Mathematical formulation and heuristic algorithms for optimisation of auto-part milk-run logistics network considering forward and reverse flow of pallets

The operational planning of distribution network for automotive industry is complex with many conditions to consider, including heterogeneous fleet, enforcing the feasibility of 3D-packing of pallets into vehicles to address the vehicle's capacity in terms of weight and volume, compatibility of orders in a vehicle, returning empty pallets from assembly-plants backwards to suppliers, and delivery time windows. A mathematical model (MILP) is proposed that takes account of these conditions to minimise total transportation costs. The network structure can be a combination of direct shipment and milk-run for both forward and reverse flow of pallets. The model is solved optimally for small-size problems. For solving larger problems, a heuristic algorithm (in two versions) is proposed that uses a similarity measure to generate a reasonable list of orders. Best/first-fit strategies are employed to generate a feasible solution with the aid of a relaxed version of the proposed MILP. Improvement heuristics are also designed. Unlike most of existing constructive heuristics, our aim for developing the heuristic approach is to force routing decision, with all of its considerations, being made optimal. We also use the proposed best-fit strategy in the body of grouping evolution strategy (GES) algorithm to attain an effective meta-heuristic approach. The effectiveness of heuristics is tested on generated instances which demonstrates they are optimal for small-size problems. They are also tested on the data of daily auto-parts shipments gathered from the largest Iranian automobile company. Results demonstrate there exists a significant potential for cost saving through milk-run strategy compared with the direct shipping strategy.     

云南镇源难处理金精矿工艺矿物学研究

利用X射线衍射、X射线荧光光谱（XRF）、X射线能谱分析（EDX）和矿物解离分析（MLA）等检测手段对云南镇源难处理金精矿的化学组成、矿物组成、硫化物特征以及金的分布情况进行了详细的工艺矿物学研究。结果显示：该金矿以硫化矿、碳酸盐和硅酸盐类矿物为主，含有3.18%的有机碳和2.37%的无机碳。通过金的诊断浸出发现96.16%的金被硫化物包裹，少量金以单体形式存在。通过对主要载金矿物黄铁矿、辉锑矿和毒砂的粒度、包裹及裸露情况进行分析，得出大部分硫化矿以解离单体的形式存在，少部分与其他矿物共生。根据MLA测试及金的诊断浸出，认为大部分金被硫化矿完全包裹，处理该矿石时应先进行硫化物包裹层的氧化处理，再进行金矿的浸出。     

Sustainable optimization of waste management network over extended planning time horizon

This study proposes a multiperiod mixed integer linear programming model for the management of a single municipal solid waste (MSW) treatment plant with sustainability as the objective. Discrete and continuous variables define the capacity selections for diverse MSW technologies, and the operation of the MSW network, respectively. The economic target is considered to maximize the net present value. The environmental impact is the minimization of a normalized environmental objective function (NEOF). The social target is the maximization of jobs. An interesting feature about the research work is the requirement of biodrying technologies for MSW moisture content control. Due to the conflicted nature among the sustainability components, a multiobjective optimization (MO) is carried out to find the Pareto optimal solutions. The MO results show that the Pareto optimal solutions vary around profit range of $4.9–8.5 billion, NEOF impact range of 3.2–3.6 units, and social benefit range of 2700–4828 jobs.     

Probabilistic tree-based representation for solving minimum cost integer flow problems with nonlinear non-convex cost functions

The minimum cost flow problem (MCFP) is the most generic variation of the network flow problem which aims to transfer a commodity throughout the network to satisfy demands. The problem size (in terms of the number of nodes and arcs) and the shape of the cost function are the most critical factors when considering MCFPs. Existing mathematical programming techniques often assume the cost functions to be linear or convex. Unfortunately, the linearity and convexity assumptions are too restrictive for modelling many real-world scenarios. In addition, many real-world MCFPs are large-scale, with networks having a large number of nodes and arcs. In this paper, we propose a probabilistic tree-based genetic algorithm (PTbGA) for solving large-scale minimum cost integer flow problems with nonlinear non-convex cost functions. We first compare this probabilistic tree-based representation scheme with the priority-based representation scheme, which is the most commonly-used representation for solving MCFPs. We then compare the performance of PTbGA with that of the priority-based genetic algorithm (PrGA), and two state-of-the-art mathematical solvers on a set of MCFP instances. Our experimental results demonstrate the superiority and efficiency of PTbGA in dealing with large-sized MCFPs, as compared to the PrGA method and the mathematical solvers.     

Enhancing stability region of time‐delayed smart power grids by non‐integer controllers

In this study, the impacts of non‐integer order controller on the stable parameter space of the microgrid (MG) frequency control system with fixed communication time delay are investigated and discussed with the help of the stability boundary locus (SBL) method. This study proposes a non‐integer order controller for the load frequency control (LFC) of the MG systems. To that end, the load frequency model of the MG is formulated and then the characteristic equations of this model are obtained. Then, with the help of this characteristic equation, the stable parameter space of the non‐integer controller is determined with regard to different time delay (τ ) and fractional integral order values (α ) using the SBL method. In order to show the accuracy of the obtained stable parameter space, time domain and generalized modified Mikhailov (GMM) criterion studies are carried out for different values of (τ ) and (α ). According to the results obtained, the areas of stable parameter space according to different α values and τ = 1.6 are calculated as 444.8860 for α = 0.4 , 342.9728 for α = 0.7 , 259.3578 for α = 1 , 216.2541 for α = 1.3 and 159.6826 for α = 1.6 . In addition, the areas of stable parameter space according to different τ values and α = 1.4 are calculated as 784.5222 for τ = 1 , 106.3219 for τ = 2 , 29.6959 for τ = 3 and 11.5946 for τ = 4 . Despite the extreme variability arising from nature of resources that make up the MG, the designed non integer order controller with the values selected within the stable parameter space stably carries out LFC control of the MG.     

