Network Design Formulation Research Articles

A mathematical model for the integrated problem of production network design and inventory positioning

In this paper, an integrated approach is addressed to tackle the production network design and inventory positioning problem in a single-sourcing, multi-product, and multi-period context. The objective of our model is to simultaneously determine the optimal network structure, safety stock amounts, and their respective locations, considering normal demand conditions. The main goal is to minimize the overall production network cost. The proposed model merges the traditional network design formulation with that for inventory positioning using the concept of guaranteed service. The developed model is implemented and tested on a case study of office furniture manufacturing, where the bill of materials is considered. The effectiveness of the proposed model is demonstrated by comparing it to a sequential approach where the network structure and safety stock decisions are made sequentially. The results reveal that the integrated approach surpasses the sequential approach, with cost savings ranging from 1.7% to 3.7%. In addition, a higher optimal cycle service level is obtained by the integrated approach compared to that of the sequential approach. To further evaluate the model's performance, a sensitivity analysis is conducted to examine the influence of the model's parameters, i.e., committed service time and coefficient of variation of demand, on its solutions. The analysis shows that when the coefficient of the demand variation remains unchanged, longer committed service times lead to lower safety stock costs and higher optimal service levels. Moreover, it is observed that more safety stocks of components are kept in the upstream layer of the network than those of finished goods.

Balancing Profitability and Social Impact: A Joint Product Line Design and Supply Chain Network Design Formulation

Balancing Profitability and Social Impact: A Joint Product Line Design and Supply Chain Network Design Formulation

Formulation and solution technique for agricultural waste collection and transport network design

Agricultural waste management in developing countries has become a challenging issue for rural planners due to the lack of an efficient planning tool. In the countries, farmers burnt agricultural waste at fields after each harvesting season to solve the issue. As a result, it has caused air and water pollution in the rural areas of the countries. In this paper, we present a mixed-integer nonlinear programming model for agricultural waste collection and transport network design that aims to stop burning waste and use the waste to produce bio-organic fertilizer. The model supports rural planners to optimally locate waste storages, and to determine the optimal set of routes for a fleet of vehicles to collect and transport the waste from the storages to the bio-organic fertilizer production facility. In the novel location-assignment-routing problem, the overall objective is to minimize total cost of locating storages, collecting waste from fields and planning vehicle routes. A solution technique is developed to linearise the mixed-integer nonlinear programming model into a model in linear form. In addition, a parallel water flow algorithm is developed to solve efficiently the large-sized instances. The efficiency of the proposed model and algorithm is validated and evaluated on the real case study in Trieu Phong district, Quang Tri province, Vietnam, as well as a set of randomly generated large-sized instances. The results show that our solution approach outperforms the general optimisation solver and tabu search algorithm. Our algorithm can find the optimal or near-optimal solutions for the large-sized instances within a reasonable time.

Daily load planning under different autonomous truck deployment scenarios

This paper presents and tests modified service network design formulations that account for five levels of truck automation in a daily load planning setting. Given daily updates of load information, the paths for the five deployment scenarios are adjusted using two daily updating strategies. Both strategies start with a base plan in which paths are generated based on the historic daily distribution of load dispatches during an average week. The two strategies are: (1) Option 1: re-optimization of pre-booked loads and new requests, and (2) Option 2: optimization of new requests only. The solutions of the two strategies are compared to the hindsight plan which assumes complete information of actual requests placed. The presented formulations are tested out on an industry partner’s network. Results show that the savings achieved with re-optimization (Option 1) compared to insertion (Option 2) increase with more demand variability; this outcome is consistent across all fleet mixes. When most of the loads are new arrivals, the computational time of the two approaches is comparable and insertion is less attractive than re-optimization. With daily re-optimization, most of the plan changes adjust the terminals visited by a load compared to just changing the dispatch and arrival times along the load’s path.

