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.     

A scatter search approach with dispatching rules for a joint decision of cell formation and parts scheduling in batches

A joint decision of cell formation and parts scheduling is addressed for a cellular manufacturing system where each type of machine and part may have multiple numbers and parts must require processing and transferring in batches. The joint decision problem is not only to assign batches and associated machine groups to cells, but also to sequence the processing of batches on each machine in order to minimise the total tardiness penalty cost. A nonlinear mixed integer programming mathematical model is proposed to formulate the problem. The proposed model, within nonlinear terms and integer variables, is difficult to solve efficiently for real size problems. To solve the model for practical purposes, a scatter search approach with dispatching rules is proposed, which considers two different combination methods and two improvement methods to further expand the conceptual framework and implementation of the scatter search so as to better fit the addressed problem. This scatter search approach interactively uses a combined dispatching rule to solve a scheduling sub-problem corresponding to each integer solution visited in the search process. A computational study is performed on a set of test problems with various dimensions, and computational results demonstrate the effectiveness of the proposed approach.     

A graph-based model for manufacturing complexity

This paper presents a graph-based model to measure the relative manufacturing complexity of and the manufacturing similarity of products in job shop manufacturing systems. This model depicts the impact of the complexity factors on the profit realisable from products based on their manufacturing process and required resources/skills. These resources deal with the process required for a component to reach assembly, the process of assembling the components to a whole product. This relative manufacturing complexity measure not only can support assembly and production cost estimation, but also can provide a guideline for creating a product with the most effective balance of manufacturing and assembly. Also, the results of this study can help improve budgeting and resource allocation, and the product life cycle cost estimation for future products. A numerical example is also presented to demonstrate the application of the proposed approach.     

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.     

A portfolio approach to maintenance: a case study of a residential estate

The choice between repairing and replacing a defective piece of equipment is an economic decision that is faced by all maintenance managers, including housing estate managers. Such decisions need to be made within the limits and constraints set by maintenance expenditure budgets and by manpower availability. Our particular problem is concerned with the development of a maintenance policy for a residential estate of the Hong Kong Housing Authority. Our approach is to treat the numerous housing systems as a portfolio and to exploit flexibilities in performing or delaying the repair/replacement of these systems. The cost of a repair/replacement plan for the portfolio is formulated as an integer programme and genetic algorithms (GAs) are employed to generate optimal and sub‐optimal solution plans. The novel features of the approach are the model developed and use of GAs in this particular optimization context. The results and discussion of the case study will help practitioners to better understand the difficulties involved in collecting relevant cost data and in formulating repair/replacement plans for a group of buildings. Copyright © 2007 John Wiley & Sons, Ltd.     

Product Assembly Cost Estimation Based on Artificial Neural Networks

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多种易变质性物品集中采购成本优化

将库存损失量看作是存贮时间和库存水平的函数,研究了一次集中采购多种易变质性物品的成本优化问题,分析了总成本的构成,以总成本最小化为目标,建立了该问题的混合整数规划模型,并给出了一种该模型的求解方法,计算实例验证了该方法的有效性.     

A mixed integer goal programming model for discrete values of design requirements in QFD

A main feature of quality function deployment (QFD) planning process is to determine target values for the design requirements (DRs) of a product, with a view to achieving a higher level of overall customer satisfaction. However, in real world applications, values of DRs are often discrete instead of continuous. Therefore, a mixed integer linear programming (MILP) model considering discrete data is suggested. As opposed to the existing literature, the fulfilment levels of DRs are assumed to have a piece-wise linear relationship with cost; because, constraints of technology and resource rarely provides a linear relationship in manufacturing systems. In the proposed MILP model, we considered customer satisfaction as the only goal. But, QFD process may be necessary to optimise cost and technical difficulty goals as well as customer satisfaction. Therefore, by developing the MILP model with multi-objective decision making (MODM) approach, a novel mixed integer goal programming (MIGP) model is proposed to optimise these goals simultaneously. Finally, MILP model solution turns out to be a more realistic approach to real applications because piece-wise linear relationship is taken into account. The solution of MIGP model provided different alternative results to decision makers according to usage of the lexicographic goal programming (LGP) approach. The applicability of the proposed models in practice is demonstrated with a washing machine development problem.     

