Two-stage Solution Approach Research Articles

A two-stage solution approach for scheduling flexible manufacturing systems with multi-fixturing pallets

A two-stage solution approach for scheduling flexible manufacturing systems with multi-fixturing pallets

Passenger Route and Departure Time Guidance Under Disruptions in Oversaturated Urban Rail Transit Networks

The urban rail transit (URT) system attracts many commuters with its punctuality and convenience. However, it is vulnerable to disruptions caused by factors such as extreme weather and temporary equipment failures, which greatly affect passengers’ journeys and diminish the system’s service quality. In this study, we propose targeted travel guidance for passengers at different space–time locations by devising passenger rescheduling strategies during disruptions. This guidance not only offers insights into route changes but also provides practical recommendations for delaying departure times when required. We present a novel three-feature four-group passenger classification principle, integrating temporal, spatial, and spatiotemporal features to classify passengers in disrupted URT networks. This approach results in the creation of four distinct solution spaces based on passenger groups. A mixed integer programming model is built based on individual level considering the first-in-first-out rule in oversaturated networks. In addition, we present a two-stage solution approach for handling the complex issues in large-scale networks. Experimental results from both small-scale artificial networks and the real-world Beijing URT network validate the efficacy of our proposed passenger rescheduling strategies in mitigating disruptions. Specifically, when compared to scenarios with no travel guidance during disruptions, our strategies achieve a substantial reduction in total passenger travel times by 29.7% and 50.9%, respectively, underscoring the effectiveness in managing unexpected disruptions.

A Two-Phase Approach for Reliability-Redundancy Optimization of a Communication Satellite

The development and launch of communication satellite projects pose significant challenges and costs. The expenses can range from several hundred million dollars, contingent on factors such as mission objectives, satellite system size and complexity including the launch vehicle, and ground infrastructure. Satellites must be designed to withstand harsh conditions in space, such as the extreme temperatures, radiation, and other hazards, while delivering reliable communication services to its users. However, once a satellite is launched, physical maintenance interventions become infeasible in the event of technical problems. Thus, reliability is a critical aspect for these expensive systems. This study aims to minimize the cost of a high-tech communication satellite by addressing design considerations that meet customer reliability requirements without exceeding power and redundant equipment limits. To achieve this goal, we propose an integer non-linear programming model in this research. To solve the satellite design problem, we adopt a two-stage solution approach. Conventional industrial practices in satellite design often involve iterative attempts to determine the redundancy level of onboard units based on customer reliability requirements. These processes rely heavily on the experience of design engineers who evaluate a limited number of alternatives to determine the number of redundant units, resulting in sub-optimal outcomes. In contrast, our proposed approach systematically handles the problem and yields optimal results. Our findings demonstrate that the proposed two-phase approach can achieve optimal redundancy levels within seconds.

A multi-objective mixed integer linear programming model for thesis defence scheduling

In this paper, we address the thesis defence scheduling problem, a critical academic scheduling management process, which has been overshadowed in the literature by its counterparts, course timetabling and exam scheduling. Specifically, we address the single defence assignment type of thesis defence scheduling problems, where each committee is assigned to a single defence, scheduled for a specific day, hour and room. We formulate a multi-objective mixed-integer linear programming model, which aims to be applicable to a broader set of cases than other single defence assignment models present in the literature, which have a focus on the characteristics of their universities. For such a purpose, we introduce a different decision variable, propose constraint formulations that are not regulation and policy specific, and cover and offer new takes on the more common objectives seen in the literature. We also include new objective functions based on our experience with the problem at our university and by applying knowledge from other academic scheduling problems. We also propose a two-stage solution approach. The first stage is employed to find the number of schedulable defences, enabling the optimisation of instances with unschedulable defences. The second stage is an implementation of the augmented ϵ-constraint method, which allows for the search of a set of different and non-dominated solutions while skipping redundant iterations. The methodology is tested for case-studies from our university, significantly outperforming the solutions found by human schedulers. A novel instance generator for thesis scheduling problems is presented. Its main benefit is the generation of the availability of committee members and rooms in availability and unavailability blocks, resembling their real-world counterparts. A set of 96 randomly generated instances of varying sizes is solved and analysed regarding their relative computational performance, the number of schedulable defences and the distribution of the considered types of iterations. The proposed method can find the optimal number of schedulable defences and present non-dominated solutions within the set time limits for every tested instance.

