Particle swarm optimization for the multi-period cross-docking distribution problem with time windows

Cross-docking has emerged as a new technique in supply chain management to replace the warehouse concept in the retail industry. This paper proposes a multi-period cross-docking distribution problem that consists of manufacturers, cross-docks and customers. This model is formulated for cases that consider multiple products, consolidation of customer orders and time windows that are available in multiple periods. The objective function is to minimise the total cost, which includes transportation cost, inventory cost and penalty cost. The penalty cost arises when demand remains in each period that cannot be satisfied. To deal with the complexity of the problem, an algorithm is developed based on particle swarm optimisation (PSO) with multiple social learning terms, GLNPSO, with two solution representations. The solution representations are a one-period solution representation (OP-SR) and a multi-period solution representation (MP-SR). The GLNPSO-based algorithm performs well in solving this problem. Moreover, both representations are proven effective when comparing the solution quality and computational time with those results obtained from CPLEX. In terms of quality, the MP-SR solution is better than the OP-SR solution for both stable and fluctuating demand instances. However, MP-SR requires more computational effort than OP-SR.     

Integration of a GA and PSO for discussing the impact of 3C product engineering changes on customisation degree

Computer, Communication, Consumer (3C) electronics products have high uncertainty of demand as customers often change their demands. Therefore, manufacturers have to deal with Engineering Change (EC) situations to meet the needs of customers. Based on a literature review, this study has found that a Genetic Algorithm (GA) can yield optimal solutions for ECs, and that Particle Swarm Optimisation (PSO) can more efficiently converge to the optimal solution. Therefore, this study integrated the GA and PSO to determine the optimal manufacturing makespan upon ECs. For 3C products, customer preference is affected by customisation degree. This study developed a deviation utility loss-based customisation degree model that can indicate the gap between the makespan required by customers and optimal makespan from manufacturers upon ECs, as well as the impact of changes on unit price and fixed cost of product of the customisation degree upon EC and parameter change of the customisation degree model. The findings can provide 3C manufacturers with references to select the optimal parameters for difference situations.     

Using fuzzy analytic hierarchy process and particle swarm optimisation for balanced and defective supply chain problems considering WEEE/RoHS directives

This research explored problems concerning production and delivery in a green supply chain, and constructed an optimal mathematical model to provide solutions. This model incorporates WEEE and RoHS in EU directives for the selection of green partners when establishing a supply chain. The weight of each component is calculated by fuzzy analytic hierarchy process (fuzzy AHP). Previous studies suggested that a supply chain is a balanced system, however, in actual practice, there may be processing damages or delivering losses. Thus, such a supply chain with production loss is known as a ‘defective supply chain’. This research analysed the defective supply chain system to discuss its supplier selection, production, and distribution. It developed an optimal mathematical model for both balanced and defective models, and adopted particle swarm optimisation (PSO) to obtain solutions for both models. Finally, case studies for both models with quality solutions were discussed to confirm the efficiency and effectiveness of the proposed approach.     

Multi-objective resource assignment problem in a product-driven supply chain using a Taguchi-based DNA algorithm

This paper conceptualises the integration of tangible and intangible factors into the design consideration of a resource assignment problem for a product-driven supply chain. The problem is formulated mathematically as a multi-objective optimisation model to maximise the broad objectives of profit, ahead of time of delivery, quality, and volume flexibility. Product characteristics are associated with the design requirements of a supply chain. Different types of resources are considered, each differing in its characteristics, thereby providing various alternatives during the design process. The aim is to design integrated supply chains that maximise the weighted sum of the objectives, the weights being decided by the desired product characteristics. The problem is solved through the proposed Taguchi-based DNA algorithm that draws its traits from random search optimisation and the statistical design of experiments. In order to minimise the effect of the causes of variations, the fundamental Taguchi method is integrated with the DNA-metaheuristic. The suggested methodology exhibits the global exploration capability to exploit the optimal or near-optimal DNA strands with a faster convergence rate. In order to authenticate the performance of the proposed solution methodology, a set of ten problem instances are considered and the results obtained are compared with that of the basic DNA, particle swarm optimisation (PSO) and its variant (PSO — time varying acceleration coefficients). The results demonstrate the benefits of the proposed algorithm for solving this type of problem.     

