A heterogeneous reliable location model with risk pooling under supply disruptions

This paper investigates a facility location model that considers the disruptions of facilities and the cost savings from the inventory risk-pooling effect and economies of scale. Facilities may have heterogeneous disruption probabilities. When a facility fails, its customers may be reassigned to other surviving ones to hedge against lost-sales costs. We first develop both an exact and an approximate expression for the nonlinear inventory cost, and then formulate the problem as a nonlinear integer programming model. The objective is to minimize the expected total cost across all possible facility failure scenarios. To solve this problem, we design two methods, an exact approach using special ordered sets of type two (SOS2) and a heuristic based on Lagrangian relaxation. We test the model and algorithms on data sets with up to 150 nodes. Computational results show that the proposed algorithms can solve the problem efficiently in reasonable time. Managerial insights on the optimal facility deployment, customer assignments and inventory control strategies are also drawn.     

Sequential optimization approach for the multi‐class user equilibrium problem in a continuous transportation system

We consider a city region with several facilities that are competing for customers of different classes. Within the city region, the road network is dense, and can be represented as a continuum. Customers are continuously distributed over space, and they choose a facility by considering both the transportation cost and market externalities. More importantly, the model takes into account the different transportation cost functions and market externalities to which different customer classes are subjected. A logit‐type distribution of demand is specified to model the decision‐making process of users' facility choice. We develop a sequential optimization approach to decompose the complex multi‐class and multi‐facility problem into a series of smaller single‐class and single‐facility sub‐problems. An efficient solution algorithm is then proposed to solve the resultant problem. A numerical example is given to demonstrate the effectiveness and potential applicability of the proposed methodology.     

Location planning for transit-based evacuation under the risk of service disruptions

The effectiveness of transit-based emergency evacuation highly depends on the location of pick-up facilities, resource allocation, and management. These facilities themselves are often subject to service disruptions during or after the emergency. This paper proposes a reliable emergency facility location model that determines both pre-emergency facility location planning and the evacuation operations afterwards, while facilities are subject to the risk of disruptions. We analyze how evacuation resource availability leverages individual evacuees’ response to service disruptions, and show how equilibrium of the evacuee arrival process could be reached at a functioning pick-up facility. Based on this equilibrium, an optimal resource allocation strategy is found to balance the tradeoff between the evacuees’ risks and the evacuation agency’s operation costs. This leads to the development of a compact polynomial-size linear integer programming formulation that minimizes the total expected system cost from both pre-emergency planning (e.g., facility set-up) and the evacuation operations (e.g., fleet management, transportation, and exposure to hazardous surroundings) across an exponential number of possible disruption scenarios. We also show how the model can be flexibly used to plan not only pre-disaster evacuation but also post-disaster rescue actions. Numerical experiments and an empirical case study for three coastal cities in the State of Mississippi (Biloxi, Gulfport, and D’lberville) are conducted to study the performance of the proposed models and to draw managerial insights.     

Design and evaluation of an integrated inventory and transportation system

This paper proposes the adoption of an integrated inventory and transportation system (IITS) to minimize the total costs of inventory and transportation. A non-linear programing is developed by analyzing transportation and inventory costs with one supplier and many retailers in the distribution environment. The paper compares the proposed model with the traditional approach in computing total costs with numerical data. The results indicate that the total costs can be optimized by adopting integrated programing rather than the traditional approach, along with achieving improved customer service levels. In particular, sensitivity analysis is applied to determine the performance of the IITS under various transportation costs, holding costs and shortage costs. It shows that the transportation cost per unit is most sensitive in the proposed model. In this situation, the IITS is more effective for cost saving when set-up cost, holding and shortage costs are high, but is less effective for situations involving high per-unit transportation costs.     

A reliable location model for heterogeneous systems under partial capacity losses