Mixed model assembly system with multiple secondary feeder lines: layout design and balancing procedure for ATO environment

The constant research for efficiency and flexibility has forced assembly systems to change from simple/single assembly lines to mixed model assembly lines, while the necessity to reduce inventory has led the transition from single to multi-line systems, where some components are assembled in secondary lines, called feeder lines, connected to the main one by a ‘pull philosophy’. A possible approach to configure such an assembly system is to balance the main line first and use the retrieved cycle time to balance each feeder line separately, which is a questionable solution, especially if operators can perform tasks on both the feeder and the main line. Moreover for its complexity the mixed model balancing problem is usually solved transforming it into a single model by creating a single ‘virtual average model’, representative of the whole production mix. The use of a virtual average model assumes that the processing times of some models are higher or lower than the cycle time, which creates overload/idle time at the stations. This approach, especially in complex multi line production systems, largely reduces the assembly line productivity and increases the buffers dimensions. This paper faces the mixed model assembly line balancing problem in the presence of multiple feeder lines, introducing an innovative integrated main-feeder lines balancing procedure in case of unpaced assembly systems. The proposed approach is compared with the classical one and validated through simulation and industrial applications.     

Extension of the hybrid linear programming method to optimize simultaneously the design and operation of groundwater utilization systems

This article proposes a hybrid linear programming (LP-LP) methodology for the simultaneous optimal design and operation of groundwater utilization systems. The proposed model is an extension of an earlier LP-LP model proposed by the authors for the optimal operation of a set of existing wells. The proposed model can be used to optimally determine the number, configuration and pumping rates of the operational wells out of potential wells with fixed locations to minimize the total cost of utilizing a two-dimensional confined aquifer under steady-state flow conditions. The model is able to take into account the well installation, piping and pump installation costs in addition to the operational costs, including the cost of energy and maintenance. The solution to the problem is defined by well locations and their pumping rates, minimizing the total cost while satisfying a downstream demand, lower/upper bound on the pumping rates, and lower/upper bound on the water level drawdown at the wells. A discretized version of the differential equation governing the flow is first embedded into the model formulation as a set of additional constraints. The resulting mixed-integer highly constrained nonlinear optimization problem is then decomposed into two subproblems with different sets of decision variables, one with a piezometric head and the other with the operational well locations and the corresponding pumping rates. The binary variables representing the well locations are approximated by a continuous variable leading to two LP subproblems. Having started with a random value for all decision variables, the two subproblems are solved iteratively until convergence is achieved. The performance and ability of the proposed method are tested against a hypothetical problem from the literature and the results are presented and compared with those obtained using a mixed-integer nonlinear programming method. The results show the efficiency and effectiveness of the proposed method for solving practical groundwater management problems.     

Order-oriented cooperative sequencing optimisation in multi-mix-model assembly lines

Order-oriented products assembly sequence among different assembly lines becomes a critical problem for mass customisation manufacturing systems. It significantly affects system productivity, delivery time, and manufacturing cost. In this paper, we propose a new approach to extend the traditional products sequencing from mixed model assembly line (MMAL) to multi-mixed model assembly lines (MMMALs) to obtain the optimal assembly sequence with the objectives of minimising consumption waviness of each material in the lines, assembly line setup cost, and lead-time. A multi-objective optimisation algorithm based on variable neighbourhood search methods (VNS) is developed. We perform an industrial case study in order to demonstrate the practicality and effectiveness of the proposed approach.     

