Combined Facility Location Research Articles

A slope scaling heuristic for the multi-period strategic planning of carbon capture and storage

Around the world, efforts are currently underway to implement various decarbonization strategies to meet net-zero emissions objectives. This includes carbon capture and storage (CCS), which involves capturing CO2 at emitter sites, and transporting it to geological reservoirs, where it is to be injected underground for long-term storage. In this work, we focus on the multi-period strategic planning of a CCS value chain involving pipeline CO2 transportation. From an Operations Research standpoint, this problem exhibits the characteristics of combined facility location and network design. To account for multiple scenarios of input parameters (e.g. market and geological variability), this problem has to be solved hundreds or thousands of times. Thus, reaching high-quality solutions quickly is crucial. As commercial solvers struggle to provide high-quality solutions under these time constraints, we propose a slope scaling heuristic based on previous work on single-period CCS planning and network design. This new heuristic approximates the cost of design variables, generates upper bounds via dynamic programming, uses a long-term memory search strategy, and includes a final improvement phase where a restricted model is solved. Computational experiments show that the proposed heuristic generates better solutions than CPLEX for most instances considered, at a fraction of the computational time.

Navigating urban logistics challenges: An optimized approach to parcel distribution in the Prague city center

In this paper, we focus on metropolitan transport logistics that has always been difficult due to the need to transport goods through a complex urban infrastructure, heavy traffic, and dense populations. The goal of this paper is to describe a micro hub location in the neighborhood of the historic center of the city of Prague, the Czech Republic in a situation where the municipalities consider prohibiting the entry of trucks with combustion engines that currently provide cargo transportation for B2B partners operating in this area. Micro hubs represent the efficient last mile consolidation and distribution facilities located in or near urban neighborhoods and serving a spatially limited, densely populated delivery area. We propose a solution combining facility location problem, vehicle routing problem and balancing with the horizontal and vertical cooperation in supply chains to locate the micro hub in the area with extremely low availability of suitable space while respecting the necessity to connect this facility to an existing network of regional terminals operated by 3PLs to ensure the distribution of cargo across the board according to the requirements of customers. For the collection and distribution of parcels within the area, we suggest to use of cargo bikes and electric vans to provide environmentally sustainable service and minimize the harmful consequences of excessive traffic for residents. We also discuss the economic implications of adopting such innovative sustainable supply chain solutions for involved horizontal and vertical supply chain partners emphasizing different motivation aspects to convince these partners to cooperate and share scarce resources.

Bi-sided facility location problems: an efficient algorithm for k-centre, k-median, and travelling salesman problems

This study introduces a general framework, called Bi-sided facility location, for a wide range of problems in the area of combined facility location and routing problems such as locating test centres and designing the network of supermarkets. It is based on a multi-objective optimisation model to enhance the service quality which the clients received, called client-side, and enhance the interconnection quality and eligibility among the centres, called center-side. Well-known problems such as k-median and k-centre for the client-side and the travelling salesman problem for the centre-side are taken into account in this paper. After discussing the complexity of this kind of combination, we propose a heuristic approximation algorithm to find approximation Pareto-optimal solutions for the problem. The algorithm is an efficient local search utilising geometric objects such as the Voronoi diagram and Delaunay triangulation as well as algorithms for computing approximation travelling salesman tour. In addition to the comprehensive theoretical analysis of the proposed models and algorithm, we apply the algorithm to different instances and benchmarks, and compare it with NSGA-II based on set coverage and spacing metrics. The results confirm the efficiency of the algorithm in terms of running time and providing a diverse set of efficient trade-off solutions. Highlights Introducing a general bi-side location model considering centres and clients’ utilities Discussing and proving the NP-hardness of the model in the general framework Considering two instances; k-centre and k-median for client-side and TSP for centre-side Proposing an efficient geometric-based algorithm for solving the problems Implementing, testing, and comparing the proposed algorithm on several benchmarks