A robust Island Parallel Genetic Algorithm for the Quadratic Assignment Problem

The Quadratic Assignment Problem (QAP) is a difficult and important problem studied in the domain of combinatorial optimisation. It is possible to solve QAP instances with 10--20 facilities using exhaustive parallel algorithms within a few days on a cluster machine. However, large QAP instances with more than 100 facilities are not solvable using exhaustive techniques. We have explored a variety of Genetic Algorithm crossover operators for this problem and verified its performance experimentally using well-known instances from the QAPLIB library. By increasing the number of processors, generations and population sizes we have been able to find solutions that are the same as (or very close to) the best reported solutions for large QAP instances in QAPLIB. In order to parallelise the Genetic Algorithm we generate and evolve separate solution pools on each cluster processor, using an island model. This model exchanges 10% of each processor’s solutions at the initial stages of optimisation. We show experimentally that both execution times and solution qualities are improved for large QAP instances by using our Island Parallel Genetic Algorithm.     

基于粒子群算法的空间直线度误差评定

提出了一种满足最小区域法的空间直线度误差评价的新方法--粒子群算法。根据最小区域条件,建立了空间直线的数学模型以及优化目标函数。阐述了粒子群优化算法的原理和实现方法,然后根据粒子群算法优化求解。实例表明该方法对于空间直线度误差评定等非线性优化问题能得到最优解,可用于三坐标测量机等测量系统的空间直线度误差测量的数据处理。     

Concurrent optimal allocation of distributed manufacturing resources using extended Teaching-Learning-Based Optimization

The optimal allocation of distributed manufacturing resources is a challenging task for supply chain deployment in the current competitive and dynamic manufacturing environments, and is characterised by multiple objectives including time, cost, quality and risk that require simultaneous considerations. This paper presents an improved variant of the Teaching-Learning-Based Optimisation (TLBO) algorithm to concurrently evaluate, select and sequence the candidate distributed manufacturing resources allocated to subtasks comprising the supply chain, while dealing with the trade-offs among multiple objectives. Several algorithm-specific improvements are suggested to extend the standard form of TLBO algorithm, which is only well suited for the one-dimensional continuous numerical optimisation problem well, to solve the two-dimensional (i.e. both resource selection and resource sequencing) discrete combinatorial optimisation problem for concurrent allocation of distributed manufacturing resources through a focused trade-off within the constrained set of Pareto optimal solutions. The experimental simulation results showed that the proposed approach can obtain a better manufacturing resource allocation plan than the current standard meta-heuristic algorithms such as Genetic Algorithm, Particle Swarm Optimisation and Harmony Search. Moreover, a near optimal resource allocation plan can be obtained with linear algorithmic complexity as the problem scale increases greatly.     

A distributed approximation approach for solving the sustainable supply chain network design problem

This paper introduces a comprehensive Mixed Integer Linear Programming (MILP) model for a sustainable supply chain network design problem, and an efficient Distributed Approximation Approach (DAA) to solve it approximately. We study a multi-echelon, multi-product and multi-modal supply chain with different transportation modes. Besides relevant costs in the supply chain such as procurement, production and distribution cost, we also explicitly consider the environmental footprint, represented by carbon emissions and water consumption from production and transportation. The approximation approach is a decomposition-based method. First, the original problem is divided into a partner selection sub-problem and a transportation planning sub-problem. Then multiple filter mechanisms are used to remove potentially infeasible solutions, and an approximate value of the objective function is calculated for each of the remaining solutions to perform a further selection. The one with the lowest approximation is chosen to be applied with a branch-and-bound method. Finally, the algorithm is paralleled and implemented in Apache Spark distributed computing framework to further improve efficiency. Experimental results show that the proposed DAA can provide high quality solutions compared to the optimal solutions of the MILP model with mostly a negligible relative gap and solve large instances in much shorter time than CPLEX. Moreover, in our numerical study, we also compare the results of our model with another version of the model that does not take the environmental footprint into consideration. The results show that explicitly incorporating environmental footprint results in a substantial decrease of CO₂ emissions and water consumption at a negligible cost increase. This insight may be of interest to managers and other decision makers and policy makers.     