基于灰色聚类评估的配送中心选址模糊多目标优化模型

将多属性决策方法与最优化方法相集成,研究了多配送中心选址优化问题。首先采用灰色聚类决策计算各候选地定性属性的综合评估值。再以选定配送中心的评估值均值最大化、系统成本最小化,以及配送中心容量利用率最大化作为3个优化目标,建立一个考虑需求点模糊需求、供应点与候选配送中心容量限制的三级供应链系统多配送中心选址模型。该模型被描述成了一个多目标的非线性混合整数规划模型。采用机会约束规划对模糊需求进行清晰化处理,并应用目标加权的方法将问题转化为单目标问题。通过算例验证了所提模型的可行性。在实际工作中,可根据决策者权重偏好得出令人满意的结果。     

Optimal selection of application loading on cloud services

There is a need for identifying computing power hours and storage utilisation along with total cost optimisation. The present paper focuses on optimal selection of application loading process on the cloud services considering relevant factors. Using this model, small companies that plan to develop applications and use cloud services may determine cost and optimal selection of service by taking into account its own as well as provider’s perspectives into consideration. The paper consists of four stages. First stage deals with the estimation of required computing power hours in the planned duration. Second stage relates to the calculation of storage capacity. Third stage corresponds to the formation of multi objective goal programme to prioritise computing power hours and storage utilisation requirements of applications and optimise total cost of usage. Finally, fourth stage deals with the mixed integer non-linear programming to minimise total cost considering other variable factors. For small application developers who cannot afford in-house IT infrastructure, we find an optimal framework for allocating number of applications on cloud services such as Infrastructure as a Service and Platform as a Service. For ease in planning, the user company can quickly decide corresponding number of applications at appropriate services, and at the same time can reduce overall usage cost. With the help of proposed method, the service provider may keep a suitable inventory of cores to provide backup computing power and storage capacity. This adds value to developers also, as company can plan for their operations corresponding to the business growth.     

Workers’ rest allowance and smoothing of the workload in assembly lines

Ergonomic aspects have a crucial role in manual assembly systems. They impact on the workers’ health, final product quality and productivity. For these reasons, there is the necessity to integrate them into the assembly line balancing phase as, whereas, only time and cost variables are considered. In this study, human energy expenditures are considered as ergonomic aspects and we integrate them, for the first time, into the assembly line balancing problem type 2 through the rest allowance evaluation. We consider as an objective function the minimization of the smoothness index. Firstly, a new optimal method based on mixed integer linear programming and a new linearization methodology are proposed. Then, a heuristic approach is introduced. To complete the study, a computational experimentation is presented to validate the mathematical model and to compare the methodologies proposed in terms of computational time, complexity and solution. Additionally, we provide a detailed analysis of the impact that rest allowance evaluation can have on productivity comparing the results obtained, taking into account the rest allowance integration before, during and after the assembly balancing process.     

Joint production and shipment lot sizing for a delivery price-based production facility

A joint economic production quantity (EPQ) and delivery quantity model for a production system is investigated in this paper. More specifically, an EPQ policy is implemented in the production system, while a smaller shipping quantity is periodically dispatched to the customer. The production system is also responsible for the shipment cost, i.e. a delivery price-based procurement from the customer. The considered cost includes setup cost to launch the batch production, inventory carrying cost, and transportation cost, where the transportation cost is a function of the delivery quantity. A per unit time cost model is developed and analysed to determine the optimal production and delivery quantities. Under some mild conditions, it can be shown that the joint cost function is convex with respect to the production quantity; and the number of delivery is an integer in each replenishment cycle. Computational study has demonstrated the significant impact of the joint decision model on the operating cost. In particular, the reduction in total cost can be more than 15% when inventory carrying costs, and/or transportation costs, are high.     

