Freight transport network design using particle swarm optimisation in supply chain–transport supernetwork equilibrium

This paper presents a discrete network design problem for optimally designing freight transport network in terms of the efficiency of supply chain. Modelling is undertaken within the framework of mathematical programmes with equilibrium constraints, which first incorporates both supply chain and transport networks explicitly. The upper level determines the best set of actions for transport network improvement, while the lower-level decision is based on a supply chain–multimodal transport supernetwork equilibrium. New variants of particle swarm optimisation are developed to approximately solve the upper level. Numerical tests reveal their superior performance and the effective freight transport-related actions.     

Dynamic electric power supply chains and transportation networks: An evolutionary variational inequality formulation

In this paper, we develop a static electric power supply chain network equilibrium model with known demands and establish the equivalence between the model and a transportation network equilibrium model with fixed demands over an appropriately constructed supernetwork. This equivalence yields a new interpretation of electric power supply chain network equilibria in path flows. We then exploit this equivalence to propose a dynamic electric power supply chain network model in which the demand varies over time using an evolutionary variational inequality formulation. Finally, we demonstrate how numerical dynamic electric power supply chain network problems can be solved utilizing recently obtained theoretical results in the unification of evolutionary variational inequalities and projected dynamical systems.     

Evolutionary variational inequalities and applications to complex dynamic multi-level models

In this paper we consider a supply chain network model with three tiers of decision-makers (manufacturers, retailers, and consumers) in the case when prices and shipments are evolving on time. Moreover, we assume that excesses of production and excesses of demand of the commodity are present. For such a framework we furnish, using the infinite dimensional duality theory, the equilibrium conditions for the representatives of each tier of the supernetwork, the time-dependent variational formulation governing the complete supply chain supernetwork, and we provide some existence theorems and a numerical example.     

Dynamics and equilibria of ecological predator-prey networks as nature’s supply chains

In this paper, we develop a dynamic network model of ecological food webs and prove that the set of stationary points of the projected dynamical system coincides with the set of solutions of a variational inequality governing the equilibrium of predator-prey networks. We also establish the equivalence between the ecological models and supply chain network equilibrium models and highlight the connections to spatial price equilibrium problems. We propose an algorithmic scheme, provide convergence results, and apply it to a food web drawn from a fisheries application.This paper is a contribution to the interdisciplinary supply chain network literature.     

The equilibrium of closed-loop supply chain supernetwork with time-dependent parameters

In this paper, we develop a closed-loop supply chain supernetwork model including suppliers, manufacturers, retailers and consumers at demand market, in which the demand for product is seasonal (t), and the sensitivity (w) of demand to price is another key factor which effects consumers’ demand. Moreover, the manufacturers invest the reverse distribution channel for incenting consumers to return more used products. Based on the Evolutionary Variational Inequalities (EVI) theory and Projected Dynamical Systems (PDS), the equilibrium condition of closed-loop supply chain is formulated, and the model is verified reasonably by numerical example.     

A freight transport optimization model for integrated network,service, and policy design

This paper presents a freight transport optimization model that simultaneously incorporates multimodal infrastructure, hub-based service network structures, and the various design objectives of multiple actors. The model has been calibrated and validated using real-life data from the case study of hinterland container transport of the Netherlands, where CO₂ pricing, terminal network configuration, and hub-service networks are chosen as the design measures. Policy packages combining multiple types of policies show better network performance as compared with the optimal performance resulting from a single policy type. This illustrates the value of incorporating multiple types of policies simultaneously in freight transport optimization.     

A strategic model of port-hinterland freight distribution networks

This paper presents a strategic model for port-hinterland freight distribution networks. The approach utilizes a combination of a multi-objective optimization model to estimate locations and networks of distribution centers and an assignment model that recognizes distributed service level preferences. Our example application concerns the European continent and is transferable to other regions. The model calibration is able to explain the European port-hinterland distribution structures satisfactorily. We compute novel performance measures that take into account port-hinterland distribution structures. The measures include port-hinterland transport cost, port-hinterland transport time, and distribution center-hinterland transport time. These measures can provide inputs for port-connectivity studies.     