Coordination of set-ups between two stages of a supply chain using multi-objective genetic algorithms

A multi-objective genetic algorithm (MOGA) solution approach for a sequencing problem to coordinate set-ups between two successive stages of a supply chain is presented in this paper. The production batches are processed according to the same sequence in both stages. Each production batch has two distinct attributes and a set-up occurs in the upstream stage every time the first attribute of the new batch is different from the previous one. In the downstream stage, there is a set-up when the second attribute of the new batch is different from that of the previous one. Two objectives need to be considered in sequencing the production batches including minimizing total set-ups and minimizing the maximum number of set-ups between the two stages. Both problems are NP-hard so attainment of an optimal solution for large problems is prohibited. The solution approach starts with an initialization stage followed by evolution of the initial solution set over generations. The MOGA makes use of non-dominated sorting and a niche mechanism to rank individuals in the population. Selected individuals taken from a given population form the succeeding generation using four genetic operators as: reproduction, crossover, mutation and inversion. Experiments in a number of test problems show that the MOGA is capable of finding Pareto-optimal solutions for small problems and near Pareto-optimal solutions for large instances in a short CPU time.     

Sequencing n Products Involving m Independent Jobs on m Machines

This article considers the problem of scheduling n products over m distinct machines. Every product consists of a set of jobs, each requiring a known processing time on a designated machine. There are no precedence constraints, and simultaneous processing of jobs requiring different machines within a product is allowed. The object of scheduling is to minimize a regular measure of performance associated with the products. It is shown that there exists an optimal schedule with the “no passing property.” Branch and bound routines are developed for finding the optimal solution for the two measures of performance: (1) total penalty cost; and (2) sum of product completion times. Comparisons between the optimal solution and solutions obtained using dispatching rules are given in the penalty cost case.     

Model-based identification of damage from sparse sensor measurements using Neumann series expansion

This paper presents a novel and effective modal data-based methodology for structural damage localization and quantification when the structure is equipped with a limited number of sensors. Damage detection problem is defined as an inverse model-based problem and a new damage-sensitive cost function is introduced using calculated Generalised Flexibility Matrix and Modal Assurance Criterion. The second-order approximation of Neumann Series Expansion-based Model Reduction approach is employed for numerically simulation of sparse sensor installation. Finally, a hybrid version of two different evolutionary optimization algorithms, named Particle Swarm Optimization–Colonial Competitive Algorithm (PSO–CCA), is suggested and utilized for solving optimization problem. This hybridization, not only can pick the positive points of the PSO and CCA for searching complex solution domain, but also can lead to achieving a powerful, fast speed optimization strategy. The efficiency of the presented method is demonstrated by studying three numerical examples under different damage patterns. Various challenges, such as the robustness of the method in the presence of random noises in the input data, are investigated. The obtained results introduce the presented method as a viable and practical strategy for structural damage identification, especially when a limited number of sensors are installed on the structure.     

Flexible work-in-process production system in supply chain management under quality improvement

For a complex product production, any flexible manufacturing system with a work-in-process inventory is recommended for a supply chain management (SCM) system. Building a flexible manufacturing system increases the total cost of the supply chain; for this reason, a discrete investment is important. For flexible production systems, production rate within a finite specific interval of production rate as work-in-process inventory is calculated. The aim of the supply chain is to reduce the total cost when demand during the lead time is a random variable with a normal distribution. A crashing cost is utilised to reduce the duration of lead time within the supply chain system. A model is proposed to obtain the optimal flexible production rate with the reduced total cost of the supply chain. A classical optimisation technique is employed to obtain the closed-form and quasi-closed-form solutions of the decision variables. An improved algorithm is designed to obtain the global minimum cost of SCM under the framework of a flexible production system. An illustrative numerical example and sensitivity analysis are given to test the model. A numerical study proves that this model obtains the minimum cost with the optimal decision variables.     