The constrained two-dimensional guillotine cutting problem with defects: an ILP formulation,a Benders decomposition and a CP-based algorithm

This paper addresses a variant of two-dimensional cutting problems in which rectangular small pieces are obtained by cutting a rectangular object through guillotine cuts. The characteristics of this variant are (i) the object contains some defects, and the items cut must be defective-free; (ii) there is an upper bound on the number of times an item type may appear in the cutting pattern; (iii) the number of guillotine stages is not restricted. This problem commonly arises in industrial settings that deal with defective materials, e.g. either by intrinsic characteristics of the object as in the cutting of wooden boards with knotholes in the wood industry, or by the manufacturing process as in the production of flat glass in the glass industry. We propose a compact integer linear programming (ILP) model for this problem based on the discretisation of the defective object. As solution methods for the problem, we develop a Benders decomposition algorithm and a constraint-programming (CP) based algorithm. We evaluate these approaches through computational experiments, using benchmark instances from the literature. The results show that the methods are effective on different types of instances and can find optimal solutions even for instances with dimensions close to real-size.     

Multi-product continuous plant scheduling: combination of decomposition,genetic algorithm,and constructive heuristic

We propose a polylithic method for medium-term scheduling of a large-scale industrial plant operating in a continuous mode. The method combines a decomposition approach, a genetic algorithm (GA) and a constructive MILP-based heuristic. In the decomposition, decisions are made at two levels, using the rolling horizon approach. At the upper level, a reduced set of products and the time period is chosen to be considered in the lower level. At the lower level, a short-term scheduling MILP-model with event-based representation is used. A heuristic solution to the lower level problem is found using a constructive Moving Window heuristic guided by a genetic algorithm. The GA is applied for finding efficient utilisation of critical units in the lower level problem. For solving the one unit scheduling problem, a parallel dynamic programming algorithm is proposed. Implementation of the dynamic programming algorithm for a graphics processing unit (GPU) is incorporated in the GA for improving its performance. The experimental study of the proposed method on a real case of a large-scale plant shows a significant improvement of the solution quality and the solving time comparing to the pure decomposition algorithm proposed in the earlier study, and confirmed suitability of the proposed approach for the real-life production scheduling. In particular, the reduction of the number of changeovers and their duration in the obtained solution as well as the CPU time of solving the problem was about 60% using the new approach.     

Development of strategic hydrogen refueling station deployment plan for Korea

The Republic of Korea government has set yearly targets of hydrogen cars and buses and plans to install hydrogen refueling stations nationwide. This paper proposes a methodology for developing a strategic deployment plan with three mathematical models. For a given target, future refueling demand locations and amount from general road and expressway are systematically estimated. First, the required number of refueling stations to satisfy the target covering ratio of the total demand set by the government is determined by the Station number determination model. Next, the locations of the capacitated stations and the allocation of demand to the stations are determined by the second Max cover and the third p-median models. Since the max covering is more important than minimizing the travel time, the two models are used sequentially. The nationwide hydrogen station deployment plan for the years 2022–2040 obtained by the proposed methodology is reported.     

基于三支决策的模糊信息系统OWA算子参数选择

在模糊信息系统中，通过有序加权平均（Ordered weighted averaging,OWA）算子计算对象相似度，可以建立λ截集的相容关系。当λ的值确定后，OWA算子中量词参数(α,β)的选取直接关系到不可区分关系的建立以及信息粒的粗细。因此合理选取参数(α,β)是值得进一步研究的问题。本文采用粗糙集三支决策理论，研究模糊信息系统 OWA算子参数选择的相关内容。基于参数的激进、中庸和消极语义，确定OWA算子(α,β)的3种常用取值；进而研究相似度、相容类、双向近似和三支区域在3种参数选择下的性质关系。最后利用实例验证分析了模糊量词参数语义解释的合理性。本文采用三支决策创新视角，得到模糊信息系统OWA算子的深入性质，为相关模糊量词参数提供语义解释与选择依据。     

Liner services network design and fleet deployment with empty container repositioning

Transportation demand of shipping container fluctuates due to the seasonality of international trade, thus, every 3–6 months, the liner company has to alter its current liner shipping service network, redeploy ships and design cargo routes with the objective of minimizing the total cost. To solve the problem, the paper presents a mixed integer linear program model. The proposed model incorporates several relevant constraints, such as weekly frequency, the transshipment of cargo between two or more service routes, and transport time. Extensive numerical experiments based on realistic date of Asia–Europe–Oceania shipping operations show that the proposed model can solve real-case problems efficiently by CPLEX. The results demonstrate that the model can reduce ship’s capacity consumption and raise ships’ capacity utilization.