Due to the interdependency between multiple infrastructure systems, the performance of a facility may depend on the resources or supplies received from other facilities. However, cross-system interdependence has seldom been studied in the location design context, probably due to the lack of a concise model describing interdependence across heterogeneous systems. This paper proposes a new heterogeneous flow scheme to describe cross-system interdependence. This scheme has two features distinguished from existing models in describing an interdependent facility location problem. First, it is a simple linear model upon which a compact facility location model can be built. Secondly, it relaxes the need to maintain flow conservation between different systems and is suitable in describing heterogeneous systems that take in and output different resources or services. Built on this scheme, this paper proposes a reliable location design model for a nexus of interdependent infrastructure systems. This model aims to locate the optimal facility locations in multiple heterogeneous systems to balance the tradeoff between the facility investment and the expected nexus operation performance. Different from other reliable facility location models, this expected performance captures interdependence among heterogeneous systems due to the resource input-output relationships. The consideration of continuous partial capacity losses complements the reliable location literature that mainly focuses on binary disruptions. Two numerical examples are conducted for investigating features and applications of the proposed model. The results indicate that with a standard off-the-shelf integer programming solver, the proposed model is able to solve optimal facility location design for problem instances of realistic scales to the near-optimum solutions with optimality gap assurance. Sensitivity analyses of key parameters indicate that improving facility capacity and reducing interdependency between systems can mitigate impacts of facility capacity losses and reduce the overall system cost.     

Green supply chain network design to reduce carbon emissions

We consider a supply chain network design problem that takes CO₂ emissions into account. Emission costs are considered alongside fixed and variable location and production costs. The relationship between CO₂ emissions and vehicle weight is modeled using a concave function leading to a concave minimization problem. As the direct solution of the resulting model is not possible, Lagrangian relaxation is used to decompose the problem into a capacitated facility location problem with single sourcing and a concave knapsack problem that can be solved easily. A Lagrangian heuristic based on the solution of the subproblem is proposed. When evaluated on a number of problems with varying capacity and cost characteristics, the proposed algorithm achieves solutions within 1% of the optimal. The test results indicate that considering emission costs can change the optimal configuration of the supply chain, confirming that emission costs should be considered when designing supply chains in jurisdictions with carbon costs.     

A cost-based maritime container assignment model

A recently proposed frequency-based maritime container assignment model (Bell et al., 2011) seeks an assignment of full and empty containers to paths that minimises expected container travel time, whereas containers are in practice more likely to be assigned to minimise expected cost. A cost-based container assignment model is proposed here. It is assumed that routes and service frequencies are given so ship operating costs are also fixed. The objective is to assign containers to routes to minimise container handling costs, container rental and inventory costs. The constraints in the model are extended to include route as well as port capacities. It is shown that the problem remains a linear program. A numerical example is presented to illustrate the properties of the model. The paper concludes by considering the many applications of the proposed maritime container assignment model.     

Maintenance optimization for transportation systems with demand responsiveness

We present a quadratic programming framework to address the problem of finding optimal maintenance policies for multifacility transportation systems. The proposed model provides a computationally-appealing framework to support decision making, while accounting for functional interdependencies that link the facilities that comprise these systems. In particular, the formulation explicitly captures the bidirectional relationship between demand and deterioration. That is, the state of a facility, i.e., its condition or capacity, impacts the demand/traffic; while simultaneously, demand determines a facility’s deterioration rate. The elements that comprise transportation systems are linked because the state of a facility can impact demand at other facilities. We provide a series of numerical examples to illustrate the advantages of the proposed framework. Specifically, we analyze simple network topologies and traffic patterns where it is optimal to coordinate (synchronize or alternate) interventions for clusters of facilities in transportation systems.     

A continuum approximation approach to competitive facility location design under facility disruption risks

This paper presents game-theoretical models based on a continuous approximation (CA) scheme to optimize service facility location design under spatial competition and facility disruption risks. The share of customer demand in a market depends on the functionality of service facilities and the presence of nearby competitors, as customers normally seek the nearest functioning facility for service. Our game-theoretical models incorporate these complicating factors into an integrated framework, and use continuous and differentiable density functions to represent discrete location decisions. We first analyze the existence of Nash equilibria in a symmetric two-company competition case. Then we build a leader–follower Stackelberg competition model to derive the optimal facility location design when one of the companies has the first mover advantage over its competitor. Both models are solved effectively, and closed-form analytical solutions can be obtained for special cases. Numerical experiments (with hypothetical and empirical data) are conducted to show the impacts of competition, facility disruption risks and transportation cost metrics on the optimal design. Properties of the models are analyzed to cast interesting managerial insights.     

An integrated model of facility location and transportation network design

Network location models have been used extensively for siting public and private facilities. In this paper, we investigate a model that simultaneously optimizes facility locations and the design of the underlying transportation network. Motivated by the simple observation that changing the network topology is often more cost-effective than adding facilities to improve service levels, the model has a number of applications in regional planning, distribution, energy management, and other areas. The model generalizes the classical simple plant location problem. We show how the model can be solved effectively. We then use the model to analyze two potential transportation planning scenarios. The fundamental question of resource allocation between facilities and links is investigated, and a detailed sensitivity analysis provides insight into the model's usefulness for aiding budgeting and planning decisions. We conclude by identifying promising research directions.     

