An optimal algorithm for selective disassembly sequencing with sequence-dependent set-ups in parallel disassembly environment

This study considers selective disassembly sequencing in parallel disassembly environment in which two or more components can be removed by a single disassembly operation. The problem is to determine the sequence of disassembly operations to extract multiple target components while satisfying the precedence relations among disassembly operations. The objective is to minimise the sum of sequence-dependent set-up and operation costs. An integer programming model is developed after representing all possible disassembly sequences using an extended process graph, and then an optimal branch and bound algorithm is proposed that incorporates the methods to obtain the lower and upper bounds as well as a dominance property to reduce the search space. To show the performance of the algorithm, computational experiments are done on various random instances, and the results are reported. In particular, it is shown from the test results that the optimal algorithm requires much shorter computation times than a competitive commercial software package. Finally, a case is reported to illustrate the extended process graph and the solution algorithm.     

Scheduling algorithms for remanufacturing systems with parallel flow-shop-type reprocessing lines

This study considers a scheduling problem for remanufacturing systems in which end-of-life products are separated into their major components at a disassembly workstation, each of them is reprocessed at its dedicated flow-shop-type reprocessing line with serial workstations, and finally, the reprocessed components, together with new components if required, are reassembled into remanufactured products at a reassembly workstation. Among various system configurations, we focus on the one with parallel flow-shop-type reprocessing lines since it is a typical remanufacturing configuration. The problem is to determine the sequence of products to be disassembled, the sequence of components to be reprocessed at each workstation of flow-shop-type reprocessing lines and the sequence of products to be reassembled for the objective of minimising the total flow time. An integer programming model is developed to represent the problem mathematically, and then, three types of heuristics, i.e. priority rule-based heuristic, Nawaz–Enscore–Ham-based heuristic and iterated greedy algorithm, are proposed due to the problem complexity. To show the performances of the heuristics, a series of computational experiments were done on various test instances, and the results are reported.     

Solution algorithms for dynamic lot-sizing in remanufacturing systems

We consider the problem of determining the lot sizes that satisfy the demands of remanufactured products over a given planning horizon with discrete time periods. Remanufacturing, in which used or end-of-life products are restored to like-new condition, typically consists of disassembly, reprocessing and reassembly processes, and hence the lot sizes are determined for each of the three processes. The objective is to minimise the sum of setup and inventory holding costs occurring at the three processes. To represent the problem mathematically, we suggest a mixed integer programming model by combining the existing ones for disassembly and assembly systems. After proving that the problem is NP-hard, we suggest two dynamic programming based heuristics, called the aggregation and the decomposition type heuristics in this paper. Computational experiments were done on various test instances, and the results show that the two heuristics give near-optimal solutions in a short amount of computation time. Also, the performances of the heuristics are compared according to different values of problem parameters.     

Selective disassembly sequencing with random operation times in parallel disassembly environment

Selective disassembly sequencing is the problem of determining the sequence of disassembly operations to extract one or more target components of a product. This study considers the problem with random operation times in the parallel disassembly environment in which one or more components can be removed at the same time by a single disassembly operation. After representing all possible disassembly sequences using the extended process graph, a stochastic integer programming model is developed for the objective of minimising the sum of disassembly and penalty costs, where the disassembly costs consist of sequence-dependent set-up and operation costs and the penalty cost is the expectation of the costs incurred when the total disassembly time exceeds a threshold value. A sample average approximation-based solution algorithm is proposed that incorporates an optimal algorithm to solve the sample average approximating problem under a given set of scenarios for disassembly operation times. The algorithm is illustrated with a hand-light case and a large-sized random instance, and the results are reported.     

Dynamic disassembly planning for remanufacturing of multiple types of products

With the increased need for remanufacturing of end-of-life products, achieving economic efficiency in remanufacturing is urgently needed. The purpose of this study was to devise a cost-minimisation plan for disassembly and remanufacturing of end-of-life products returned by consumers. A returned end-of-life product is disassembled into remanufacturable parts, which are supposed to be used for new products after being remanufactured. Each end-of-life product is disassembled into parts at variable levels and through variable sequences as needed, taking into account not only disassembly but also manufacturing, remanufacturing, and holding inventory of remanufacturable parts. This study proposes a mixed integer linear programming (MILP) model for derivation of the optimal disassembly plan for each returned product, under deterministically known demand and return flows. For the purposes of an illustrative example, the proposed model was applied to the formulation of an optimal disassembly and remanufacturing plan of ‘fuser assembly’ of laser printers. The solution reveals that variable-level disassembly of products saves a significant remanufacturing cost compared with full disassembly.     