A robust optimization model for location-transportation problem of disaster casualties with triage and uncertainty

Emergency medical services (EMS) are essential components for post-disaster rescue activities. Considering injury heterogeneity and deterioration over time of the casualties, the uncertainty in the number of the casualties can effectively improve the medical service performance. This paper develops a robust optimization model for combined facility location and casualty transportation under uncertainty in the number of casualties. We divide casualties into two types: mild casualties who are transported to on-site clinics with rescue vehicles and serious casualties who are transported to general hospitals with helicopters. Meanwhile, we consider the Injury Severity Score (ISS) increment to describe the injury deterioration of the casualties over time. The objective is to minimize the total weighted ISS increment of mild casualties and serious casualties. Then, we employ the robust optimization method to deal with the uncertainty and derive the robust counterpart of the proposed model in this paper. Case studies based on Yushu Earthquake show that the model can get the optimal emergency facility location and casualty transportation scheme to minimize the total weighted ISS increment. The total weighted ISS increment increases as the constraint violation probability decreases, which reflects the trade-off between performance and robustness. Sensitivity analyses show that the greater uncertainty of the casualty number is, the greater the impact on the total weighted ISS increment is, the more conservative the decision scheme is. The capacity of general hospitals has a greater effect on the objective value compared with the capacity of on-site clinics and the decision scheme of the robust optimization model has a greater optimality compared with the deterministic model when the problem size is magnified.

Corrigendum to “Combining Facility Location and Routing Decisions in Sustainable Urban Freight Distribution under Horizontal Collaboration: How Can Shippers Be Benefited?”

Corrigendum to “Combining Facility Location and Routing Decisions in Sustainable Urban Freight Distribution under Horizontal Collaboration: How Can Shippers Be Benefited?”

Exact robust solutions for the combined facility location and network design problem in hazardous materials transportation

We consider a leader-follower game in the form of a bi-level optimization problem that simultaneously optimizes facility locations and network design in hazardous materials transportation. In the upper level, the leader intends to reduce the facility setup cost and the hazmat exposure risk, by choosing facility locations and road segments to close for hazmat transportation. When making such decisions, the leader anticipates the response of the followers who want to minimize the transportation costs. Considering uncertainty in the hazmat exposure and the hazmat transport demand, we consider a robust optimization approach with multiplicative uncertain parameters and polyhedral uncertainty sets. The resulting problem has a min-max problem in the upper level and a shortest-path problem in the lower level. We devise an exact algorithm that combines a cutting plane algorithm with Benders decomposition

Combined facility location and distribution network design problem: Progressive models and a case study

This paper addresses to the facility location problem of ammunition stores considering the design of distribution network from stores to geographically dispersed army forces. The problem is to determine the construction sites of the ammunition stores among candidate sites and to give the decision on how many stores will be built from which kind. The problem also contains designing of a distribution network to concurrently determine the amounts of several military equipment transported from stores to army forces. A mathematical model is proposed to minimize the cost of the whole system, caused by the construction of the ammunition stores and the transportation of different equipment in diverse quantities from stores to dispersed army forces. The model is then improved progressively and several variants are presented to reflect the real-world conditions through a case study. Numerical results obtained from solving the case study using the proposed models coded in General Algebraic Modelling System (GAMS) are exhibited. The effect of the size of problem specific parameters on the model execution time is also investigated via experimental tests. The results demonstrate the promising problem-solving capacity of the proposed models, which can be applied practically.

Combining Facility Location and Routing Decisions in Sustainable Urban Freight Distribution under Horizontal Collaboration: How Can Shippers Be Benefited?