Risk-Based Formulation of the Transit Priority Network Design

Demand uncertainties are inevitable in transportation networks. The transit priority network design problem over more than a decade of development has been solved under deterministic conditions. This paper proposes a model to find the optimal transit priority scheme in a multimodal transportation network under uncertain demand. This model is formulated as a risk-based bi-level optimization problem. At the upper-level, a risk measure of expected social cost is minimized subject to a chance constraint on total travel time with a user-specified confidence level and a budget constraint. At the lower-level, a mode choice, a traffic user equilibrium assignment, and a transit assignment are applied. An ant colony algorithm is utilized to solve this complex design problem. Numerical results using a real world middle-size city network empirically demonstrate that the demand uncertainty has a significant impact on the solution and the proposed model is applicable to realistic networks.

Tactical capacity planning in an integrated multi-stakeholder freight transportation system

This study focuses on investigating the tactical planning of an integrated multi-stakeholder system in which revenue management concepts including shipper categories, demand classification, penalty costs for demand satisfaction outside of prescribed time-windows, and offering services with bundles are addressed. The aim of the tactical planning in this system is to design the demand and supply sides of this integrated system simultaneously. To this end, a scheduled service network design formulation on a space-time network is developed to build a transportation plan by selecting profitable requests from non-contract shippers, selecting a subset of individual and bundled transportation scheduled services, and identifying the itineraries of the shipments on the selected service network with the objective of maximizing the profit of the system. Using realistic-size instances, an extensive computational analysis is performed on the split and unsplit shipment-flow versions of the problem. The aim of the analysis is twofold: 1) assess the computational effort required to solve the developed optimization model and 2) investigate the structural characteristics of the obtained tactical plans for different system settings.

Multi-period transportation network investment decision making and policy implications using econometric framework

Transportation infrastructure projects take numerous years of planning before they are scheduled for construction. Prioritization of such projects over a multi-period planning horizon (under a limited budget) is a difficult task, as it is usually formulated as a bilevel network design problem (NDP). Although multi-period network investment is studied in the literature, its application by public agencies is limited because of the complexities involved in network design problems and the computational time needed to analyze large scale networks (i.e., performing the traffic assignment at the lower level of the NDP). The contribution of this research is two-fold. First, it extends a previously published single year discrete network design formulation to a multi-period discrete network design problem (MPNDP) to capture both the spatial and temporal patterns of multi-period network investment decisions. Second, using the MPNDP investment results; and the network characteristics, this research develops and evaluates a new econometric model the Multi-Period Econometric Network Investment Model (MENIM). MENIM can be used by agencies in place of MPNDP to approximate network investments. The proposed model is calibrated and validated using medium to large scale networks and results show that it provides comparable results to MPNDP within acceptable computational times. Patterns of multi-period network investments from these numerical experiments are also extensively discussed along with policy recommendations for public agencies.

Scheduled service network design with resource management for two-tier multimodal city logistics

We address the tactical-planning problem for an extended two-tiered City Logistics system. This more realistic problem setting, compared to the literature, integrates inbound and outbound demands, different transportation modes combining traditional, road-based, carriers with modes and vehicles of mass transport, such as light and regular rail. Aside from the assignment of customers to consolidation distribution centers and satellites, we manage a number of major resources, such as the multiple satellite capacity measures and the structure, allocation, and size of the heterogeneous fleets. We propose a scheduled service network design formulation for the tactical planning of such extended systems, and develop an efficient Benders decomposition algorithm, which includes a tailored partial decomposition technique for deterministic mixed-integer linear-programming formulations. The results of extensive numerical experiments show the efficiency of the proposed solution method, as well as the benefits of integrating several demand types and multimodal transportation networks into a single formulation.

QoS-aware protection in elastic optical networks with distance-adaptive and reconfigurable modulation formats