Disassembly line design with multi-manned workstations: a novel heuristic optimisation approach

As the first and the most time consuming step of product recovery, disassembly is described as the systematic separation of constituent parts from end-of-life products through a series of operations. In this context, designing and balancing disassembly lines are critical in terms of the efficiency of product recovery. Recent research on disassembly line balancing (DLB) has focused on classical stations where only one worker is allocated. However, such a line results in larger space requirement and longer disassembly lead time. In this paper, disassembly line balancing problem (DLBP) with multi-manned stations is introduced to the relevant literature as a solution to overcome these disadvantages. A mixed integer linear programming (MILP) model and two novel framework heuristic algorithms are developed to minimise the number of workers and workstations. MILP model has been applied to a dishwasher disassembly system. The application results indicate the superiority of establishing multi-manned stations over classical disassembly system design with single-worker stations with shorter disassembly lead time (80.9%) and line length (60.2%). Moreover, the proposed heuristics have been compared on newly generated test problems (instances) for DLBP. The results validate that the heuristics provide acceptable solutions in a reasonable amount of time even for large-sized problems.     

Mathematical models and a hunting search algorithm for the no-wait flowshop scheduling with parallel machines

Majority of researches in no-wait flowshop scheduling assume that there is only one machine at each stage. But, factories commonly duplicate machines in parallel for each operation. In this case, they balance the speed of the stages, increase the throughput of the shop floor and reduce the impact of bottleneck stages. Despite their importance, there is no paper to study the general no-wait flowshop with parallel machines. This paper studies this problem where the objective is to minimise makespan. Since there is no mathematical model for the problem, we first mathematically formulate it in form of two mixed integer linear programming models. By the models, the small instances are optimally solved. We then propose a novel hunting search metaheuristic algorithm (HSA) to solve large instances of the problem. HSA is derived based on a model of group hunting of animals when searching for food. A set of experimental instances are carried out to evaluate the algorithm. The algorithm is carefully evaluated for its performance against an available algorithm by means of statistical tools. The related results show that the proposed HSA provides sound performance comparing with other algorithms.     

Disassembly process planning algorithms for end-of-life product recovery and environmentally conscious disposal

Disassembly process planning is an act of preparing detailed operation instructions for disassembling used or an end-of-life (EOL) product to recover or dispose of its constituent parts or subassemblies. The main decisions are: (a) disassembly level; (b) disassembly sequence; and (c) EOL options such as reuse, remanufacturing, recycling, incineration, landfill, etc. This study deals with the three decision variables simultaneously in the parallel disassembly environment for the objective of maximising the profit. Unlike previous studies, we consider practical constraints, i.e., reuse probability and environmental impacts of parts or subassemblies, sequence-dependent setup costs, regulation on recovery rate, and incineration capacity. To represent and solve the problem, we develop an extended AND/OR graph, and then suggest a two-phase algorithm. To show the effectiveness of the proposed algorithm, two case studies have been carried out on an automatic pencil and a telephone. Also, test results on other general product structures are reported.     

Modelling and a tabu search solution for the slab reallocation problem in the steel industry

This paper considers a slab reallocation problem arising from operations planning in the steel industry. The problem involves reallocating steel slabs to customer orders to improve the utilisation of slabs and the level of customer satisfaction. It can be viewed as an extension of a multiple knapsack problem. We firstly formulate the problem as an integer nonlinear programming (INLP) model. With variable replacement, the INLP model is then transformed into a mixed integer linear programming (MILP) model, which can be solved to optimality by MILP optimisers for very small instances. To obtain satisfactory solutions efficiently for practical-sized instances, a heuristic algorithm based on tabu search (TS) is proposed. The algorithm employs multiple neighbourhoods including swap, insertion and ejection chain in local search, and adopts solution space decomposition to speed up computation. In the ejection chain neighbourhood, a new and more effective search method is also proposed to take advantage of the structural properties of the problem. Computational experiments on real data from an advanced iron and steel company in China show that the algorithm generates very good results within a short time. Based on the model and solution approach, a decision support system has been developed and implemented in the company.     