This article investigates the potential economic, environmental, and social effects of combining depot location and vehicle routing decisions in urban road freight transportation under horizontal collaboration. We consider a city in which several suppliers decide to joint deliveries to their customers and goods are delivered via intermediate depots. We study a transportation optimization problem from the perspective of sustainability development. This quantitative approach is based on three‐objective mathematical model for strategic, tactical, and operational decision‐making as a two‐echelon location routing problem (2E‐LRP). The objectives are to minimize cost and CO2 emissions of the transportation and maximize the created job opportunities. The model was solved with the ε‐constraint method using extended known instances reflecting the real distribution in urban area to evaluate several goods’ delivery strategies. The obtained results by comparing collaborative and noncollaborative scenarios show that collaboration leads to a reduction in CO2 emissions, transportation cost, used vehicles, and travelled distances in addition to the improvement of the vehicles load rate but collaboration affects negatively social impact. To evaluate the effect of the method used to allocate the total gains to the different partners, we suggest to decision makers a comparison between well‐known allocation methods.

3D coverage location modeling of Wi-Fi access point placement in indoor environment

Many traditional facility location models have sought optimal solutions in two-dimensional space. However, certain locations in reality need to be modeled in three-dimensional space. This paper addresses a location problem in three-dimensional space from the application perspective. Specifically, we introduce a 3D coverage location model of Wi-Fi access points (APs) in an indoor environment. To do this, we first incorporate a generic radio propagation assuming typical obstructions of a building into the standard coverage model, using 3D Euclidean distance characterizing radio signal penetration. The suggested model is then applied for an efficient AP placement plan in a multi-story building at a university campus. The empirical results present 3D representations of the solutions for multi-floor deployment of Wi-Fi APs. This research is expected to provide a useful modeling framework for combining facility location model with wireless network design in a 3D environment.

A Reliable Budget-Constrained FL/ND Problem with Unreliable Facilities

The combined facility location and network design problem is an important practical problem for locating public and private facilities. Moreover, incorporating aspects of reliability into the modeling of facility location problems is an effective way to hedge against disruptions in the system. In this paper, we consider a combined facility location/network design problem that considers system reliability. This problem has a number of applications, many of which fall into the category of service systems, such as regional planning and locating schools, health care service centers and airline networks. Our model also includes an investment budget constraint. We propose a mixed integer programming formulation to model this problem, as well as an efficient heuristic based on the problem’s LP relaxation. Numerical results demonstrate that the proposed heuristic significantly outperforms CPLEX in terms of solution speed, while still maintaining excellent solution quality. Our results also suggest a favorable tradeoff between the “nominal cost” (including fixed facility location costs and link construction costs, as well as transportation costs) and system reliability; that is, substantial improvements in reliability are often possible with only slight increases in the total cost of investment and transportation.

Modeling Influenza Pandemic and Planning Food Distribution

Based on the recent incidents of H5N1, H1N1, and influenza pandemics in history (1918, 1957, and 1968) experts believe that a future influenza pandemic is inevitable and likely imminent. Although the severity of influenza pandemics vary, evidence suggests that an efficient and rapid response is crucial for mitigating morbidity, mortality, and costs to society. Hence, preparing for a potential influenza pandemic is a high priority of governments at all levels (local, state, federal), nongovernmental organizations (NGOs), and companies. In a severe pandemic, when a large number of people are ill, infected persons and their families may have difficulty purchasing and preparing meals. Various government agencies and NGOs plan to provide meals to these households. In this paper, in collaboration with the American Red Cross, we study food distribution planning during an influenza pandemic. We develop a disease spread model to estimate the spread pattern of the disease geographically and over time, combine it with a facility location and resource allocation network model for food distribution, and develop heuristics to find near-optimal solutions for large instances. We run our combined disease spread and facility location model for the state of Georgia and present the estimated number of infections and the number of meals needed in each census tract for a one-year period along with a design of the supply chain network. Moreover, we investigate the impact of voluntary quarantine on the food demand and the food distribution network and show that its effects on food distribution can be significant. Our results could help decision makers prepare for a pandemic, including how to allocate limited resources and respond dynamically.