SSABA: Search Step Adjustment Based Algorithm

Finding the suitable solution to optimization problems is a fundamental challenge in various sciences. Optimization algorithms are one of the effective stochastic methods in solving optimization problems. In this paper, a new stochastic optimization algorithm called Search Step Adjustment Based Algorithm (SSABA) is presented to provide quasi-optimal solutions to various optimization problems. In the initial iterations of the algorithm, the step index is set to the highest value for a comprehensive search of the search space. Then, with increasing repetitions in order to focus the search of the algorithm in achieving the optimal solution closer to the global optimal, the step index is reduced to reach the minimum value at the end of the algorithm implementation. SSABA is mathematically modeled and its performance in optimization is evaluated on twenty-three different standard objective functions of unimodal and multimodal types. The results of optimization of unimodal functions show that the proposed algorithm SSABA has high exploitation power and the results of optimization of multimodal functions show the appropriate exploration power of the proposed algorithm. In addition, the performance of the proposed SSABA is compared with the performance of eight well-known algorithms, including Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Teaching-Learning Based Optimization (TLBO), Gravitational Search Algorithm (GSA), Grey Wolf Optimization (GWO), Whale Optimization Algorithm (WOA), Marine Predators Algorithm (MPA), and Tunicate Swarm Algorithm (TSA). The simulation results show that the proposed SSABA is better and more competitive than the eight compared algorithms with better performance.     

基于仿真的三级供应链成本优化

针对供应链这种非线性和复杂系统,为了优化供应链的总成本,提高供应链的整体竞争力,提出了一种基于仿真的优化方法。首先建立了一个三级协作供应链的系统动力学模型,供应链上的企业需要求解多个决策变量来降低供应链总成本。然后详细展示了将系统动力学模型转换为Matlab程序模型的过程,并在两个模型中使用了多组随机参数进行对比验证。最后设计了适当的遗传算法进行求解。结果表明,这种基于仿真的优化方法不仅能反映出供应链系统的动态特征,而且求解速度快、精度高,能有效解决供应链系统中的单目标或多目标规划问题。系统动力学模型结构相对固定,也不适合异构的交互环境,该方法给系统动力学模型提供了良好的补充。转换为Matlab程序模型后,可以进行深入的仿真研究,灵活设置目标函数和约束条件,详细分析系统的动态变化过程,还能为其它应用提供交互接口。     

供应链管理环境下的单周期库存控制建模及优化

传统的库存控制理论已经不能够适应供应链管理的要求。在建立了供应链库存成本的组成模型的基础上对供应链管理中的单周期库存控制过程进行了深入的分析，建立了相应的数学模型，求出了最优解。     

Improved imperialist competitive algorithms for rebalancing multi-objective two-sided assembly lines with space and resource constraints

In this paper, a mathematical model and an improved imperial competition algorithm (IICA) are proposed to solve the multi-objective two-sided assembly line rebalancing problem with space and resource restrictions (MTALRBP-SR). The aim is to find lines’ rebalance with the trade-off between efficiency, rebalancing cost and smoothing after reconfiguration. IICA utilises a new initialisation heuristic procedure based on classic heuristic rules to generate feasible initial solutions. A novel heuristic assimilation method is developed to vigorously conduct local search. In addition, a group-based decoding heuristic procedure is developed to fulfil the final task reassignment with the additional restrictions. To investigate the performance of the proposed algorithm, it is first tested on MTALRBP of benchmark problems and compared with some existing algorithms such as genetic algorithm, variable neighbourhood search algorithm, discrete artificial bee colony algorithm, and two iterated greedy algorithms. Next, the efficiency of the proposed IICA for solving MTALRBP-SR is revealed by comparison with a non-dominated sorting genetic algorithm (NSGA-II) and two versions of original ICA. Computational results and comparisons show the efficiency and effectiveness of IICA. Furthermore, a real-world case study is conducted to validate the proposed algorithm.     

