Integer Linear Programming Mathematical Model Research Articles

Efficiency-oriented vehicle relocation of shared autonomous electric fleet in station-based car-sharing system

Long waiting delays for users and significant imbalances in vehicle distribution are bothering traditional station-based one-way electric car-sharing system operators. To address the problems above, a “demand forecast-station status judgement-vehicle relocation” multistage dynamic relocation algorithm based on the automatic formation cruising technology was proposed in this study. In stage one, a novel trip demand forecast model based on the long short-term memory network was established to predict users' car-pickup and car-return order volumes at each station. In stage two, a dynamic threshold interval was determined by combining the forecast results with the actual vehicle distribution among stations to evaluate the status of each station. Then vehicle-surplus, vehicle-insufficient, vehicle-normal stations, and the number of surplus or insufficient vehicles for each station were counted. In stage three, setting driving mileage and carbon emission as the optimization objectives, an integer linear programming mathematical model was constructed and the optimal vehicle relocation scheme was obtained by the commercial solver Gurobi. Setting 43 stations and 187 vehicles in Jiading District, Shanghai, China, as a case study, results showed that rapid vehicle rebalancing among stations with minimum carbon emissions could be realized within 15 min and the users’ car-pickup and car-return demands could be fully satisfied without any refusal.

A multi-objective fuzzy mathematical model for circular economy with leasing as a strategy

PurposeThis paper aims at developing a multi-objective mathematical model of circular economy that integrates key concept of leasing as a strategy in addition to reuse, refurbishing, primary recycling, secondary recycling and disposal.Design/methodology/approachThis paper proposes multi-objective fuzzy mixed integer linear programming mathematical model considering multi-product, multi-echelon and multi-capacitated concepts of the circular economy. The three objectives of the proposed model, namely, economic, environmental and social are solved simultaneously using constraint approach to obtain balanced trade-off between the objective functions. The model is validated by solving a case study from the literature. The proposed model is made pragmatic for industrial application by considering multi-external suppliers multi-customer zones, multi-disassembly centers, multi-collection centers and multi-refurbishing centers and accounting for purchasing, processing, transportation, set-up costs and capacity constraints at the same time.FindingsThe results show that the leasing of the products improves the economic function in addition to the known environmental improvements. The proposed model also shows that the circular economy can generate the jobs for the unskilled people at different locations.Research limitations/implicationsThe proposed model can be further improved by considering the non-linearity due to economy of scale at various centers and in transportation. The model can be further extended to make it multi-period model.Practical implicationsThe proposed model of circular economy can be used by the organizations as a policy tool to decide the optimum number of collection centers, disassembly centers, refurbishing centers, recycling centers and disposal centers and their optimum locations and allocations. The organizations can also trade-off among economic, environmental and social benefits of their proposed decisions in circular economy.Originality/valueThe originality of the proposed mathematical model is consideration of leasing as a strategy to have better control over the supply chain for circularity; considering the training of unskilled people for backward supply chain jobs and accounting for primary recycling and secondary recycling separately for economical computation.

A cascaded flowshop joint scheduling problem with makespan minimization: A mathematical model and shifting iterated greedy algorithm

This paper studies a cascaded flowshop joint scheduling problem that has critical applications in the electronic information equipment manufacturing industry but has received limited attention in the scheduling field. The cascaded flowshop joint scheduling problem encompasses both a distributed permutation flowshop scheduling problem and a hybrid flowshop scheduling problem. This paper investigates the efficient scheduling of a set of jobs in two heterogeneous flowshops to minimize the makespan. We present a mixed integer linear programming mathematical model and a shifting iterated greedy algorithm, which constantly changes its search space to explore different solution spaces. Based on the specific characteristics of the problem, a hybrid scheduling approach that combines forward and backward scheduling, a step-by-step destruction and reconstruction operator, and three adaptive reconstructive methods that combine coarse-tuning and fine-tuning are proposed to explore the near-optimal solution. Through comprehensive computational comparison and statistical analysis, the results demonstrate that the proposed shifting iterated greedy algorithm performs significantly better in relative deviation index values at the same CPU running time.

