A stochastic model of a reconfigurable manufacturing system Part 2: Optimal configurations

Various products required by customers are classified into several product families, each of which is a set of similar products. A reconfigurable manufacturing system (RMS) manages to satisfy customers, with each family corresponding to one configuration of the RMS. Then, the products belonging to the same family will be produced by the RMS under the corresponding configuration. The manufacturing system possesses the reconfigurable function for different families. In the design period of a RMS, there may exist several feasible configurations for each family. Then, an important issue in a RMS is the optimal configurations for the families. Based on a stochastic model, an optimization problem stemmed from the issue is formulated. Two algorithms are devised to solve the optimization problem. Numerical examples are presented for evaluating the efficiency of the algorithms.     

A stochastic model of a reconfigurable manufacturing system Part 1: A framework

Products required by customers are classified into several product families, each of which is a set of similar products. A reconfigurable manufacturing system (RMS) manages to satisfy customers, with each family corresponding to one configuration of the RMS. Then the products belonging to the same family will be produced by the RMS under the corresponding configuration. The manufacturing system possesses the reconfigurable function for different families. In an RMS there are three important issues: the optimal configurations in the design, the optimal selection policy in the utilization, and the performance measure in the improvement. This paper proposes a framework for a stochastic model of an RMS, which involves the above issues. Two optimization problems and the performance measure stemmed from the issues are formulated. An example is given for illustration. Some discussions are presented for future research work.     

A stochastic model of a reconfigurable manufacturing system - Part 4: Performance measure

Various products required by customers are classified into several product families, each of which is a set of similar products. A reconfigurable manufacturing system (RMS) manages to satisfy customers, with each family corresponding to one configuration of the RMS. Then, the products belonging to the same family will be produced by the RMS under the corresponding configuration. The manufacturing system possesses the reconfigurable function for different families. A performance measure is defined as service levels for the families. A semi-Markov process is formulated for obtaining the performance measure. When a larger fluctuation in the market happens, the manufacturer can adjust the system to improve the performance measure. An optimization of a reassigning problem is discussed, which reassigns the maximum numbers of orders to the families. Two solution approaches are proposed to solve the problem. Numerical examples are given for illustrating the methodologies.     

Optimal configuration selection for reconfigurable manufacturing system using NSGA II and TOPSIS

Reconfigurable Manufacturing Systems provide the functionality and capacity needed, when needed. The Reconfigurable Machine Tool (RMT) plays a pivotal role in the fulfilment of this objective through their modular structure consisting of basic and auxiliary modules along with the open architecture software. In the present work, a novel approach based on the module interactions and machine capability is proposed to measure the machine reconfigurability and operational capability of an RMT. The developed performance measures along with cost are considered as the multiple objectives for the optimal machine assignment for a single part flow line allowing paralleling of similar machines. The multi-objective optimisation problem in hand is targeted in two phases. In the first phase, non-dominated sorting genetic algorithm II is applied to obtain the non-dominated solutions. In the subsequent stage, a multiple attribute decision-making approach is employed to rank the pareto frontiers. The proposed solutions are ranked based on Shannon entropy weight and Technique for Order Preference by Similarity to Ideal Solution method. The study reveals that the developed performance measures along with the hybrid approach have a great potential in handling the RMS optimisation and cost–benefit issues.     

Optimal manufacturing policy in a reverse logistic system with dependent stochastic returns and limited capacities

The stochastic models of systems with reverse logistics usually assume that the quantity of products returned is independent of sales. This hypothesis is obviously not true and can lead to suboptimal production policies. In this paper a new sales-dependent returns model is described. In this model, the returns depend on the useful life of the products sold and on the probability of an end-of-life product being returned. A Markov decision problem is formulated in order to obtain the optimal manufacturing policy. A numerical example is provided to illustrate the use of the defined model. An approximated Markov decision model is defined where the optimal policy is easily obtained. The optimal policies of the original and the approximated models are compared.     

Optimal selection of module instances for modular products in reconfigurable manufacturing systems

A method for optimizing the variety of a modular products, manufactured in a Reconfigurable Manufacturing System, is proposed. The optimization is achieved through appropriately selecting the subsets of module instances from given sets. The problem is formulated as an integer nonlinear programming problem to find a trade-off between the quality loss due to modularity and the cost of reconfiguration for given sets of customer requirements. The proposed formulation is general in the sense that products can have any number of modules. The formulation is an extension to the available formulation that was developed for products with only two modules. Moreover, the current work addresses the effect of different order priorities, customer importance, and demands. The proposed method has been applied to a modular assembly problem and found to be efficient in determining optimum subsets of module instances.     

