions are found in the cases of Harstad, Narvik, and Tromsø, where, despite the short distance between Harstad and Narvik, the correlation is weaker than between Harstad and Tromsø due to certain cases of disruptions affecting Narvik alone.

Computational Results

In this chapter, we extract managerial insight from the problem of finding the optimal set of SPODs to achieve the DM’s objective. The SPOD set {Narvik, Trondheim, Göteborg} denoted “Benchmark” will be used for comparing SPOD selections derived from different considerations regarding travel times, as well as the solution from the stochastic MILP. Software used is Python 3.10 and Gurobi (2023). Computation was performed on an AMD EPYC 7543P 32-core processor (2.79 GHz) with 64.0 GB of RAM, running the MSW11 Enterprise operating system.

Selection based on travel times

Table 10 contains results for a subset of potential SPODs. The deterministic travel time, m1, represents travel under perfect road conditions. The average travel time across all days with an available path is denoted m2, while m3 denotes the maximum observed combination of waiting and travel time. Figure 5 shows that SPODs with low average travel times (those in the High North) are also more prone to road disruptions that reduce or remove connectivity, resulting in large m3 values.

Table 10

SPOD Round Trip Travel Times (in Hours). Deterministic travel time: m1; average travel time when paths exist: m2; maximum recorded waiting and travel time: m3. Bold font indicates the best performance in one of the criteria. SPODs are sorted by latitude.

PORT	DESTINATIONS
	ALTA			LAKSELV			SALLA			KAJAANI			LAPPEENRANTA
	m1	m2	m3	m1	m2	m3	m1	m2	m3	m1	m2	m3	m1	m2	m3
Tromsø	10	11	62	15	15	67	17	17	65	21	21	69	30	30	78
Harstad	14	15	66	19	19	71	17	18	69	21	21	73	29	29	82
Narvik	13	13	64	16	17	70	15	16	67	19	19	71	27	27	80
Bodø	25	25	102	27	27	105	21	21	98	21	21	98	29	29	106
Mo i Rana	24	24	34	26	26	36	20	20	30	21	21	31	28	29	38
Trondheim	33	33	37	34	35	36	28	28	31	29	29	31	37	37	39
Tjeldbergodden	36	36	40	38	38	40	32	32	34	32	32	34	40	40	43
Oslo	39	39	44	41	41	42	34	34	37	35	35	37	43	43	45
Göteborg	39	39	45	41	41	42	35	35	37	35	35	37	43	43	46

Figure 5

Depending on the DMs priorities, we end up with different sets of SPODs, as shown in Table 11.

Table 11

SPOD Selection Criteria and Results.

NAME	SPOD SELECTION CRITERION	SPOD SELECTED	DESTINATIONS SUPPLIED
Benchmark	Marked as key areas for defence logistics in the region by the Nordic Chiefs of Defence.	Narvik Trondheim Göteborg	Not specified
M1	Lowest deterministic travel time to at least one of the destinations, i.e. travel time under perfect road conditions.	Tromsø Narvik	Alta and Lakselv Salla, Kajaani and Lappeenranta
M2	Lowest average travel time (when path exists) to at least one of the destinations across all scenarios in the correlated set.	Tromsø Narvik	Alta and Lakselv Salla, Kajaani and Lappeenranta
M3	Lowest recorded maximum waiting and travel time to at least one of the destinations across all scenarios in the correlated set.	Mo i Rana	All destinations

The selection based on M1 is located towards the bottom right of Figure 5, and happens to be the same as M2 in our data. Since there are no disadvantages to having more SPOD options, and the benchmark contain three SPODs, we will consider the set {Tromsø, Narvik, Harstad} to represent M1 and M2. The selection based on M3 is located in the far left of Figure 5. Although only Mo i Rana is selected, we will consider the set {Mo i Rana, Trondheim, Tjeldbergodden} as M3.