Model uncertainty and the management of a system of infrastructure facilities

The network-level infrastructure management problem involves selecting and scheduling maintenance, repair, and rehabilitation (MR&R) activities on networks of infrastructure facilities so as to maintain the level of service provided by the network in a cost-effective manner. This problem is frequently formulated as a Markov decision problem (MDP) solved via linear programming (LP). The conditions of facilities are represented by elements of discrete condition rating sets, and transition probabilities are employed to describe deterioration processes. Epistemic and parametric uncertainties not considered within the standard MDP/LP framework are associated with the transition probabilities used in infrastructure management optimization routines. This paper contrasts the expected costs incurred when model uncertainty is ignored with those incurred when this uncertainty is explicitly considered using robust optimization. A case study involving a network-level pavement management MDP/LP problem demonstrates how explicitly considering uncertainty may limit worst-case MR&R expenditures. The methods and results can also be used to identify the costs of uncertainty in transition probability matrices used in infrastructure management systems.     

Joint optimization of freight facility location and pavement infrastructure rehabilitation under network traffic equilibrium

Establishment of industry facilities often induces heavy vehicle traffic that exacerbates congestion and pavement deterioration in the neighboring highway network. While planning facility locations and land use developments, it is important to take into account the routing of freight vehicles, the impact on public traffic, as well as the planning of pavement rehabilitation. This paper presents an integrated facility location model that simultaneously considers traffic routing under congestion and pavement rehabilitation under deterioration. The objective is to minimize the total cost due to facility investment, transportation cost including traffic delay, and pavement life-cycle costs. Building upon analytical results on optimal pavement rehabilitation, the problem is formulated into a bi-level mixed-integer non-linear program (MINLP), with facility location, freight shipment routing and pavement rehabilitation decisions in the upper level and traffic equilibrium in the lower level. This problem is then reformulated into an equivalent single-level MINLP based on Karush–Kuhn–Tucker (KKT) conditions and approximation by piece-wise linear functions. Numerical experiments on hypothetical and empirical network examples are conducted to show performance of the proposed algorithm and to draw managerial insights.     

A multiobjective hierarchical model for locating public facilities on a transportation network: A goal programming approach

This paper introduces a Multiobjective Hierarchical Model (MOHLM) for locating public facilities on a transportation network. The proposed model combines the multiobjective nature of the location-allocation problem with the hierarchical character of some public service systems, such as health care delivery. The model examines both maximum and total weighted travel time, facility utilization, and total travel time from the master facility to the attached subordinate facilities. An iterative goal programing algorithm is used to solve the problem. An example related to the location of health care facilities in a rural area of Greece is used to illustrate the application of the proposed model.     

Stochastic capacity expansion models for airport facilities

It is important and also challenging to plan airport facilities to meet future traffic needs in a rapidly changing environment, which is characterized by various uncertainties. One key issue in airport facility development is that facility performance functions (delay levels as functions of capacity utilization rates) are nonlinear, which complicates the solution method design. Potential demand fluctuations in a deregulated aviation market add another dimension to the decision making process. To solve this problem, a deterministic total cost minimization model is proposed and then extended into stochastic programs, by including uncertainties in traffic forecasts. After the exploration of properties of the delay cost function, an Outer-Approximation (OA) technique which is superior to the existing discrete approximation is designed. After model enhancements, an efficient solution framework based on the OA technique is used to solve the model to its global optimality by interactively generating upper and lower bounds to the objective. Computational tests demonstrate the validity of developed models and efficiency of proposed algorithms. The total cost is reduced by 18.8% with the stochastic program in the numerical example.     

Sizing parking facilities at airports

Established rules-of-thumb and industry guidelines for estimating the supply of parking at airports are based on uncertain quantities such as design year enplanements and number of airport employees, and are independent of cost. In the presence of continued uncertainty and increasing competition for limited space in and around airports, it is important that facilities are sized in relation to cost of providing and using them. A probabilistic model based on the classical “newsboy” problem is proposed to determine the optimal supply of parking in relation to expected total cost while treating demand as a random quantity. Empirical data are used to demonstrate the application of the proposed model for decision making. In addition to construction and maintenance costs, and user costs, decisions are shown to be sensitive to the level of uncertainty of design year enplanements.     