Joint optimisation of tracking capability and price in a supply chain with endogenous pricing

Tracking systems have been widely used to resolve the issues of product recall and food safety. Thus far, few researches have been done on designing the tracking capability from the perspective of supply chain. In this paper, using the traceable unit size at the manufacturer level to measure the tracking capability, we propose a non-convex non-linear programming to jointly optimise the tracking capability and price considering the tracking cost and recall cost in a supply chain with endogenous pricing. Results show that, in both centralised and decentralised supply chains, there is a unique tracking capability and retailing/wholesale price with closed-form solutions to optimise the supply chain profit. When the cost ratio (unit tracking cost/unit recall cost) is sufficiently large and small, the optimal tracking strategy is barcode tracking and unit tracking, respectively, and otherwise, the optimal tracking strategy is batch tracking with an economic traceable unit size which depends on the cost ratio, quality inspection threshold, supply defection rate and the supplier’s tracking capability. Furthermore, in the context of large and small cost ratio, we find that improving tracking capability will enlarge and mitigate the effect of double marginalisation, respectively. In particular, we find that the strict tracking regulation policy is more robust than the subsidy policy to improve the supply chain tracking capability.     

Modelling on vendor-managed inventory policies with equal and unequal shipments under GHG emission-trading scheme

This paper studies five different stock control policies in the supply chain management. The lead time can be shortened by extra investment between two entities. The vendor produces a single product and delivers the order quantity in a number of unequal shipments to the buyer. The unit holding cost is divided into financial and storage components. The vendor takes care of financial component until the products are sold to the end customers to encourage them to buy more products. In order to reduce emissions from production and to protect the environment, some legislative actions have been taken such as implementing taxes and penalties. The cost function also includes these taxes and penalties. The optimal solutions of this constrained mixed integer non-linear programming problem are obtained by using the Genetic Algorithm (GA). Numerical examples are employed and comparison works are carried out with other existing literatures. Results show that the performance of the system is better when it is operated under unequal shipment policies and vendor-managed inventory (VMI) agreement.     

A surrogate-assisted particle swarm optimization algorithm based on efficient global optimization for expensive black-box problems

Evolutionary algorithms cannot effectively handle computationally expensive problems because of the unaffordable computational cost brought by a large number of fitness evaluations. Therefore, surrogates are widely used to assist evolutionary algorithms in solving these problems. This article proposes an improved surrogate-assisted particle swarm optimization (ISAPSO) algorithm, in which a hybrid particle swarm optimization (PSO) is combined with global and local surrogates. The global surrogate is not only used to predict fitness values for reducing computational burden but also regarded as a global searcher to speed up the global search process of PSO by using an efficient global optimization algorithm, while the local one is constructed for a local search in the neighbourhood of the current optimal solution by finding the predicted optimal solution of the local surrogate. Empirical studies on 10 widely used benchmark problems and a real-world structural design optimization problem of a driving axle show that the ISAPSO algorithm is effective and highly competitive.     

A cyclic policy for the loading of multiple products on a vehicle with different compartment sizes

In this paper, we address a multi-product loading problem in which a vehicle (a truck or a ship) is used to transfer multiple products. The product demands are different but stationary over time. The vehicle consists of compartments of different sizes and each compartment can contain only one product type during each shipment. No shortages are permitted, and we assume that the inventory holding cost is significantly lower than the delivery cost. The objective is to minimize the setup rate, that is, the number of deliveries per time unit. A cyclic policy is shown to be optimal, and a heuristic algorithm is developed to determine the cycle length as well as the assignments of products to the compartments during each of the requisite number of shipments made during that cycle. A comparison of the solutions obtained by the proposed algorithm with the optimal solutions (or a bound) indicate that the algorithm provides solutions with optimal setup rates in most of the problem instances considered and, when not optimal, the setup rates of these solutions are close to optimal values.