Stochastic Mixed Integer Linear Program Results

To evaluate the performance of the different SPOD selections under correlated disruptions, we conduct a numerical example. The model is run with each SPOD selection in Table 11 and optimal vehicle allocation, with parameter values according to Table 12. We also run the model (MILP R) for the optimal SPOD selection when using the randomized set of disruptions (as explained in Table 4). Finally, we include the optimal solution for the correlated set (MILP). The model is run for two demand parameters (q_k,d), namely 25 and 30, to each destination d ∈ D in each time period k ∈ K, meaning a total daily demand of 500 and 600, respectively.

Penalties for backlog (cⁱ) and vehicle assignment (c^w) are small to encourage replenishment and avoid wasteful assignment, without being drivers of the results. Meeting demand is prioritized, and we therefore assume a high time penalty (c^u) of five days of travel time per unit of unmet demand. Each destination has safety stock ($h_d^i$) of 200, which equals 2 days of demand. Safety stock is assumed fixed due to available storage facilities which cannot be changed in the short term.

Figure 6 shows the average unmet demand per day across the entire time horizon for each SPOD selection. Selection based on the lowest maximum recorded travel time (M3) results in the most delivery failures because the average travel times are too long for the vehicles to handle all demand, in spite of disruptions having little effect.

Figure 6

In our case, selecting SPODs based on the randomized dataset (MILP R) leads to the same SPODs as in a deterministic case (M1). This means that the value of options (e.g., Mo i Rana) is concealed when not considering correlations in the disruptions. While the difference in average vehicle deficit between the MILP R and MILP solutions is negligible, the value of the option becomes clear when considering recorded weekly vehicle deficits. Figure 7 highlights the worst-performing weeks for each selection and shows that the MILP solution performs significantly better.

Figure 7

The model also allows us to observe how changing the season and the level of demand leads to changes to optimal SPOD selection, vehicle allocation, and vehicle usage. We measure the latter in how many vehicles travel between the SPODs and the destinations across the time periods: $\frac{{\sum }_d{\sum }_k{y}_{k,s,d}}{\theta } \forall s\in S$ where $\theta = {\sum }_k{\sum }_s{\sum }_d y_{k,s,d}$ (the total number of vehicles dispatched).

Since most road disruptions have occurred between January and March, we also run the model over these months specifically to assess how SPOD selections would perform during winter season.

Figure 8 illustrates shifts in vehicle allocation and usage at different demand levels, particularly as demand approaches delivery capacity. Furthermore, the southernmost SPOD (Mo i Rana) is affected by the fewest disruptions and is therefore increasingly preferred during winter. Our results show that both season and the relationship between supply and demand affect SPOD selection, optimal vehicle allocation and usage.

Figure 8

In spite of good deterministic performance (Table 10), Narvik loses vehicles in the optimal solution during the winter months and as demand increases due to disruptions along the European route E10, the preferred road between Narvik and destinations in Finland. Figure 9 illustrates how disruptions along E10 requires re-routing to the north in order to reach Finland.

Figure 9

Our dataset contains historical disruptions on some arcs along E10 (see Figure 2). One or more of these arcs are disrupted in 248 (9.2%) days, of which 172 are during winter. Without the disrupted days, the model strictly prefers SPODs Narvik and Tromsø for all levels of demand, safety stock, and penalties (see Figure 10).

Figure 10

This means that the remaining 90% of historical network data have no impact on SPOD selection, and no significant impact on vehicle allocation compared to selection based on deterministic travel times. Similarly, increasing safety stock at the destinations makes the deterministic solution optimal because disruptions have no impact as long as the backlog can be refilled in periods without disruptions.

Discussion

This paper has sought to provide insight into the trade-offs in selecting SPOD locations while accounting for regional weather conditions.

Results from the stochastic MILP show that decision makers must be aware of the existence of weather- and network-induced correlations, because these correlations affect travel times, delays, and overall readiness. By extending on existing military port selection literature (Longhorn et al., 2021), our findings suggests that the DMs will lose important SPOD options by relying solely on deterministic travel times. Similarly, disregarding correlations in time and space can obscure potential SPOD options, as seen with the exclusion of Mo i Rana under randomized weather conditions.