Workload balancing and scheduling in picking tower systems considering different storage strategies

Picking tower systems are particularly suitable in the e-commerce distribution field. They permit to stock and pick a wide variety of items by maximizing storage capacity and space utilization. Such types of systems are comparable to zone picking solutions, since pickers work on one floor during the same working shift. However, differences also exist since, for example, once the picking tower system is designed, it is not possible to improve or reduce the area of each floor. Thus, a proper workload balancing is required to avoid an efficiency reduction of this system. This paper proposes a mixed integer linear programming mathematical model to assign pickers to floors and jointly schedule the picking list of each of them aiming to minimize the completion time of all orders. The model is applied to a real case study and first managerial insights are derived by investigating how the number of floors, the storage strategy and the number of pickers allowed on each floor influence the workload and the completion time. The results show that, for the considered case, the most effective configuration is the brand-based storage strategy with four picking levels.

Optimization of production planning using integer linear programming method (case study of bakpia menik)

Bakpia Menik is a Small and Medium Enterprise (UKM) which operates in the field of bakpia production. Bakpia is one of the local cakes which is the main souvenir from Yogyakarta, so there is a big potential for increasing production. However, SMEs still lack production management planning to optimize resource use. So it is difficult to capture this big opportunity to maximize profits for SMEs. Seeing these problems, this research designed an integer linear programming mathematical model to optimize profits by using existing resources. Integer Linear Programming (ILP) is a mathematical model for maximizing profit and minimizing cost based on a mathematical model involving integer variables represented in a linear relationship. This research produces an integer linear programming model that presents the variables, resources, and constraints of Bakpia Menik. The model output shows that the optimal production amount by maximizing resource use is 31232 units and the maximum profit is IDR 33,431,750. From the model output, it can also show the advantages and disadvantages of Bakpia resources, so that resource availability planning can be carried out which can minimize holding costs.

An effective adaptive iterated greedy algorithm for a cascaded flowshop joint scheduling problem

This paper addresses a novel scheduling problem, namely the cascaded flowshop joint scheduling problem (CFJSP), which has critical applications in the modern electronic information equipment manufacturing industry. The CFJSP is composed of a distributed permutation flowshop scheduling problem and hybrid flowshop scheduling problem. This paper considers how to arrange a variety of jobs for the two flowshops together to minimize total flowtime. We present a mixed integer linear programming mathematical model and an effective adaptive iterated greedy (AIG) algorithm with a decomposition and collaboration mechanism, which optimizes each production phase sequentially and ultimately optimizes the whole process. Combining the problem-specific characteristic, an adaptive inverse bounded heuristic, an adaptive bounded range local search, and an odd/even random insertion reconstruction mechanism are proposed to explore more valuable space. Comprehensive computational experiments and statistical analyses are conducted to verify the effectiveness of the proposed AIG. The experimental results show that the proposed AIG significantly outperforms the state-of-the-art competing algorithms from the literature in relative deviation index values at the same CPU running time.

Multiobjective U-Shaped Disassembly Line Balancing Problem Considering Human Fatigue Index and an Efficient Solution

The progress of science and technology speeds up the replacement of products and produces a large number of end-of-life products. Traditional incineration causes a waste of resources and pollution to the environment. Disassembling and recycling end-of-life products are the recommended way to maximize the utilization of resources and reduce environmental pollution. Disassembly performance is affected by many factors, such as the disassembly posture of the human body, the fatigue of workers on a workstation, disassembly profit, and task precedence relationship. In this article, a mixed integer linear programming mathematical model for U-shaped layout disassembly line balancing problems is developed, in which the balance of workers’ fatigue indices is an optimization objective in addition to disassembly profits. An efficient solution to the problem that uses a collaborative resource allocation strategy of the multiobjective evolutionary algorithm is proposed. The linear programming solver CPLEX is used to verify the accuracy of the model and compared with the proposed algorithm. Experiments demonstrate that the algorithm is significantly superior to the CPLEX solver in handling large-scale cases. The proposed algorithm is also compared with two well-known algorithms, which further verifies its superiority.

DRL-assisted joint allocation of antenna, radio, and front-haul resources in TWDM-PON-based NG-RANs with mMIMO-enabled beamforming