Evaluation of the logistic model of the reconfigurable manufacturing system based on generalised stochastic Petri nets

To reveal the influence on system performance by the logistic model of reconfigurable manufacturing system (RMS), the generalised stochastic Petri nets (GSPN) modular modelling approach is presented in this paper. It is based upon the characteristics of a bottleneck service. According to this approach, the bottleneck service in the production process is found first. By corresponding different resources in the service to different modules of the GSPN, the module is reconfigured. The analysis of the model using the Markov chain is hereby presented, as is the average utilisation factor of RMS. Following this, the production capacity of different products and the average productivity of reconfigurable manufacturing cells (RMCs) are discussed.     

Part selection policy for a flexible manufacturing cell feeding several production lines

Analysis of the part selection policy in the case of a flexible manufacturing cell producing different parts for several emanating lines is presented. The discrete response control problem is formulated as an undiscounted semi-Markovian decision problem whose decision epochs occur when the cell completes a part and must decide what type of part to fabricate next. Design objective is to minimize the expected shortage penalty per unit time incurred by the production lines when they run out of inputs. Optimal production policies are characterized, and a discussion of related industrial implementation issues is given.     

Logical reconfiguration of reconfigurable manufacturing systems with stream of variations modelling: a stochastic two-stage programming and shortest path model

Designing flexible manufacturing systems in general, and flexible material handling system in particular, is a complex problem, typically approached through several stages. Here the focus is on the conceptual design stage during which valid approximation-based methods are needed. The segmented flow topology (SFT) AGV systems were developed to facilitate control of complex automated material handling systems. This paper introduces a decomposition method, directly derived from timed Petri nets (TPN) theories, to calculate the expected utilization of AGVs (as servers of SFT systems) and to derive simple operational decision rules leading to maximum system productivity at steady state, for a given deterministic routeing of discrete material through the manufacturing system.     

Optimal policy in a hybrid manufacturing/remanufacturing system with financial hedging

This paper proposes a hybrid manufacturing/remanufacturing model with the financial hedging in the case where the randomness in demand is correlated with the financial markets. The provided models are mainly for those risk-averse remanufacturers who faced with random demand and yield. The aim of this paper is to maximise remanufacturer utility by purchasing financial instruments and producing new and remanufactured products. A hybrid manufacturing/remanufacturing system production planning model is first built under mean-variance framework, and then the financial hedging is integrated into the hybrid production system. There are three main findings. First, the variance of profit with financial hedging is always less than the variance of the model without financial hedging. Second, the remanufacturer with high (low) risk aversion is more likely to produce new (remanufactured) products. Third, the model without (with) financial hedging tends to produce new (remanufactured) products unless remanufacturing cost is low (high) enough. All those findings proved that financial hedging can reduce the operational uncertainty effectively and increase the proportion of remanufacturing, which will make remanufacturing firms more economical and environmentally friendly. Therefore, remanufacturing firms can consider using financial hedging to reduce operational uncertainty.     

Design of delayed reconfigurable manufacturing system based on part family grouping and machine selection

To improve the convertibility of reconfigurable manufacturing system (RMS), the concept of delayed reconfigurable manufacturing system (D-RMS) was proposed. RMS and D-RMS are both constructed around part family. However, D-RMS may suffer from ultra-long system problem with unacceptable idle machines using generic RMS part families. Besides, considering the complex basic system structure of D-RMS, machine selection of D-RMS should be addressed, including dedicated machine, flexible machine, and reconfigurable machine. Therefore, a system design method for D-RMS based on part family grouping and machine selection is proposed. Firstly, a part family grouping method is proposed for D-RMS that groups the parts with more former common operations into the same part family. The concept of longest relative position common operation subsequence (LPCS) is proposed. The similarity coefficient among the parts is calculated based on LPCS. The reciprocal value of the operation position of LPCS is adopted as the characteristic value. The average linkage clustering (ALC) algorithm is used to cluster the parts. Secondly, a machine selection method is proposed to complete the system design of D-RMS, including machine selection rules and the dividing point decision model. Finally, a case study is given to implement and verify the proposed system design method for D-RMS. The results show that the proposed system design method is effective, which can group parts with more former common operations into the same part family and select appropriate machine types.     