Profit-oriented disassembly-line balancing

As product and material recovery has gained importance, disassembly volumes have increased, justifying construction of disassembly lines similar to assembly lines. Recent research on disassembly lines has focused on complete disassembly. Unlike assembly, the current industry practice involves partial disassembly with profit-maximization or cost-minimization objectives. Another difference between assembly and disassembly is that disassembly involves additional precedence relations among tasks due to processing alternatives or physical restrictions. In this study, we define and solve the profit-oriented partial disassembly-line balancing problem. We first characterize different types of precedence relations in disassembly and propose a new representation scheme that encompasses all these types. We then develop the first mixed integer programming formulation for the partial disassembly-line balancing problem, which simultaneously determines (1) the parts whose demand is to be fulfilled to generate revenue, (2) the tasks that will release the selected parts under task and station costs, (3) the number of stations that will be opened, (4) the cycle time, and (5) the balance of the disassembly line, i.e. the feasible assignment of selected tasks to stations such that various types of precedence relations are satisfied. We propose a lower- and upper-bounding scheme based on linear programming relaxation of the formulation. Computational results show that our approach provides near optimal solutions for small problems and is capable of solving larger problems with up to 320 disassembly tasks in reasonable time.     

Balancing transfer lines using Benders decomposition and ant colony optimisation techniques

In this paper, we investigate a transfer line balancing problem in order to find the line configuration that minimises the non-productive time. The problem is defined at an auto manufacturing company where the cylinder head is manufactured. Technological restrictions among design features and manufacturing operations are taken into consideration. The problem is represented by an integer programming model that assigns design features and cutting tools to machining stations, and specifies the number of machines and production sequence in each station. Three algorithms are developed to efficiently solve the problem under study. The first algorithm uses Benders decomposition approach that decomposes the proposed model into an assignment problem and a sequencing problem. The second algorithm is a hybrid algorithm that mixes Benders decomposition approach with the ant colony optimisation technique. The third algorithm solves the problem using two nested ant colonies. Using 15 different problem dimensions, we compare results of the three algorithms in a computational study. The first algorithm finds optimal solutions of small problem instances only. Second and third algorithms demonstrate optimality gaps less than 4.04 and 3.8%, respectively, when compared to the optimal results given by the first algorithm. Moreover, the second and third algorithms are very promising in solving medium and large-scale problem instances.     

Minimising interference for scheduling two parallel machines with a single server

In this paper, we consider the problem of scheduling a set of jobs on two parallel machines with set-up times. The set-up has to be performed by a single server. The objective is to minimise the forced idle time. The problem of minimising the forced idle time (interference problem) is known to be unary NP-hard for the case of two machines and equal set-up and arbitrary processing times. We propose a mixed integer linear programming model, which describes a special class of schedules where the jobs from a list are scheduled alternatively on the machines, and a heuristic algorithm is tested on instances with up to 100,000 jobs. The computational results indicate that the algorithm has an excellent performance even for very large instances, where mostly an optimal solution is obtained within a very small computational time.     

考虑班种约束的呼叫中心排班优化模型与算法

一些呼叫中心设置早班、晚班和两段班班种;排班时规定员工周内同班种的班次当班,并且限制两段班当班员工占比。构建该实际情景的坐席人员排班问题整数规划模型。鉴于问题难解性,首先通过问题结构层次分解,以及对班种与班次覆盖区段人力需求量化指标的表征刻画,提出启发式算法生成解方案;然后采用基于模拟退火机制的邻域搜索算法改善解方案。计算实验表明整数规划模型适于求解小规模排班问题最优解,而上述两阶段优化算法能够获得大规模问题优化解。研究表明,在优化人力成本情况下可兼顾坐席人员工作时间高规律性。     

Heuristic algorithms for minimising total recovery cost of end-of-life products under quality constraints

Recently, the optimisation of end-of-life (EOL) product recovery processes has been highlighted. At the inspection phase after disassembly, each part can have various recovery options such as reuse, reconditioning, remanufacturing, and disposal. Depending on the selected options of parts, the values of recovered products that are made by reassembling parts will be different. Hence, it is important to decide appropriate recovery options of parts at the treatment of EOL products, in order to maximise the values of recovered products. To this end, this study deals with a decision making problem to select the best recovery options of parts for minimising the total recovery cost of products under quality constraints. This problem is formulated with a mixed integer nonlinear programming model and heuristic search algorithms are proposed to resolve it. A case study for a turbocharger product is introduced with computational experiments of the proposed algorithms.     