A two-echelon two-indenture warranty distribution network development and optimization under batch-ordering inventory policy

The use of the warranty distribution network (WDN) to support after-sales service contributes to the stakeholders’ market competition and becomes popular in the modern business. However, there are two major challenges in the development of WDN: 1) locating repair centers and allocating corresponding customers, and 2) choosing the spare parts inventory policy for each repair center. In order to address these two challenges, this paper proposes a customized location-allocation WDN model under batch-ordering inventory policy where repair center acts as a two-layer system (two-echelon) to support a set of customers in a two-layer network (two-indenture). In this network, a depot repair center is selected to meet the orders through a high-capacity supplier in the first echelon and a certain number of sub-repair centers are determined to cover customers in the second echelon. To optimize the proposed model, a two-stage solution approach based on Monte-Carlo simulation and Variable Neighborhood Search is developed. The electric vehicle battery system case study is used to validate the proposed model and solution approach. The obtained results showed that depending on the budget available, spare parts inventory level in the operational repair centers is positively associated their distance to the depot repair center.

A two-stage solution approach for unequal area facility layout problem with bi-directional relaxed flexible bay structure

PurposeThe purpose of this article is to develop a bi-directional relaxed flexible bay structure (BRFBS) in the layout for the unequal area facility layout problems (UA-FLPs) and test the suitability of the proposed approach using literature data.Design/methodology/approachThis research adopts a two-stage solution approach for UA-FLPs to form BRFBS in the layout. The solution to UA-FLPs is carried out in discrete space. The proposed heuristic method optimises the layout plan for minimising the material handling cost (MHC), and also, it indirectly optimises the space utilisation by reducing the empty space in the layout. The first stage of layout design assumes that all facilities are equal in size and uses quadratic assignment problem (QAP) model. QAP is solved with a simulated annealing heuristic method. In the second stage, a heuristic method is proposed to find the optimum width for each bay and the dimension for facilities. The proposed heuristic method is tested with numerical data available in the literature. Results are compared with the results obtained by layout planning software, and with the simulated annealing algorithm for flexible bay structure (SA-FBS) heuristic procedure for continuous space UA-FLPs.FindingsThe proposed two-stage solution approach gives the BRFBS for the UA-FLPs. BRFBS helps to create proper aisle structure in the layout plan. The layout configuration and solution of the proposed method is better than the layout planning software solution and SA-FBS solution. The application of the proposed heuristic method to case data gave lesser MHC, better space utilisation and better aisle formation than the existing layout.Research limitations/implicationsThe proposed approach has the limitation that it can be applied only to UA-FLPs solved in discrete space. When the UA-FLPs are solved in continuous space, then it is not possible to make application of this approach to form bi-directional relaxed flexible bays in the layout plan.Practical implicationsMost of the modern industries are automated, and they use material handling equipment (MHE) like automated guided vehicles (AGVs). Design of layout plans that help to create proper aisle structure for AGV’s in the layout plan is a challenging to the researchers. The BRFBS configuration is more suitable in the flexible manufacturing system where AGVs are used for material transportation.Originality/valueThis paper proposes a novel two-stage heuristic method for solving the UA-FLPs in discrete space. The proposed approach generates a BRFBS in the layout plan. The BRFBS helps to create a proper aisle structure suitable for better material handling operations. Hence, this type of layout helps in easy interaction of the MHE (e.g. AGVs) with the boundaries of the facilities touching the aisle.

A Two-Stage Approach With a Departure Time Based Solution Representation for Electric Bus Vehicle Scheduling

Vehicle scheduling problem (VSP) in public transit refers to arranging a fleet of vehicles to make vehicles’ departure times coincide with the times in given bus timetables. It is vital for bus enterprises to ensure the service quality and save operational cost. Due to the limited driving range and charging requirements of electric vehicles, how to efficiently schedule electric vehicles is a challenging task with the popularization of electric bus vehicles. In this paper, we propose a two-stage solution approach (SA-LS) combining a simulated annealing (SA) and a local search (LS) for an electric vehicle scheduling problem (EVSP) in public transport. This approach is based on a novel solution coding that represents a scheduling solution by departure times of a fleet of vehicles. The decoding procedure considers limited driving range and recharging time of electric vehicles. The SA is used to find a set of solutions able to be potentially improved by LS. The LS combined with a departure-time adjustment procedure (DTAP) is devised to improve the solutions found by SA. Evaluation functions are devised separately for SA and LS to guide their search. The proposed approach is applied to real world vehicle scheduling problem of three bus lines in Qingdao city, China. Experiments show that SA-LS is able to generate high-quality scheduling solutions within short computational time.