Facility Location-Network Design Problem: Reliability and Investment Budget Constraint

The simultaneous consideration of combined facility location and network design is an attractive empirical topic for locating public and private facilities and for reducing transportation costs. Moreover, applying a reliable facility location problem is one of the most effective ways to protect against occasional failures of the system, because of considering unexpected failures and possible customer reassignment when locating facilities. Accordingly, this study concerns a reliable combined facility location–network design problem regarding the investment budget constraint and proposes a mixed integer nonlinear programming formulation to model this constraint. The proposed model is linearized by suitable techniques. Also, a practical case study subject to sustainable design in urban health care development is presented in detail to illustrate the application of the proposed mathematical model. Finally, a sensitivity analysis is conducted to provide insights into the behavior of the proposed model in response to the changes of key parameters of the problem.

A bi-objective optimization of supply chain design and distribution operations using non-dominated sorting algorithm: A case study

This paper considers simultaneous optimization of strategic design and distribution decisions for three-echelon supply chain architecture consisting of following three players; suppliers, production plants, and distribution centers (DCs). The key design decisions considered are: the number and location of plants in the system, the flow of raw materials from suppliers to plants, the quantity of products to be shipped from plants to distribution centers, so as to minimize the combined facility location, production, inventory, and shipment costs and maximize fill rate. To achieve this, three-echelon network model is mathematically represented and solved using swarm intelligence based Multi-objective Hybrid Particle Swarm Optimization algorithm (MOHPSO). This heuristic incorporates non-dominated sorting (NDS) procedure to achieve bi-objective optimization of two conflicting objectives. The applicability of proposed optimization algorithm was then tested by applying it to standard test problems found in literature. On achieving comparable results, the approach was applied to actual data of a pump manufacturing industry. The results show that the proposed solution approach performs efficiently.

A combined facility location and network design problem with multi-type of capacitated links

This article presents a mixed-integer model to optimize the location of facilities and the underlying transportation network at the same time to minimize the total transportation and operating costs. In this problem, it is assumed that for connecting two nodes, there are several types of links in which their capacity, transportation and construction costs are different. The developed model has various applications in telecommunication, emergency, regional planning, pipeline network, energy management, distribution, to just name a few. To solve the model effectively, this paper also proposes a fix-and-optimize heuristic based on the evolutionary fire-fly algorithm. Finally, to validate the model and evaluate the algorithm’s performance, a series of test instances with up to 100 nodes and 600 candidate links with three different levels of quality are reported.

Constrained optimisation of distribution network using new hybrid PSO optimiser

The efficient and effective movement of goods from raw material sites to processing facilities, component fabrication plants, finished goods assembly plants, distribution centres, retailers and customers are critical in today’s competitive environment. These in turn depend on facility location decisions taken during strategic planning. These facilities are expensive to construct and difficult to modify. Inefficient locations for production and assembly plants as well as distribution centres will result in excess costs being incurred throughout the lifetime of the facilities, no matter how well the production plans, transportation options, inventory management, and information sharing decisions are optimised in response to changing conditions. This paper addresses design of network model for facility location and capacity allocation where in a set of customer locations with demands and a set of candidate facility locations will be known in advance. If a facility is located at a candidate site, a known fixed location cost is incurred. There is a known unit shipment cost between each candidate site and each customer location. The problem is to find the locations of the facilities and the shipment pattern between the facilities and the customers to minimise the combined facility location and shipment costs subject to a requirement that all customer demands be met. To optimise this, the distribution network model is mathematically represented and solved using hybrid PSO algorithm.