Embedding economies of scale concepts for hub network design

We explore the idea of endogenous hub location on a network. In contrast to much of the literature, we propose that hub networks may emerge naturally out of a set of assumptions and conditions borrowed from equilibrium traffic assignment. To this end, we focus on applying a nonlinear cost function that rewards economies of scale on all network links. A model is presented and implemented in a GIS environment using both a 100-node intercity matrix and several synthesized interaction matrices. We compare solutions for different assumptions about network costs, and visualize the results. We find that under discounted conditions, network flow is re-routed to take advantage of the cost savings for amalgamation and that several cities emerge as centers through which large amounts of flow pass. Larger cities such as Los Angeles, New York and Chicago serve gateway functions. We also find that smaller cities such as Oklahoma City, Pittsburgh, Indianapolis, and Knoxville serve major gateway functions because of their locational advantages. Our paper should be of interest to the planner of a surface transportation system, or those interested in nodal concepts such as gateways and transport geography. Results are discussed in light of hub and spoke networks and suggestions are made for future research.     

Supply chain network competition in price and quality with multiple manufacturers and freight service providers

In this paper, we develop both static and dynamic supply chain network models with multiple manufacturers and freight service providers competing on price and quality. The manufacturers compete with one another in terms of price and quality of the product manufactured, whereas the freight service providers compete on price and quality of the transportation service they provide for multiple modes. Both manufacturers and freight service providers maximize their utilities (profits) while considering the consequences of the competitors’ prices and quality levels. Bounds on prices and quality levels are included that have relevant policy-related implications. The governing equilibrium conditions of the static model are formulated as a variational inequality problem. The underlying dynamics are then described, with the stationary point corresponding to the variational inequality solution. An algorithm which provides a discrete-time adjustment process and tracks the evolution of the quality levels and prices over time is proposed, and convergence results given. Numerical examples illustrate how such a supply chain network framework, which is relevant to products ranging from high value to low value ones, can be applied in practice.     

A supply chain network equilibrium model

In this paper, an equilibrium model of a competitive supply chain network is developed. Such a model is sufficiently general to handle many decision-makers and their independent behaviors. The network structure of the supply chain is identified and equilibrium conditions are derived. A finite-dimensional variational inequality formulation is established. Qualitative properties of the equilibrium model and numerical examples are given.     

Supply chain network design under profit maximization and oligopolistic competition

In this paper, we model the supply chain network design problem with oligopolistic firms who are involved in the competitive production, storage, and distribution of a homogeneous product to multiple demand markets. The profit-maximizing firms select both the capacities associated with the various supply chain network activities as well as the product quantities. We formulate the governing Nash–Cournot equilibrium conditions as a variational inequality problem and identify several special cases of the model, notably, a generalization of a spatial oligopoly and a classical oligopoly problem to include design capacity variables. The proposed computational approach, which is based on projected dynamical systems, fully exploits the network structure of the problems and yields closed form solutions at each iteration. In order to illustrate the modeling framework and the algorithm, we also provide solutions to a spectrum of numerical supply chain network oligopoly design examples.This paper makes a contribution to game theoretic modeling of competitive supply chain network design problems in an oligopolistic setting.     

Integration of inland waterway transport in the intermodal supply chain: a taxonomy of research challenges

This paper identifies research opportunities which will enable the further integration of inland waterway transport in the intermodal supply chain. Intermodal transport may be interpreted as a chain of actors who supply a transport service. Inland navigation can play a crucial role in increasing supply chain service performance. A first group of research challenges lies in the evolving relationship between transport geography and logistics activities. The next set of research challenges has the objective to encourage efficient operations in IWT: development of a system wide model for IWT, integration of operational planning systems and analysis of bundling networks. A third group of research efforts is directed towards shippers and consignees who use the intermodal transport chain to send or receive their goods: further development of models that integrate intermodal transport decisions with supply chain decisions and creation of green supply chains. A fourth cluster of research challenges concerns the problem domain of external cost calculations. Finally detailed time series data on freight transport should be collected to support these future research tracks.     

A note on supply chain network equilibrium models

This paper is concerned with the supply chain network equilibrium models proposed by Nagurney et al. [Nagurney, A., Dong, J., Zhang, D., 2002. A supply chain network equilibrium model. Transportation Research 38E, 281–303] and Dong et al. [Dong, J., Zhang, D., Nagurney, A., 2004. A supply chain network equilibrium model with random demands. European Journal of Operational Research 156, 194–212]. It demonstrates that these models possess the unconstrained continuously differentiable minimization formulations, whose any stationary point is the solution of the corresponding model. Accordingly, not only is the Quasi-Newton algorithm capable of finding a solution of the model, but also it can overcome the difficulty experienced by the modified projection method in choosing an appropriate predetermined step size. In addition, 11 benchmark examples are employed to show the advantage of the unconstrained minimization formulation.     

Designing the distribution network in a supply chain

This paper describes a framework for designing the distribution network in a supply chain. Various factors influencing the choice of distribution network are described. We then discuss different choices of distribution networks and their relative strengths and weaknesses. The paper concludes by identifying distribution networks that are best suited for a variety of customer and product characteristics.     