Machine learning and optimization models for supplier selection and order allocation planning

Supplier selection and order allocation have significant roles in supply chain management. These processes become major challenges when the demand is uncertain. This research presents a new two-stage solution approach for supplier selection and order allocation planning where a forecasting procedure is integrated with an optimization model. In the first stage, the demand is forecasted to handle the demand vagueness. A novel Relational Regressor Chain method is introduced to determine the future demand, which is compared with the Holt's Linear Trend and the Auto-Regressive Integrated Moving Average methods to ensure the forecasting accuracy. The forecasted demand is then fed to the second stage where a multi-objective programming model is developed to identify suitable suppliers and order quantities from each supplier. Weighted-sum and ε-constraint methods are utilized to obtain the efficient solutions. To our knowledge, this paper is the first study that has integrated demand forecasting with the supplier selection and order allocation planning. A real dataset from a Canadian food supply network is used to examine the results of the forecasting methods and to determine the orders allocated to each supplier. The results of the forecasting methods show that the proposed Relational Regressor Chain method can forecast demand with a higher precision than the other forecasting methods considered in this paper. It is also evident from the results that the selection of the forecasting methods may have impact on both the selection of suppliers and the orders allocated to them.

Two-stage battery recharge scheduling and vehicle-charger assignment policy for dynamic electric dial-a-ride services

Coordinating the charging scheduling of electric vehicles for dynamic dial-a-ride services is challenging considering charging queuing delays and stochastic customer demand. We propose a new two-stage solution approach to handle dynamic vehicle charging scheduling to minimize the costs of daily charging operations of the fleet. The approach comprises two components: daily vehicle charging scheduling and online vehicle–charger assignment. A new battery replenishment model is proposed to obtain the vehicle charging schedules by minimizing the costs of vehicle daily charging operations while satisfying vehicle driving needs to serve customers. In the second stage, an online vehicle–charger assignment model is developed to minimize the total vehicle idle time for charges by considering queuing delays at the level of chargers. An efficient Lagrangian relaxation algorithm is proposed to solve the large-scale vehicle-charger assignment problem with small optimality gaps. The approach is applied to a realistic dynamic dial-a-ride service case study in Luxembourg and compared with the nearest charging station charging policy and first-come-first-served minimum charging delay policy under different charging infrastructure scenarios. Our computational results show that the approach can achieve significant savings for the operator in terms of charging waiting times (–74.9%), charging times (–38.6%), and charged energy costs (–27.4%). A sensitivity analysis is conducted to evaluate the impact of the different model parameters, showing the scalability and robustness of the approach in a stochastic environment.

Joint Radio Resource Management and Link Adaptation for Multicasting 802.11ax-Based WLAN Systems

Adopting OFDMA and MU-MIMO techniques for both downlink and uplink IEEE 802.11ax will help next-generation WLANs efficiently cope with large numbers of devices but will also raise some research challenges. One of these is how to optimize the channelization, resource allocation, beamforming design, and MCS selection jointly for IEEE 802.11ax-based WLANs. In this paper, this technical requirement is formulated as a mixed-integer non-linear programming problem maximizing the total system throughput for the WLANs consisting of unicast users with multicast groups. A novel two-stage solution approach is proposed to solve this challenging problem. The first stage aims to determine the precoding vectors under unit-power constraints. These temporary precoders help re-form the main problem into a joint power and radio resource allocation one. Then, two low-complexity algorithms are proposed to cope with the new problem in stage two. The first is developed based on the well-known compressed sensing method while the second seeks to optimize each of the optimizing variables alternatively until reaching converged outcomes. The outcomes corresponding to the two stages are then integrated to achieve the complete solution. Numerical results are provided to confirm the superior performance of the proposed algorithms over benchmarks.

Optimal heterogeneous search and rescue asset location modeling for expected spatiotemporal demands using historic event data

The United States Coast Guard is charged with coordinating all search and rescue missions in maritime regions within the United States’ purview. Given the size of the Pacific Ocean and limited available resources, the service seeks to posture its fleet of organic assets to reduce the expected response time for such missions. Leveraging 7.5 years of historic event records for the region of interest, we demonstrate a two-stage solution approach. In the first stage, we develop a stochastic zonal distribution model to evaluate spatiotemporal trends for emergency event rates and response strategies. In the second stage, results from the aforementioned analysis enable parameterization of a bi-objective MILP to identify the best locations to station limited heterogeneous search and rescue assets. This research models both 50th and 75th percentile forecast demands across both the set of current homeports, and a larger set of feasible basing locations. Results provide a minimum 9.6% decrease in expected response time over current asset basing. Our analysis also reveals that positioning assets to respond to 75th percentile demands sacrifices, at most, 2.5% in response time during median demand months, whereas positioning for median demand results in operationally inadequate response capability when 75th percentile demands are encountered.