The high spectrum efficiency of massive multiple input multiple output (mMIMO)-enabled beamforming is attractive for solving the massive number of connections in next-generation radio access networks (NG-RANs). However, the beamforming based on multiple antenna sub-arrays to support multi-connections would introduce extra 2D antenna sub-array selection and radio resource block (RB) allocation; meanwhile, considering the front-haul bandwidth consumption would reduce as much as possible the redundant data transmitting over front-haul in the NG-RANs. Therefore, a key issue is how to coordinate 2D antenna sub-array selection and radio RB allocation to minimize the front-haul bandwidth and maximize the radio RB utilization when accommodating a set of beam antenna array (BAA) requests. In this paper, we first establish a 3D BAA mapping model to jointly optimize 2D antenna sub-array selection and radio RB allocation, which would in turn affect the allocation of the front-haul wavelength bandwidth in a time and wavelength division multiplexed passive optical network (TWDM-PON)-based front-haul with the mMIMO antenna system. An integer linear programming mathematical model is formulated, and a novel deep reinforcement learning (DRL)-based algorithm is proposed to optimize the front-haul bandwidth and radio RB utilization. Besides, two heuristic algorithms are developed with different antenna sub-array selection policies as the benchmarks. The extensive simulation results show that our proposed DRL-based algorithm can attain the lowest average cost (AC) for different numbers of BAA requests considered by seeking the optimal trade-off between the front-haul bandwidth consumption and the number of the used antennas. Compared with the inter-sub-array benchmark, the DRL-based algorithm can achieve up to 7.5% AC reduction, which is mainly attributed to the 21.2% reduction of the front-haul bandwidth without increasing the number of used antennas.

A station location-allocation optimization problem in star-star pipeline network layout

The oil and gas field surface gathering pipeline network is an important hub for transporting oil and gas products outward, and its optimal design is crucial to reducing the construction cost of the pipeline system. Star-star topology is often applied to the layout of surface gathering pipeline networks in oil and gas fields. However, the optimization of star-star topology is often carried out under the constraint of the fixed station type, which may easily lead to a waste of station capacity and increase investment or make the optimization results meaningless. In this article, a mixed integer linear programming mathematical model for the overall optimization of star-star pipeline network layout considering the station location-allocation problem is constructed in discrete space with coupled station type constraints, and the branch-and-bound method is used to obtain the global optimal solution. Three cases verify the feasibility and effectiveness of the model and algorithm. The results show that the maximum avoided capacity waste is 20 × 104 m3/d and the maximum investment can be reduced by 8961.6 × 104 Yuan, which shows that the proposed model can effectively improve the economy and rationality of the pipeline system, and has important guiding significance for the construction of oil and gas fields.

A simulation-based optimisation for the stochastic green capacitated p-median problem

Purpose: This paper aims to propose a new model called the stochastic green capacitated p-median problem with a simulation-based optimisation approach. An integer linear programming mathematical model is built considering the total emission produced by vehicles and the uncertain parameters including the travel cost for a vehicle to travel from a particular facility to a customer and the amount of CO2 emissions produced. We also develop a simulation-based optimisation algorithm for solving the problem.Design/methodology/approach: The authors proposed new algorithms to solve the problem. The proposed algorithm is a hybridisation of Monte Carlo simulation and a Variable Neighbourhood Search matheuristic. The proposed model and method are evaluated using instances that are available in the literature.Findings: Based on the results produced by the computational experiments, the developed approach can obtain interesting results. The obtained results display that the proposed method can solve the problems within a short computational time and the solutions produced have good quality (small deviations).Originality/value: To the best of our knowledge, there is no paper in the previous literature investigating the simulation-based optimisation for the stochastic green capacitated p-median problem. There are two main contributions in this paper. First, to build a new model for the capacitated p-median problem taking into account the environmental impact. Second, to design a simulation-based optimisation approach to solve the stochastic green capacitated p-median problem incorporating VNS-based matheuristic and Monte Carlo simulation.

Feeder delivery vehicle scheduling optimization of high-speed railway express based on trunk and branch intermodal transportation

In view of the traditional branch line end express delivery centralized mode cannot adapt to the growing demand of high-speed rail (HSR) express, resulting in poor connection between trunk and branch line, high cost and poor timeliness. In this paper, the problem of scheduling optimization of branch-line flexible distribution vehicles relying on intermodal transportation of trunk and branch lines is proposed. Considering the number of vehicles, vehicle capacity, customer service time window and other constraints, an integer linear programming mathematical model with the minimum total cost of vehicle transportation cost, usage cost and time window penalty cost as the optimization objective is established. A two-level nested heuristic algorithm with two-level coding structure is proposed to solve the problem. Finally, a simulation example is given to verify the effectiveness of the model and the algorithm. The results show that the vehicle scheduling optimization problem studied in this paper can effectively improve the timeliness and accuracy of HSR express delivery, and can significantly reduce the total vehicle delivery cost.