Supply chain micro-communities in urban areas

An increase in urban freight transport is inevitable as growing urban populations require more goods, more conveniently. A deeper understanding of the geography and trends of urban freight transport must recognise that it is the aggregate result of a complex web of supply chain interactions. To understand the trends, the behaviour of the underlying supply chains must be understood. Using Global Positioning System (GPS) traces of commercial vehicles and network theory concepts, this paper examines the characteristics of supply chain micro-communities in three urban areas in South Africa. The similarity in the structure of these micro-communities across the three, very diverse, areas suggests that the dynamics that drive supply chain interaction are not dependent on local geography. Four prominent archetypes were identified that account for more than half of the micro-communities in each area. Directionality, geographic dispersion and the balance of importance in the micro-communities are studied in the context of these archetypes. This paper presents a first puzzle piece in deducing urban freight transport patterns from supply chain interaction. Furthermore the results are an empirical benchmark that can validate theoretic models of urban supply chain interaction.     

Modeling downstream petroleum supply chain: The importance of multi-mode transportation to strategic planning

This paper proposes a deterministic mixed integer linear programming (MILP) model for downstream petroleum supply chain (PSC) network to determine the optimal distribution center (DC) locations, capacities, transportation modes, and transfer volumes. The model minimizes multi-echelon multi-product cost along the refineries, distribution centers, transportation modes and demand nodes. The relationship between strategic planning and multimodal transportation is further elucidated. A case study was considered with real data from the U.S. petroleum industry and transportation networks within Geographic Information System (GIS). A scenario analysis is also conducted to demonstrate the impact of key parameters on PSC decisions and total cost.     

The optimization of the closed-loop supply chain network

This paper develops a model of a general closed-loop supply chain network, which includes raw material suppliers, manufacturers, retailers, consumers and recovery centers. The objective of this paper is to formulate and optimize the equilibrium state of the network by using the theory of variational inequalities. Several examples and figures are used to describe the effects of parameters (the return ratio, the transformation rate of raw materials, and the transformation rate of recyclable products) on the equilibrium shipments and net revenues.     

Optimal commodity price stabilization as a multi-period spatial equilibrium problem: A supernetwork approach with public buffer stocks

This paper addresses the seasonal agricultural commodity price stabilization problem both with and without price bands using a spatial and temporal supernetwork framework. The problem is formulated as an extension of the classic spatial price equilibrium problem and solved with the gradient projection algorithm. Results from the model support the use of interseasonal storage mechanisms and confirm that the use of price bands is less effective as it lowers total society surplus while providing inaccurate signaling and therefore dampening market perceptions of product scarcity or excess. An illustrative numerical example provides a comparison between policy alternatives.     

An inventory-based simulation model for annual-to-daily temporal freight assignment

In the aggregate freight demand modeling literature, temporal assignment (annual to daily flows) is often oversimplified or neglected altogether. Unlike passenger flows, freight flows over the course of a year are not uniform and can vary significantly as the result of trade-offs between inventory and transportation cost management. We introduce the first temporal assignment model that explicitly considers these trade-offs for aggregate freight forecasting. A two-stage model is proposed that first decomposes aggregate annual zonal flows to firm group annual flows using a supply chain network model, which are then temporally assigned by simulating purchase order transactions throughout supply chains. Lot sizes are estimated with an Economic Order Quantity (EOQ) model and calibrated with monthly inventory data. The result is an aggregate-disaggregate-aggregate model that fits into aggregate freight forecasting models but makes use of more disaggregate logistical data. The model is illustrated with a simple replicable example, followed by a case study conducted with California statewide data to break out the distributed zonal flows into average daily volumes for network assignment. Calibration results using 2007 IMPLAN data showed a median percentage difference of simulated annual flows from FAF³ data of 2.38%, and a median percentage difference of simulated inventories from IMPLAN data of 4.85%, which suggests an excellent fit. Empirical validation results showed the model outperforms fixed factor approaches in mean value accuracy by 15–31%.     

A location-inventory-pricing model in a supply chain distribution network with price-sensitive demands and inventory-capacity constraints

This paper presents a location-inventory-pricing model for designing the distribution network of a supply chain with price-sensitive demands and inventory-capacity constraints. The supply chain has market power and uses markup pricing. An efficient Lagrangian relaxation algorithm is proposed to solve the model. Our numerical study shows that by moderately increasing the number of possible values for pricing decisions, the model can be used to find near-optimal solutions of a similar location-inventory-pricing problem with continuous pricing decisions. The approach used here to incorporate pricing decisions can be applied to other supply-chain design and planning problems with price-sensitive demands.