A general ontological timetabling-model driven metaheuristics approach based on elite solutions

Timetabling is a managerial problem that recurringly appears in various domains such as education, transport, sports, and staff management. The combinatorial nature of this problem poses solution challenges that aggravate with an increase in the problem size. While heuristics and metaheuristics initially offered promise, the progress plateaued as attempts to solve even bigger problems showed exorbitant costs while sampling feasible solutions. This issue is criticized for the lack of exploiting the underlying problem structure and the prevailing fragmentation in modeling and solution approaches. To address these issues, we first propose a novel timetabling ontology that serves as a common modeling basis, resolving the existing heterogeneity across various application domains. This ontology facilitates mapping the anatomy of any real timetabling problem onto its general structure. Second, it offers a unique two-stage solution approach for solving this generalized problem. The first stage of this approach entails generating elite initial solutions by exploiting this general problem structure, while the second stage uses a metaheuristic to improve these solutions at a very low computational cost. Using a university timetabling problem, we demonstrate the applicability of this approach. The numerical results show that the proposed algorithm converges within a fraction of computational costs incurred by other techniques for comparable problem sizes. This research paves the way for consolidating efforts for the development of generalizable cross-domain timetabling approaches.

Districting for parcel delivery services – A two-Stage solution approach and a real-World case study

This paper studies a real-world problem arising in the context of parcel delivery. Given a heterogeneous set of resources, i.e., different drivers and different vehicles, the problem for each day consists of assigning a driver and a vehicle to each customer requiring service. Two conflicting aspects must be taken into account. On the one hand, service consistency is desirable, meaning that a customer should always be served by the same driver. On the other hand, daily demand fluctuations and tight resource constraints prohibit fixed resource assignments. With the aim of finding a reasonable compromise between these aspects, we propose a novel two-stage districting approach, which establishes delivery districts in the first stage and adapts them to the daily demand realizations in the second stage. For the first stage problem we propose three models that differ in the level of detail of their input data, their expected compliance with service consistency and the driver’s contractual working times, and their computational effort. Our two-stage approach merges the two dominant approaches in the literature, which either determine a priori routes and then adapt them on a daily basis, or derive fixed service regions for drivers. We present a case study based on a real-world data set. The results highlight the differences between the three first stage models and show that only few adaptations of the districts are necessary in the second stage to achieve feasible daily delivery tours along with a very good workload balance for drivers. We also analyze the effects of a homogeneous vs a heterogeneous fleet, of full time drivers vs full and part time drivers, and of the location of the depot and the length of the planning horizon.

A two-stage solution approach for plastic injection machines scheduling problem

One of the most common plastic manufacturing methods is injection molding. In injection molding process, scheduling of plastic injection machines is very difficult because of the complex nature of the problem. For example, similar plastic parts should be produced sequentially to prevent long setup times. On the other hand, to produce a plastic part, its mold should be fixed on an injection machine. Machine eligibility restrictions should be considered because a mold can be usually fixed on a subset of the injection machines. Some plastic parts which have same shapes but different colors are used same mold so these parts can only be scheduled simultaneously if their mold has copies, otherwise resource constraints should be considered. In this study, a multi-objective mathematical model is proposed for parallel machine scheduling problem to minimize makespan, total tardiness, and total waiting time. Since NP-hard nature of problem, this paper presents a two-stage mathematical model and a two-stage solution approach. In the first stage of mathematical model, jobs are assigned to the machines and each machine is scheduled separately in the second stage. The integrated model and two-stage mathematical model are scalarized by using goal programming, compromise programming and Lexicographic Weighted Tchebycheff programming methods. To solve large-scale problems in a short time, a two-stage solution approach is also proposed. In the first stage of this approach, jobs are assigned to machines and scheduled by using proposed simulated annealing algorithm. In the second stage of the approach, starting time, completion time and waiting time of the jobs are calculated by using a mathematical model. The performance of the methods is demonstrated on randomly generated test problems.

A two-stage solution approach for personalized multi-department multi-day shift scheduling

In this paper, we address a personalized multi-department multi-day shift scheduling problem with a multi-skill heterogeneous workforce where employees can be transferred between departments under some restrictions. The objective is to construct a schedule that minimizes under-coverage, over-coverage, transfer and labor costs. We propose a novel two-stage approach to solve it: the first stage considers an approximate and smaller problem based on data aggregation and produces approximate transfers. The second stage constructs personalized schedules based on the information deduced from the first stage. An exhaustive experimental study is conducted and proves the efficiency of the proposed approach in terms of solution quality and computing times.