Effects of switching costs on customer attitude loyalty to an airport in a multi-airport region

The purpose is to analyze impacts of switching costs on customer attitude loyalty to an airport operator in a Norwegian multi-airport region. A sample of 167 respondents is analyzed by a structural equations modelling approach. Irrespective of customers’ perceptions of switching costs, service quality seems to be the most important customer loyalty driver. For low switching costs customers flight offers are also an important loyalty driver. For high switching costs customers facilities are important. An anticipated reduction in switching costs due to improvements in the regions’ infrastructure thus implies that more attention should be paid to an upgrading of the flight offers in order to create more airport loyalty in future. This may also have some interesting policy implications, which is briefly discussed in the paper.     

Strategies for customer service level protection under multi-echelon supply chain disruption risk

We model a multi-echelon system where disruptions can occur at any stage and evaluate multiple strategies for protecting customer service if a disruption should occur. The strategies considered take advantage of the network itself and include satisfying demand from an alternate location in the network, procuring material or transportation from an alternate source or route, and holding strategic inventory reserves throughout the network. Unmet demand is modeled using a mix of backordering and lost sales. We conduct numerical analysis and provide recommendations on selecting strategic mitigation methods to diminish the impact of disruptions on customer service. We demonstrate that the greatest service level improvements can be made by providing both proactive inventory placement to cover short disruptions or the start of long disruptions, and reactive back-up methods to help the supply chain recover after long or permanent disruptions.     

Trails,lanes, or traffic: Valuing bicycle facilities with an adaptive stated preference survey

This study evaluates individual preferences for five different cycling environments by trading off a better facility with a higher travel time against a less attractive facility at a lower travel time. The tradeoff of travel time to amenities of a particular facility informs our understanding of the value attached to different attributes such as bike-lanes, off-road trails, or side-street parking. The facilities considered here are off-road facilities, in-traffic facilities with bike-lane and no on-street parking, in-traffic facilities with a bike-lane and on-street parking, in-traffic facilities with no bike-lane and no on-street parking and in-traffic facilities with no bike-lane but with parking on the side. We find that respondents are willing to travel up to twenty minutes more to switch from an unmarked on-road facility with side parking to an off-road bicycle trail, with smaller changes associated with less dramatic improvements.     

A study on smart parking guidance algorithm

Parking problem becomes one of major issues in the city transportation management since the spatial resource of a city is limited and the parking cost is expensive. Lots of cars on the road should spend unnecessary time and consume energy during searching for parking due to limited parking space. To cope with these limitations and give more intelligent solutions to drivers in the selection of parking facility, this study proposes a smart parking guidance algorithm. The proposed algorithm supports drivers to find the most appropriate parking facility considering real-time status of parking facilities in a city. To suggest the most suitable parking facility, several factors such as driving distance to the guided parking facility, walking distance from the guided parking facility to destination, expected parking cost, and traffic congestion due to parking guidance, are considered in the proposed algorithm. To evaluate the effectiveness of the proposed algorithm, simulation tests have been carried out. The proposed algorithm helps to maximize the utilization of space resources of a city, and reduce unnecessary energy consumption and CO₂ emission of wandering cars since it is designed to control the utilization of parking facility efficiently and reduce traffic congestion due to parking space search.     

Quantifying the environmental and economic benefits of cooperation: A case study in temperature-controlled food logistics

Inefficient road transportation causes unnecessary costs and polluting emissions. This problem is even more severe in refrigerated transportation, in which temperature control is used to guarantee the quality of the products. Organizing logistics cooperatively can help decrease both the environmental and the economic impacts. In Joint Route Planning (JRP) cooperation, suppliers and customers jointly optimize routing decisions so that cost and emissions are minimized. Vendor Managed Inventory (VMI) cooperation extends JRP cooperation by optimizing routing and inventory planning decisions simultaneously. However, in addition to their economic advantages, VMI and JRP may also yield environmental benefits. To test this assertion, we perform a case study on cooperation between a number of supermarket chains in the Netherlands. The data of this case study are analyzed to quantify both the economic and environmental benefits of implementing cooperation via JRP and VMI, using vehicle routing and an inventory routing models. We found that JRP cooperation can substantially reduce cost and emissions compared with uncooperative routing. In addition, VMI cooperation can further reduce cost and emissions, but minimizing cost and minimizing emissions no longer result in the same solution and there is a trade-off to be made.