Harmony search optimization algorithm for a novel transportation problem in a consolidation network

This article presents a new harmony search optimization algorithm to solve a novel integer programming model developed for a consolidation network. In this network, a set of vehicles is used to transport goods from suppliers to their corresponding customers via two transportation systems: direct shipment and milk run logistics. The objective of this problem is to minimize the total shipping cost in the network, so it tries to reduce the number of required vehicles using an efficient vehicle routing strategy in the solution approach. Solving several numerical examples confirms that the proposed solution approach based on the harmony search algorithm performs much better than CPLEX in reducing both the shipping cost in the network and computational time requirement, especially for realistic size problem instances.     

Profit-oriented partial disassembly line design: dealing with hazardous parts and task processing times uncertainty

This paper addresses the problem of profit-oriented disassembly line design and balancing considering partial disassembly, presence of hazardous parts and uncertainty of task processing times. Few papers have studied the stochastic disassembly line balancing problem and existing approaches have focused on heuristic and metaheuristic methods. Most existing work has concentrated on complete disassembly where task times are assumed to be normal random variables and where AND/OR graphs are not considered. The objective of this paper is the design of a serial line that obtains the maximum revenue and then balances the workload under uncertainty. The processing time of a disassembly task is assumed to be a random variable with any known probability distribution. An AND/OR graph is used to model the precedence relationships among tasks. Stochastic programming models and exact-based solution approaches combining the L-shaped algorithm and Monte Carlo sampling techniques are proposed. The relevance and applicability of the proposed models and solution methods are shown by solving efficiently a set of disassembly problem instances from the literature.     

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.     

Loading and scheduling for flexible manufacturing systems with controllable processing times

This study addresses the problem of determining the allocation of operations and their tools to machines, the operation processing times and the allocation/sequence of the parts to be processed on each machine for flexible manufacturing systems with controllable processing times. Tool lives, tool copies and tool sharing are also considered. An integer programming model is developed for the objective of minimizing the sum of operation processing and tardiness costs. Then, iterative algorithms are proposed that solve the two subproblems iteratively, where the loading subproblem is solved by a modified bin packing algorithm under initial processing times and the resulting scheduling subproblem is solved by a priority scheduling method while modifying the loading plans and operation processing times iteratively. Computational experiments were carried out, and the results are reported.     

Mathematical modelling and optimisation of energy-conscious hybrid flow shop scheduling problem with unrelated parallel machines

This paper investigates an energy-conscious hybrid flow shop scheduling problem with unrelated parallel machines (HFSP-UPM) with the energy-saving strategy of turning off and on. We first analyse the energy consumption of HFSP-UPM and formulate five mixed integer linear programming (MILP) models based on two different modelling ideas namely idle time and idle energy. All the models are compared both in size and computational complexities. The results show that MILP models based on different modelling ideas vary dramatically in both size and computational complexities. HFSP-UPM is NP-Hard, thus, an improved genetic algorithm (IGA) is proposed. Specifically, a new energy-conscious decoding method is designed in IGA. To evaluate the proposed IGA, comparative experiments of different-sized instances are conducted. The results demonstrate that the IGA is more effective than the genetic algorithm (GA), simulating annealing algorithm (SA) and migrating birds optimisation algorithm (MBO). Compared with the best MILP model, the IGA can get the solution that is close to an optimal solution with the gap of no more than 2.17% for small-scale instances. For large-scale instances, the IGA can get a better solution than the best MILP model within no more than 10% of the running time of the best MILP model.     

A hybrid flowshop scheduling problem for a cold treating process in seamless steel tube production

Seamless steel tubes often have various categories and specifications, which further require complicated operations in production, especially in the cold treating process (CTP). This paper investigates the scheduling problem using the seamless tube plant of Baoshan Iron and Steel Complex as a study background. By considering the practical production constraints such as sequence-dependent setup times, maintenance schedule, intermediate material buffers, job-machine matches, we formulate the hybrid flowshop scheduling problem with a non-linear mixed integer programming model (NMIP). In addition, our model provides a flexibility to remove the permutation assumption, which is often a limitation in early studies. In order to obtain the solution of the above NMIP problem, a two-stage heuristic algorithm is proposed and it combines a modified genetic algorithm and a local search method. With real production instances, our computation experiments indicate that the proposed algorithm is efficient and it outperforms several other approaches. Industrial implementation also shows that such a scheduling tool brings a cost saving of more than 10% and it substantially reduces the computation time. Our study also illustrates the need of relaxing permutation assumption in such a scheduling problem with complicated operation sequences.