Furthermore, the results show that the risk of lengthy delays varies significantly between SPOD options. While SPODs in the high north have shorter travel times, they are more vulnerable to disruptions due to harsh weather and network sparsity, with the road E10 being a driver of the results, implying its strategic importance. Thus, our approach complements that of Muckensturm and Longhorn (2019) by providing an additional way of assessing route vulnerability.

Additionally, we have found that evaluating SPODs solely based on travel time correlations is insufficient to determine whether they provide redundancy as backup options or if they tend to be concurrently unavailable. In our case, the travel times for Tromsø and Narvik are strongly correlated (Figure 4) – yet both SPODs are included in the optimal solution. This is because the SPODs have short deterministic travel times, and also because they partially serve as backups for each other. In contrast, while Narvik and Harstad exhibit similar correlations, Harstad is not included in the optimal solution because Narvik, in the majority of instances, consistently performs better.

In line with previous research (Bardal, 2018), expected travel times in the MILP increase during winter due to road closures. The practical implication of this may be reduced readiness. Safety stock near destinations can mitigate these disruptions, but it may also introduce additional costs and operational risks not discussed here.

In practice, rail has proved to be a critical mode of transport in the most recent war in Europe (Skoglund et al., 2022). While the key Nordic SPODs for defence logistics all indicate reliance on railway lines (Johnsen & Kristiansen, 2022), our findings suggest strategic value in road-based alternatives. However, the impact of railways access on SPOD selection, particularly in light of recent rail closures between Norway and Sweden (Nilsen, 2024; NRK.no, 2025), requires further research.

In addition to NATO doctrine (2022b), the DM must recognize that optimizing SPOD selection involves not only considerations regarding geographic location and network connectivity but also the expected demand and the positioning of available distribution resources in the event of disruptions. The Nordic region is already subject to harsh weather (Bardal, 2017), and with the intensification of weather conditions that climate change is expected to bring, the subset of days that drive the results, currently at <10%, may increase. Additional and increasing advantages are therefore likely to be obtained both by developing potential SPODs and by considering re-allocating vehicles based on season, forecasts and expected future demand.

Lastly, we emphasize that the optimal set of SPODs is likely to change when assumptions are adjusted. Most notably, factors like supply requests at other destinations, access to rail and ferries, new bridges, interim facility requirements, supply arrivals via mainland Europe and adversarial actions, could significantly impact SPOD selection.

Conclusion

This work offers a tool for the improvement of the military distribution network in the Nordic region. The purpose is to provide DMs with managerial insight into the trade-offs of SPOD selection in the Nordic region. We formulate a stochastic MILP with the goal of finding the best set of SPODs and their respective vehicle allocation, capable of meeting demand while minimizing travel time of road-based transports.

The historical road conditions from the region are relevant when considering travel times between SPODs and respective destinations over time. Furthermore, incorporating stochastic disruptions in a way that preserves correlations in both time and space significantly affects SPOD selection and resource allocation.

Moreover, the inherent characteristics of the distribution network in the Nordics can alter the optimal SPOD selection depending on several factors, including geographic location, correlation in road disruptions and vehicle availability, trade-offs regarding expected and maximum recorded travel times, likelihood of delays and their significance, expected demand and seasonal changes in network connectivity and disruption patterns.

Over time, the model suggested in this paper may contribute to improvements in logistical performance, readiness, and military sustainability, compared to the existing plans and current distribution network. The methodological approach presented in this paper, together with the managerial insights, can be used to provide support to DMs currently evaluating military distribution concepts relevant to the Nordic military theatre. This paper and following work should therefore be considered by regional military entities as a tool serving the development of new, and revisions of the region’s current defence plans.

Future Work

The planning of the reception, staging and onward movement (RSOM) process remains essential to facilitating the operations of NATO in the Nordics. Managing multi-modal transportation operations of main bodies of reinforcements from arriving PODs to their respective destinations is a distribution problem with specific characteristics, requiring a different approach to that of the problem discussed in this paper.

The Nordic transport network is also vulnerable to disruptions beyond severe weather. Given the region’s proximity to a potential adversary, future models should incorporate both naturally occurring disruptions and deliberate interdictions in a single stochastic framework.

Competing Interests

The authors have no competing interests to declare.