Modified particle swarm algorithm for scheduling agricultural products

Industries tend to manufacture higher quality products with a low cost due to the competitive environmental loop and dynamic customers’ demand. The integration of intelligent manufacturing planning to agricultural operations and products will permit a spike in efficiency of yield, especially in the regions of agriculturally based economies. Though, to gain a vivid exploitation, the old-fashioned agriculture products manufacturing planning and scheduling techniques needs to be revised, especially the methodology in job shop planning must be augmented with efficient operational sequential scheduling. Cellular Manufacturing Systems (CMS) inclined to possess a higher complexity than the traditional manufacturing systems. Three major problems are coping in CMS domain: cell formation, product family selection, and product scheduling. This work deals with the problem of product scheduling in the CMS environment. A mixed integer linear programming mathematical model is introduced for the conflicting performance measures i.e. minimization of work in process (WIP) and maximization of average machine cell utilization. Since the current problem is considered as NP-hard problem, so a modified particle swarm optimization (MPSO) algorithm is proposed to find the optimum scheduling under the given constraint model of conflicting objectives. In the proposed MPSO, basic PSO is integrated with NEH heuristic to achieve better optimal sequence in less computation time. The obtained results are compared with other hybrid PSO algorithms with seed solutions from Gupta and Palmer heuristics. Furthermore, results are also compared against meta-heuristics such as genetic algorithm (GA), standard PSO, and artificial bee colony (ABC) algorithm. It shows that the proposed MPSO algorithm performs better than the existing compared algorithms. A real time case scenario of agriculture-based manufacturing industry is solved to validate the proposed planning algorithm.

Hub location problem in round-trip service applications

In this paper, we introduce a new hub-and-spoke structure for service networks based on round-trips as practiced by some transport service providers. This problem is a variant of Uncapacitated Hub Location Problem wherein the spoke nodes allocated to a hub node form round-trips (cycles) starting from and ending to the hub node. This problem is motivated by two real-life practices in logistics wherein runaway nodes and runaway connections with their associated economies of scale were foreseen to increase redundancy in the network. We propose a mixed integer linear programming mathematical model with exponential number of constraints. In addition to the separation routines for separating from among exponential constraints, we propose a hyper-heuristic based on reinforcement learning and its comparable counterpart as a variable neighborhood search. Our extensive computational experiments confirm efficiency of the proposed approaches.

Supply planning for shelters and emergency management crews

This paper addresses the problem of supplying provisions to civilians affected by an emergency and to the intervention groups that provide post emergency relief. We define the Emergency Supply using Heterogeneous Fleet Problem (ESHFP) using a Mixed Integer Linear Programming mathematical model that describes the complexities involved in these operations. Furthermore, we propose a novel heuristic algorithm which constructs a plan comprising a set of efficient vehicle routes in order to minimize the total supply time, respecting constraints concerning timing, demand, capacity and supply. The characteristics of the problem have been studied by solving an extensive set of test cases. The efficiency and practicality of the algorithm has been tested by applying it to a large scale ESHFP instance and to a case study involving a forest fire in the Province of Teruel, Spain.

Maintenance scheduling within rolling stock planning in railway operations under uncertain maintenance durations

Optimizing railway and rolling-stock operations, reducing costs and improving service reliability are goals that should be pursued and adapted to the current and future customer demand, while complying with maintenance and safety requirements. This paper presents an integer linear programming mathematical model, which schedules maintenance tasks for a given period, within the normal rolling-stock service operations. This model is applied to a case study and a reliability analysis is conducted, assessing the impact of uncertainty associated with maintenance durations in the optimal value for the objective function, as well as in the feasibility of such a maintenance schedule.

Location-allocation problem of reverse logistics for end-of-life vehicles based on the measurement of carbon emissions

Faced with the contradiction between the rapid growth of car ownership and the low recovery rate of end-of-life vehicles, the reverse logistics services led by third-party recycling and dismantling companies for end-of-life vehicles (ELVs) in China are experiencing great challenges under the background of the low-carbon economy. This paper constructs a four-tier reverse logistics network model, which includes ELV sources, collection centers, remanufacturing centers and dismantlers. Meanwhile, this paper also develops a mixed integer linear programming mathematical model and solves the problem using the global optimization software Lingo. The optimization results of a real case in Xi’an prove the validity of the model in both present normal demands and increasing demand situations in the future. The total logistics network and the environmental costs are both reduced, and the utilization rate of the dismantling center is improved. The location and capacity rating strategies in dismantling centers have key effects on the total cost in the logistics network that are far beyond other decision variables. The supply capacity of the key facilities in Xi’an’s ELV recycling network is far greater than the level of demand, causing a serious waste of resources. Hence, the layout model of an industrial park can help to reduce the total cost of the reverse logistics network if the dismantling center has a high utilization rate.