• Proposal on QoS-aware protection combined with reconfigurable modulation formats. • A novel network design formulation for QoS-aware protection. • Protection based on traffic differentiation brings significant spectral saving. Elastic optical networks have recently emerged as one of the most promising technologies for creating next-generation optical core networks thanks to the adaptive spectrum allocation mechanism. In order to achieve higher spectrum efficiency and exploit elastic optical networking technology, in this paper, we introduce a novel perspective on re-designing dedicated path protection for elastic optical networks. First, inspired by the observation that, in distance-diverse network topologies, the transmission margin between the working and protection route could be wide enough and therefore, the most feasibly spectrum-efficient modulation format could be assigned according to the specific condition of each route rather than applying a single modulation format that is able to cope with the worse condition of the route as currently adopted in traditional designs. Such more granular in transmission adaption is powered by the fast reconfiguration of state-of-the-art elastic transponders and this paves new opportunities in leveraging the spectrum efficiency. Second, the characteristics of traffic traveling in fiber links could be furthermore exploited to tailor the protection services to the actual requirement instead of enforcing the same level of protection for the entire traffic. Specifically, premium traffic today accounts for only 25 % and the remained traffic is best-effort and in taking advantage of this insight, dedicated path protection could be re-designed to ensure just-enough bandwidth provision for premium traffic in case of failures while possibly accepting best-effort traffic discard. In exploiting both the reconfiguration capability and traffic differentiation, a new quality-of-service aware protection framework for the design of elastic optical networks with the capability of distance-adaptive and reconfigurable modulation format assignment is provided. We introduce the node architecture supporting our proposal and provide an optimal design formulation in the form of integer linear programming model to maximize the spectral utilization efficiency. We have also applied extensively experimental simulations to evaluate the performance of our proposed solution in comparison with that of appropriate conventional approaches on a realistic network topology, i.e. COST239. The obtained numerical results prove that our developed solution significantly outperforms the conventional ones, in terms of spectrum efficiency, and it has been revealed that permitting reconfiguration of transmission parameters in switching from working routes to protection ones could result up to 20 % spectral saving in most favorable conditions. Furthermore, incorporating the protection service differentiation could substantially boost spectrum efficiency. For the present ratio of premium traffic– roughly 25 % , our proposal reveals that a spectral saving of up to more than 80 % could be attained and on the whole, the developed solution tends to be more profitable with the medium and high-load traffic conditions.

Integrating Resource Management in Service Network Design for Bike-Sharing Systems

Station-based bike-sharing systems rely on bike redistribution to provide users with an adequate service level. We propose a novel formulation of service network design that coordinates redistribution decisions in space and time to plan regular master tours. This formulation explicitly integrates resource-management decisions by considering a limited redistribution budget to acquire and operate vehicles, as well as an accurate time representation of pickups and deliveries of bikes at stations. We propose a matheuristic relying on a neighborhood search scheme to find solutions of good quality for real-world-sized problem instances in reasonable time. To produce starting solutions, we propose a construction heuristic decomposing the daytime redistribution process into three sequential phases: determine pickups and deliveries, link pickups and deliveries into transport requests, and assign transport requests to master tours. We evaluate the operational performance of master tours with a discrete-event simulation approach. We show that master tours improve the level of service in bike-sharing systems with high and regular mobility patterns, for example, commuting activities.

Sensor network design based on system-wide reliability criteria. Part II: Formulations and applications

In part I of this series of articles, the concept of overall system reliability was presented for two applications: reliable estimation of variables for steady state linear flow processes, and reliable fault detection and diagnosis for any process. In this part, systematic generation of the proposed system-wide reliability expression is discussed. In particular, an approach for generating the system reliability using the sum of disjoint product method is presented. This serves as the objective function to be maximized in various constrained optimization formulations for sensor network design, which are also proposed in this work for both applications. A heuristic is proposed to solve the resulting nonlinear integer programming problems. The sensor network design formulations are applied to two benchmark case studies: (1) Tennessee Eastman process, (2) Steam metering process. Results indicate the utility of the proposed sensor network design approach in designing optimal sensor networks that maximize system reliability.

Optimal Design and Synthesis of MEA Power System Architectures Considering Reliability Specifications

Aircraft electrification requires novel designs to supply the growing demand for electric power onboard through efficient and reliable production and distribution of electrical energy. Moreover, the aircraft power system will be a key enabler for the integration of future technologies. Pledging to these intentions, we propose a formulation to synthesize a power system architecture that complies with safety specifications following a platform-based design methodology that optimizes the main aerospace drivers. Due to the nonlinear nature of the design problem, this article presents reliability-based MILP network design formulations for topology synthesis. The novelty of this approach relies on the adoption of network design optimization for MEA power system construction that allows explicit design formulations as MILP problems. This approach will provide an effective way to include safety specifications by introducing reliability and resiliency constraints.