Bi‐objective optimization of distribution scheduling using MOPSO optimizer

PurposeThe paper aims at the bi‐objective optimization of a two‐echelon distribution network model for facility location and capacity allocation where in a set of customer locations with demands and a set of candidate facility locations will be known in advance. The problem is to find the locations of the facilities and the shipment pattern between the facilities and the distribution centers (DCs) to minimize the combined facility location and shipment costs subject to a requirement that maximum customer demands be met.Design/methodology/approachTo optimize the two objectives simultaneously, the location and distribution two‐echelon network model is mathematically represented in this paper considering the associated constraints, capacity, production and shipment costs and solved using hybrid multi‐objective particle swarm optimization (MOPSO) algorithm.FindingsThis paper shows that the heuristic based hybrid MOPSO algorithm can be used as an optimizer for characterizing the Pareto optimal front by computing well‐distributed non‐dominated solutions. These aolutions represent trade‐off solutions out of which an appropriate solution can be chosen according to industrial requirement.Originality/valueVery few applications of hybrid MOPSO are mentioned in literature in the area of supply chain management. This paper addresses one of such applications.

Location and allocation decisions for multi-echelon supply chain network – A multi-objective evolutionary approach

This paper aims at multi-objective optimization of single-product for four-echelon supply chain architecture consisting of suppliers, production plants, distribution centers (DCs) and customer zones (CZs). The key design decisions considered are: the number and location of plants in the system, the flow of raw materials from suppliers to plants, the quantity of products to be shipped from plants to DCs, from DCs to CZs so as to minimize the combined facility location and shipment costs subject to a requirement that maximum customer demands be met. To optimize these two objectives simultaneously, four-echelon network model is mathematically represented considering the associated constraints, capacity, production and shipment costs and solved using swarm intelligence based Multi-objective Hybrid Particle Swarm Optimization (MOHPSO) algorithm. This evolutionary based algorithm incorporates non-dominated sorting algorithm into particle swarm optimization so as to allow this heuristic to optimize two objective functions simultaneously. This can be used as decision support system for location of facilities, allocation of demand points and monitoring of material flow for four-echelon supply chain network.

Approximation Algorithms for Soft-Capacitated Facility Location in Capacitated Network Design

Answering an open question published in Operations Research (54, 73–91, 2006) in the area of network design and logistic optimization, we present the first constant-factor approximation algorithms for the problem combining facility location and cable installation in which capacity constraints are imposed on both facilities and cables. We study the problem of designing a minimum cost network to serve client demands by opening facilities for service provision and installing cables for service shipment. Both facilities and cables have capacity constraints and incur buy-at-bulk costs. This Max SNP-hard problem arises in diverse applications and is shown in this paper to admit a combinatorial 19.84-approximation algorithm of cubic running time. This is achieved by an integration of primal-dual schema, Lagrangian relaxation, demand clustering and bi-factor approximation. Our techniques extend to several variants of this problem, which include those with unsplitable demands or requiring network connectivity, and provide constant-factor approximate algorithms in strongly polynomial time.

Approximation Algorithms for Problems Combining Facility Location and Network Design

We present approximation algorithms for integrated logistics problems that combine elements of facility location and transport network design. We first study the problem where opening facilities incurs opening costs and transportation from the clients to the facilities incurs buy-at-bulk costs, and provide a combinatorial approximation algorithm. We also show that the integer-programming formulation of this problem has small integrality gap. We extend the model to the version when there is a bound on the number of facilities that may be opened.

Technical and clinical validation of a serum IGF-1 assay

This paper aims at multi-objective optimization of single-product for four-echelon supply chain architecture consisting of suppliers, production plants, distribution centers (DCs) and customer zones (CZs). The key design decisions considered are: the number and location of plants in the system, the flow of raw materials from suppliers to plants, the quantity of products to be shipped from plants to DCs, from DCs to CZs so as to minimize the combined facility location and shipment costs subject to a requirement that maximum customer demands be met. To optimize these two objectives simultaneously, four-echelon network model is mathematically represented considering the associated constraints, capacity, production and shipment costs and solved using swarm intelligence based Multi-objective Hybrid Particle Swarm Optimization (MOHPSO) algorithm. This evolutionary based algorithm incorporates non-dominated sorting algorithm into particle swarm optimization so as to allow this heuristic to optimize two objective functions simultaneously. This can be used as decision support system for location of facilities, allocation of demand points and monitoring of material flow for four-echelon supply chain network.