Electric Vehicles for merchandise transportation: Integrated planning taking into acount the electrical distribution system

Electric Vehicles (EVs) represent an option that contributes substantively to improve mobility and decrease pollution, generating great expectations for the future of transportation sector, with pilot projects of companies using EVs for delivering products. In this work, a novel approach for optimal planning of EVs for cargo transportation is presented, considering battery swap stations (BSSs) location and the impact on the power distribution network (PDN). This integrated planning is formulated through a mixed integer linear programming mathematical model. To evaluate the model performance three test systems of different sizes are proposed (considering transportation network and PDN). The results show a tradeoff between EVs routing, energy losses of PDN and BSSs location.

Simultaneous balancing, sequencing, and workstation planning for a mixed model manual assembly line using hybrid genetic algorithm

Abstract Balancing and sequencing are two important challenging problems in designing mixed-model assembly lines. A large number of studies have addressed these two problems both independently and simultaneously. However, several important aspects such as assignment of common tasks between models to different workstations, and minimizing the number and length of workstations are not addressed in an integrated manner. In this paper, we proposed a mixed integer linear programming mathematical model by considering the above aspects simultaneously for a continuously moving conveyor. The objective function of the model is to minimize the length and number of workstations, costs of workstations and task duplications. Since the proposed model cannot be efficiently solved using commercially available packages, a multi-phased linear programming embedded genetic algorithm is developed. In the proposed algorithm, binary variables are determined using genetic search whereas continuous variables corresponding to the binary variables are determined by solving linear programming sub-problem using simplex algorithm. Several numerical examples with different sizes are presented to illustrate features of the proposed model and computational efficiency of the proposed hybrid genetic algorithm. A comparative study of genetic algorithm and simulated annealing is also conducted.

Energy-Efficient Data Gathering Framework-Based Clustering via Multiple UAVs in Deadline-Based WSN Applications

This paper proposes a new method for energy-efficient data gathering using multiple unmanned aerial vehicles (UAVs) in deadline-based wireless sensor networks (WSNs). This method collects WSN node data in minimum energy by providing the optimal position and trajectory of UAVs, the minimum travel time, and the minimum number of UAVs in a determined deadline. First, in order to minimize the energy consumption of WSN nodes and determine the positions of where to place UAVs for receiving network nodes data, this paper clusters the nodes in a distributed form and considers the centers of these clusters as a place to meet the UAVs. Then, beginning and ending virtual nodes are used for controlling the minimum number of UAVs. This paper attempts to complete the proposed solution and obtain the minimum travel time of UAV required for collecting data from the network. In order to find the optimal solution for this problem, a mixed integer linear programming mathematical model is presented, followed by normalizing and putting weights on each part of an objective function. Results obtained in the simulation step show that the presented model has an optimal performance in providing the position and optimal trajectory of UAVs, energy consumption, minimum travel time, and the number of UAVs used.

A decision model for selecting parts feeding policies in assembly lines

Purpose – The purpose of this paper is to develop an optimization model allowing the choice of parts feeding policy to assembly lines in order to minimize total cost. Design/methodology/approach – An integer linear programming mathematical model is developed to assign the optimal material feeding policy to each part type. The model allows choice between kitting, line stocking and just in time delivery policies. Findings – The choice of assembly lines feeding policy is not trivial and requires a thorough economic comparison of alternatives. It is found that a proper mix of parts feeding policies may be better that adopting a single material delivery policy for all parts. Research limitations/implications – The model is aimed at single-model assembly lines operating in a deterministic environment, but can be extended to the multi-model line case. While relevant quantitative cost drivers are included, some context-related qualitative factors are not included yet. The model assumes that information about product structure and part requirements are known and that a preliminary design of the assembly system has been carried out. Practical implications – Production managers are given a quantitative-decision tool to determine the optimal mix of material supply policies at an early decision stage. Originality/value – Respect previous simplified literature models, this approach allows to quantify a number of additional factors which are critical for successful implementation of cost-effective parts feeding systems, allowing comparison of alternative policies on a consistent basis.