Optimal cost design of flow lines with reconfigurable machines for batch production

Modular reconfigurable machines offer the possibility to efficiently produce a family of different parts. This paper formalises a cost optimisation problem for flow lines equipped with reconfigurable machines which carry turrets, machining modules and single spindles. The proposed models take into account constraints related to: (i) design of machining modules, turrets, and machines, (ii) part locations, and (iii) precedence relations among operations. The goal is to minimise equipment cost while reaching a given output and satisfying all the constraints. A mixed integer programming model is developed for the considered optimisation problem. The approach is validated through an industrial case study and extensive numerical experiments.     

Determination of unit load sizes of AGV in multi-product multi-line assembly production systems

This study deals with the problem of determining unit load sizes of automated guided vehicles (AGVs) in multi-product and multi-line assembly production systems. It is assumed that an AGV delivers assembly parts to each workstation of assembly lines from a miniload automated storage/retrieval system (AS/RS), and conveyor lines transport subassemblies between workstations. In this system, determination of the unit load sizes of parts carried by the AGV becomes an important decision factor due to its effects on the work-in-process inventory level and the operating cost of the system. Under a proposed AGV dispatching policy, a nonlinear mathematical model which allows unequal unit load sizes among assembly lines is formulated. Based on the characteristics of the objective function and feasible regions, a heuristic solution algorithm is developed. To illustrate the model, problems are chosen and solved.     

Batch sizing with controllable production rates in a multi-stage production system

In this paper, a comprehensive model is presented for cell formation and layout design in cellular manufacturing systems (CMS). The proposed model incorporates an extensive coverage of important operational features and especially layout design aspects to determine optimal cell configuration and Intra and Inter-cell layout in CMS. Hence, proposed integrated approach attempts to design intra and inter-cell layout and material handling flow path structure simultaneously. We examine the great potential benefits of providing these features consist of routing flexibility, operation sequence, machine capacity, considering number of cells as a decision variable, un-equal dimension of machines, free machines and cells orientation, and considering pickup and drop off station for each cell. In order to show the effects and important of integrated design in the CMS, two approaches, sequentially and integrated, have been investigated and demonstrate the integrated approach improve the quality of obtained solution. The proposed model is a mixed integer non-linear programme. Linearisation procedures are proposed to transfer it into a linearised mixed integer programming formulation. Computational results are presented with the linearised formulation. We presented several enhancements in terms of valid inequalities and extensions to the proposed model in order to improve its computational performance. Finally, concluding remarks are provided.     

Optimal acquisition policy in remanufacturing under general core quality distributions

The quality of acquirable used products (cores) is highly variable, which has made production planning and control of remanufacturing systems difficult. This paper studies an acquisition problem in presence of uncertain core quality. In order to derive optimal acquisition policy, the problem is formulated as a non-linear integer programming model in the framework of order statistics. The model is a strictly discrete convex problem with a unique global minimal solution. Then, a single bisection method is developed to obtain the optimal solution under a general continuous quality distribution. Moreover, the expressions of the optimal solution in some frequently used quality distributions are derived. Furthermore, the model is extended to the case of a general remanufacturing cost function, and corresponding results are presented. Finally, numerical experiments are conducted to test the effects of quality distribution, cost relationships of acquirable cores and remanufacturing cost function.     

Closed loop supply chain network design and optimisation using fuzzy mixed integer linear programming model

Owing to the revolution in sustainable and green manufacturing the production planning and network design of closed loop supply chain concept has got the attention of researchers and managers. In this paper, a multi-product, multi-facility capacitated closed-loop supply chain framework is proposed in an uncertain environment including reuse, refurbish, recycle and disposal of parts. The uncertainty related to demand, fraction of parts recovered for different product recovery processes, product acquisition cost, purchasing cost, transportation cost, processing, and set-up cost is handled with fuzzy numbers. A fuzzy mixed integer linear programming model is proposed to decide optimally the location and allocation of parts at each facility and number of parts to be purchased from external suppliers in order to maximise the profit of organisation. The proposed solution methodology is able to generate a balanced solution between the feasibility degree and degree of satisfaction of the decision maker. The proposed model has been tested with an illustrative example.