Strategic Network Design for Parcel Delivery with Drones Under Competition

This paper studies the economic desirability of unmanned aerial vehicle (UAV) parcel delivery and its effect on e-retailer distribution networks while taking into account technological limitations, government regulations, and customer behavior. We consider an e-retailer offering multiple same-day delivery services including a fast UAV service and develop a distribution network design formulation under service-based competition where the services offered by the e-retailer not only compete with the stores (convenience, grocery, etc.) but also with each other. Competition is incorporated using the multinomial logit market share model. To solve the resulting nonlinear mathematical formulation, we develop a novel logic-based Benders decomposition approach. We build a case based on New York City, carry out extensive numerical testing, and perform sensitivity analyses over delivery charge, delivery time, government regulations, technological limitations, customer behavior, and market size. The results show that government regulations, technological limitations, and service charge decisions each play a vital role in the future of UAV delivery.

Optimal placement of data concentrators for expansion of the smart grid communications network

Evolving power systems with increasing renewables penetration, along with the development of the smart grid, calls for improved communication networks to support these distributed generation sources. Automatic and optimal placement of communication resources within the advanced metering infrastructure is critical to provide a high-performing, reliable, and resilient power system. Three network design formulations based on mixed-integer linear and non-linear programming approaches are proposed to minimise network congestion by optimising residual buffer capacity through the placement of data concentrators and network routeing. Results on a case study show that the proposed models improve network connectivity and robustness, and increase average residual buffer capacity. Maximising average residual capacity alone, however, results in both oversaturated and underutilised nodes, while maximising either minimum residual capacity or total reciprocal residual capacity can yield much-improved network load allocation. Consideration of connection redundancy improves network reliability further by ensuring quality-of-service in the event of an outage. Analysis of multi-period network expansion shows that the models do not deviate significantly from optimal when used progressively (within 5% deviation), and are effective for utility planners to use for smart grid expansion.

Link Transmission Model-Based Linear Programming Formulation for Network Design

This article presents a linear programming formulation to solve the network design problem using the link transmission model (LTM) as the underlying traffic flow model. The original LTM was adapted by incorporating link-sending and receiving flows using linear inequalities. Furthermore, route choice was relaxed, and transfer flow variables were used to model vehicles’ routing decisions within the network. The objective function of the linear program aimed to minimize the total difference between the cumulative vehicle numbers (CVN) at the upstream and at the downstream boundaries of each link subject to flow-conservation and budget constraints. CVN were represented using transfer flows from connected links. The resulting formulation is a linear program that represents a dynamic system optimum traffic flow pattern, embedding the LTM’s network loading procedure. In contrast to the single-destination system optimum dynamic traffic assignment, based on the cell transmission model, the proposed formulation requires considerably fewer decision variables, thus potentially providing a more scalable approach. The proposed formulation was implemented on an example network to illustrate the behavior of the model, and was compared with the cell-based formulation. We show that the model describes free-flow and congested traffic flow states accurately in terms of shock-wave propagation, queuing of vehicles, and optimal total system travel time.

Service Network Design for Same Day Delivery with Mixed Autonomous Fleets

Two-tier city logistics is a well-established concept to achieve high levels of consolidation in urban freight distribution. With the recent shift towards offering same day delivery, service providers in parcel delivery are looking at new solutions to deal with the resulting challenges. We introduce autonomous vehicles as an upcoming technology to this field of research and consider a mixed fleet in the first tier of city logistics. Because autonomy cannot be ensured on all roads of the network, we handle the heterogeneous infrastructure with manually operated vehicles serving as platoon leaders. In our proposed MILP formulation of service network design for autonomous vehicles in platoons (SNDAVP), we show how platooning can be incorporated into this tactical planning problem. Computational experiments on first instances are conducted using CPLEX.