Considering chain-to-chain competition on environmental and social concerns in a supply chain network design problem

ABSTRACTThe supply chain network design problem has been widely studied as one of the most important issues in supply chain management. In recent years, competitive nature of markets caused researchers to attend the competition issue in their studies. In this research, a multi-objective mathematical model for dynamic and integrated network design of a competitive and sustainable supply chain is presented. In the proposed model, a chain-to-chain competition between two supply chains, who compete on environmental and social concerns, is considered. To solve this competitive model, a two-stage solution approach is introduced. A game theory approach is initially used to determine the equilibrium values for competitive decisions. Then, according to results of the competitive stage and respecting complexity of the proposed model, a Pareto-based multi-objective meta-heuristic algorithm is applied to solve the achieved network design problem. Finally, to evaluate the efficiency of the proposed model and presented solution approach, several generated numerical examples are graphically and statistically studied.

A two-stage solution approach for the Directed Rural Postman Problem with Turn Penalties

In this paper, we consider the Directed Rural Postman Problem with Turn Penalties (DRPP-TP). A solution is a tour that traverses all required arcs of the graph. The total cost of the tour is the sum of the lengths of the traversed arcs plus the penalties associated with the turns. One solution approach involves transforming the arc routing problem into an equivalent node routing problem. An alternative direct approach (without graph transformation) that involves two stages has been proposed in the literature. In the first part of this paper, we investigate the applicability of the direct approach. We identify several characteristics of the input instance that make this approach effective and present several limitations of this approach. In the second part of this paper, we describe an integer linear program that is combined with a local search algorithm. This combination produces high-quality solutions to the DRPP-TP in a reasonable amount of computing time.

다중치구 장착 팔렛과 가변 가공시간을 고려하는 유연제조셀에 대한 이중 기준 스케줄링

This study considers a scheduling problem for a single machine flexible machining cell in which each pallet can load multiple parts and part processing times are controllable with different processing costs. The problem is to determine the set of parts to be loaded on each pallet, the part processing times, the pallet input sequence and the pallet processing sequence. To investigate the trade-off between part processing cost and scheduling performance, we consider a bi-criterion objective of minimizing the total processing cost and the total flow time. A two-stage solution approach is proposed in which part loading/pallet input sequencing are done using a priority rule and part process timing/pallet process sequencing are done using an iterative heuristic. Simulation experiments were done, and the results show that the two-stage solution approach gives better Pareto solutions than the rule combination based solution approach.

Two-stage multi-objective OPF for AC/DC grids with VSC-HVDC: Incorporating decisions analysis into optimization process

A two-stage solution approach for solving the problem of multi-objective optimal power flow (MOPF) is proposed for hybrid AC/DC grids with VSC-HVDC. First, a MOPF model for hybrid AC/DC grids is built to coordinate the economy, voltage deviation and environmental benefits. Then, a two-stage solution approach, incorporating decision analysis into optimization process, is presented to solve the model. The first stage of the approach is consisted of a multi-objective particle swarm optimization algorithm with a hybrid coding scheme employed to find multiple Pareto-optimal solutions. The second stage will have the obtained solutions clustered into different groups using fuzzy c-means (FCM) clustering, and then the ‘best’ compromise solutions are obtained by calculating the priority memberships of the solutions belonging to the same groups via grey relation projection (GRP) method. The novelty of this approach lies primarily in incorporating the FCM-GRP based decisions analysis technique into MOPF studies, thereby assisting decision makers to automatically identify the ‘best’ operation points. The effectiveness of the proposed approach is verified based on the test results of the IEEE 14- and 300- bus systems.

A TWO-STAGE SOLUTION APPROACH FOR THE LARGE-SCALE HOME HEALTHCARE ROUTEING AND SCHEDULING PROBLEM

The purpose of this study is to introduce a two-stage solution approach for a large-scale home healthcare routeing and scheduling problem (HHCRSP). In the first part of the two-stage solution approach, a cluster-assign algorithm is employed, based on the home location and the time to obtain feasible clusters. In the second stage, using these clusters, route construction heuristics start to create schedules and routes, taking the side constraints of the model into consideration. Using the novelty of this two-stage solution approach, higher diversification is achieved with a series of newly-developed cross movement strategies. The computational results show that our solution approach offers certain advantages, such as an increase in the efficient use of human resources, and a decrease in the working time of nurses.