In this paper, we focus on how cost allocation can be used as a means to create incentives for collaboration among companies, with the aim of reducing the total transportation cost. The collaboration is assumed to be preceded by a simultaneous invitation of the companies to collaborate. We make use of concepts from cooperative game theory, including the Shapley value, the Nucleolus and the EPM, and develop specific cost allocation mechanisms aiming to achieve large collaborations among many companies. The cost allocation mechanisms are tested on a case study that involves transportation planning activities. Although the case study is from a specific transportation sector, the findings in this paper can be adapted to collaborations in other types of transportation planning activities. Two of the cost allocation mechanisms ensure that any sequence of companies joining the collaboration represents a complete monotonic path, that is, any sequence of collaborating companies is such that the sequences of allocated costs are non-increasing for all companies.

Transportation, together with transportation planning for goods, provides good conditions for economic growth and is a natural part of modern society. However, transportation has negative side effects, including emissions and traffic congestion. A freight forwarder may consolidate shippers’ goods in order to reduce some of the negative side effects, thus reducing emissions and/or congestion as well as operational costs. The negative side effects as well as operational costs can be further reduced if a number of freight forwarders cooperate and consolidate their collective goods flows. Consolidation refers to the process of merging a number of the freight forwarders’ shipments of goods into a single shipment. In this case, the freight forwarders are cooperating with competitors (the other freight forwarders).

Fair cost allocations are important for establishing and maintaining cost-efficient cooperation among competing stakeholders. Cooperative game theory defines a number of criteria for fair cost allocations and the problem associated with the decision process for allocating costs is referred to as the cost allocation problem. In this thesis, cooperative game theory is used as an academic tool to study cooperation among stakeholders in two transportation planning applications, namely 1) the distribution of goods bound for urban areas and 2) the transportation of wood between harvest areas and industries.

In transportation planning application 1, there is a cooperation among a number of freight forwarders and a municipality. Freight forwarders’ goods bound for an urban area are consolidated at a facility located just outside the urban area. In this thesis, operational costs for distributing the goods are assessed by solving vehicle routing problems. Common methods from cooperative game theory are used for allocating the operational costs among the freight forwarders and the municipality. In transportation planning application 2, forest companies cooperate in terms of the supply and transportation of common resources, or more specifically, different types of wood. Each forest company has harvest areas and industries to which the wood is transported. The resources may be bartered, that is, the forest companies may transport wood from each other’s harvest areas.

In the cooperative game theory literature, the stakeholders are often treated equally in the context of transportation planning. However, there seems to be a lack of studies on cooperations where at least one stakeholder differs from the other stakeholders in some fundamental way, for instance, as an initiator or an enabler of the cooperation. Such cooperations are considered in this thesis. The municipality and one of the forest companies are considered to be the initiators in their respective applications.

Five papers are appended to this thesis and the overall aim is to contribute to the research into cooperative transportation planning by using concepts from cooperative game theory to develop methods for allocating costs among cooperating stakeholders. The purpose of this thesis is to provide decision support for planners in the decisionmaking process of transportation planning to establish cost-efficient and stable cooperations.

Some of the main outcomes of this thesis are viable and practical methods that could be used in real-life situations to allocate costs among cooperating stakeholders, as well as support for decisionmakers who are concerned with transportation planning. This is done by demonstrating the potential of cooperation, such as cost reduction, and by suggesting how costs can be allocated fairly in the transportation planning applications considered. Lastly, a contribution to cooperative game theory is provided; the introduction of a development of the equal profit method for allocating costs. The proposed version is the equal profit method with lexicography, which, in contrast to the former, guarantees to yield at most one solution to any cost allocation problem. Lexicography is used to rank potential cost allocations and the unambiguously best cost allocation is chosen.  

When a set of players cooperate, they need to decide how the collective cost should be allocated amongst them. Cooperative game theory provides several methods or solution concepts, that can be used as a tool for cost allocation. In this note, we consider a specific solution concept called the Equal Profit Method (EPM). In some cases, a solution to the EPM is any one of infinitely many solutions. That is, it is not always unique. This leads to a lack of clarity in the characterization of the solutions obtained by the EPM. We present a modified version of the EPM, which unlike its precursor ensures a unique solution. In order to illustrate the differences, we present some numerical examples and comparisons between the two concepts.

A freight forwarder may consolidate its goods transportations in order to achieve a more efficient operation. When goods transportations are consolidated, they may reduce operational costs, e.g. labor and fuel. This can be further improved if a number of freight forwarders cooperate and consolidate their collective goods transportations, i.e. it is a cooperation between competitors, a coopetition. In order to maintain the cooperation, a suitable business model, in which fair cost allocations plays an important role is essential. The potential by cooperating is not exclusive to freight forwarders, but in fact, any type of goods transportation planning may benefit from cooperation. In this thesis, cooperative game theory is used as an academic tool to study cooperation between stakeholders in different transportation planning applications. Cooperative game theory defines a number of criteria for fair cost allocations.

In Paper 1, the role of the municipality as an enabler of a cooperation between fictitious freight forwarders in an urban area, is studied. In this case, the municipality acts as a stakeholder with unusual characteristics. It is shown that a stable cooperation can be achieved if the municipality is willing to carry some of the cost. This cost is specified and discussed in Paper 1. The results of Paper 2 contribute to game theory by introducing a further development of a cost allocation method. Some small numerical examples are presented in order to illustrate the resulting changes. In Paper 3, the process of establishing a cooperation is studied, where the stakeholders, in this case forest companies, join the cooperation sequentially. Who will join and in what order, is not predetermined. It is shown that a stable cooperation can be achieved despite the uncertainty. This is done by using the cost allocation methods presented.