Covering and connectivity constraints in loop-based formulation of material flow network design in facility layout

The shortest loop covering at least one edge of each workcenter in a manufacturing facility layout is an instance of the generalized traveling salesman problem. The optimal solution to this problem is a promising design for non-vehicle-based material handling, typical of most types of conveyors and power-and-free systems, where the length of the path is the main driver of the total investment costs. The loop formulation is usually embedded within a larger problem of the concurrent design of the loop and the input/output stations for vehicle-based material handling typical of automatically guided vehicles and autonomous delivery robots. In these systems, it is not the length, but the total flow of the loaded and empty vehicles that drives the objective function. It has been shown that the shortest loop provides an effective heuristic scheme to achieve prosperous and robust solutions for the concurrent design of the loop and input/output stations. We review and compare covering constraints formulations, provide new insight into connectivity constraints, improve the model formulation and its solution procedure, and report computational results.

Circulation network design for urban rail transit station using a PH(n)/PH(n)/C/C queuing network model

Width is crucial to the performance of circulation network in urban rail transit station. However, poor performance has been observed in most existing circulation systems. In fact, randomness and state-dependence exist in circulation network where blocking and feedback cannot be ignored. In this paper, we develop a PH(n)/PH(n)/C/C state-dependent queuing network model with an analytical solution. This model describes the random and state-dependent arrival interval as well as service time by phase-type distribution. Feedback is also taken into account. The existing M/M(n)/C/C is a special case of the proposed PH(n)/PH(n)/C/C queuing network model, and the existing M/G(n)/C/C and D/D/1/C models can be approximated by the proposed network model. Then we present a programming formulation for circulation network design with blocking probability control based on the queuing network model. Finally, we illustrate the applicability of the proposed design method by comparing it with the existing design methods. The results show that: 1) the blocking probability is quite small and evenly distributed in the network designed by the new method, while much bigger and fluctuating blocking probabilities exist in networks designed by the other two methods; 2) other performance measures, like area per passenger, dwell time and throughput, are also considerably improved in the new method; 3) performance measures of the proposed method enjoy high performance-cost elasticity compared with the other two methods. An interesting insight is also obtained that the squared coefficient of variation for arrival interval plays an important role in determining the optimal width for circulation network.

Hybrid simulation and optimization approach for green intermodal transportation problem with travel time uncertainty

The increasing volumes of road transportation contribute to congestion on road, which leads to delays and other negative impacts on the reliability of transportation. Moreover, transportation is one of the main contributors to the growth of carbon dioxide equivalent emissions, where the impact of road transportation is significant. Therefore, governmental organizations and private commercial companies are looking for greener transportation solutions to eliminate the negative externalities of road transportation. In this paper, we present a novel solution framework to support the operational-level decisions for intermodal transportation networks using a combination of an optimization model and simulation. The simulation model includes stochastic elements in form of uncertain travel times, whereas the optimization model represents a deterministic and linear multi-commodity service network design formulation. The intermodal transportation plan can be optimized according to different objectives, including costs, time and CO_2e emissions. The proposed approach is successfully implemented to real-life scenarios where differences in transportation plans for alternative objectives are presented. The solutions for transportation networks with up to 250 services and 20 orders show that the approach is capable of delivering reliable solutions and identifying possible disruptions and alternatives for adapting the unreliable transportation plans.

Two-phase stochastic program for transit network design under demand uncertainty

This paper develops a reliability-based formulation for rapid transit network design under demand uncertainty. We use the notion of service reliability to confine the stochastic demand into a bounded uncertainty set that the rapid transit network is designed to cover. To evaluate the outcome of the service reliability chosen, flexible services are introduced to carry the demand overflow that exceeds the capacity of the rapid transit network such designed. A two-phase stochastic program is formulated, in which the transit line alignments and frequencies are determined in phase 1 for a specified level of service reliability; whereas in phase 2, flexible services are determined depending on the demand realization to capture the cost of demand overflow. Then the service reliability is optimized to minimize the combined rapid transit network cost obtained in phase 1, and the flexible services cost and passenger cost obtained in phase 2. The transit line alignments and passenger flows are studied under the principles of system optimal (SO) and user equilibrium (UE). We then develop a two-phase solution algorithm that combines the gradient method and neighborhood search and apply it to a series of networks. The results demonstrate the advantages of utilizing the two-phase formulation to determine the service reliability as compared with the traditional robust formulation that pre-specifies a robustness level.