Energy-oriented bi-objective optimisation for a multi-module reconfigurable manufacturing system

This paper investigates a multi-module reconfigurable manufacturing system for multi-product manufacturing. The system consists of a rotary table and multiple machining modules (turrets and spindles). The production plan of the system is divided into the system design phase and the manufacturing phase, where the installation cost and the energy consumption cost correspond to the two phases, respectively. A mixed-integer programming model for a more general problem is presented. The objectives are to minimise the total cost and minimise the cycle time simultaneously. To solve the optimisation problem, the ε-constraint method is adopted to obtain the Pareto front for small size problems. Since the ε-constraint method is time consuming when problem size increases, we develop a multi-objective simulated annealing algorithm for practical size problems. To demonstrate the efficiency of the proposed algorithm, we compare it with a classic non-dominated sorting genetic algorithm. Experimental results demonstrate the efficiency of the multi-objective simulated annealing algorithm in terms of solution quality and computation time.     

Operation allocation and materials-handling system selection in a flexible manufacturing system: A sequential modelling approach

Materials-handling systems are an integrating component of manufacturing operations and as such must be considered within a common framework in manufacturing systems design. This work proposes a first approach to the simultaneous consideration of the operation allocation and the materials-handling system selection problems in a flexible manufacturing system. The objective of the operation allocation model is to select a group of machines where the operations of the part types will be performed and then to assign those operations to the selected machines. The operation allocation model interfaces with the materials-handling system selection model by providing input data in the form of the manufacturing operations to be performed at each machining centre. The selection of the materials-handling system is centred on the matching of the parts visiting a machining centre to perform a manufacturing operation and the abilities of the handling equipment to perform the required materials handling functions of those part types. The objective is to select an optimal group of materials-handling equipment to be assigned to a cell.     

Optimal replacement policy for a redundant system

Summary This paper considers the reliability of a system which consists ofn components connected in series, the i^thcomponent being supported by (m _i – 1) units in parallel and obtains the optimal policy of replacement by dynamic programming. In the case of a system consisting of identical pairs, the decision depends on the number of operable pairs. For this case sample calculations are presented.

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Zusammenfassung Wir untersuchen die Zuverlässigkeit eines Seriensystems ausn Komponenten, bei dem für diei-te Komponentem _i – 1 Reserveelemente zur Verfügung stehen. Mit Hilfe der dynamischen Optimierung bestimmen wir die optimale Ersetzungspolitik. Besteht das System aus identischen Paaren, hängt die Entscheidung von der Zahl der intakten Paare ab. Für diesen Fall geben wir beispielhaft einige numerische Ergebnisse.

     

The planning of a manufacturing system: a dynamic model

The paper studies a dynamical model of a manufacturing process taking into account:

the purchase of raw materials;

the scheduling of production;

the planning of sales.

We particularly deal with the planning of the production rate and of sales.

The basic hypotheses are:

the orders of each finished product are known over a given period of time

T;

the inventory levels are the state variables of the process;

the control variables are the purchase, productiqn and sale rates.

The goal of the ‘controller’ is to determine a policy which allows him to minimize at the time T the ‘capital’. As ‘capital’ we consider both the financial means and the technological resources employed in the process. Bilateral constraints in state and control variables have been introduced in our model.

The Maximum Principle has been used to formulate the problem and to obtain a solution.     

Reliability assessment for a stochastic manufacturing system with reworking actions

This article evaluates the system reliability of a manufacturing system with reworking actions, where the system reliability is an essential indicator to determine whether the manufacturing system is capable or not. Based on the path concept, we transformed the manufacturing system into a stochastic-flow network in which the capacity of each machine is stochastic (i.e., multistate) due to failure, partial failure, and maintenance. In such a manufacturing network, the input flow (raw materials/WIP; work-in-process) processed by each machine might be defective and thus the output flow (WIP/products) would be less than the input amount. To analyze the different sources processed by the manufacturing network, we decomposed the network into one general processing path and several reworking paths by a graphical technique. Subsequently, an algorithm for the manufacturing network was proposed to generate the lower boundary vector which allows sufficient products to satisfy the demand. In terms of such a vector, the system reliability can be derived easily.     

Airworthiness of aircraft. Part 1. A stochastic model

It is argued that a stochastic approach to airworthiness analysis is necessary because of the inherent random variations in aircraft performance. It is then shown that the history of any performance variable in fleet service is best regarded as a ‘stochastic corrective process’, characterised by slow deterioration punctuated by rapid improvements at overhauls. Considering specifically the engine-out take-off climb performance of an aircraft, a model is proposed by taking into account gradient changes due to the deterioration of airframe, engine and propeller (if present), the frequency and effectiveness of overhauls, and the occurrence of deviations in the gradient achieved on any flight from the true capability of the aircraft. In analysing the effect of overhauls a distinction is made between maintenance by rectification and by replacement. In the model proposed a total of 14 parameters govern the probability distribution of the achieved gradient in fleet history, and consequently also the incident rate during take-off climb.     

Optimal inventory costs in a complementary flexible manufacturing system

Flexible manufacturing systems (FMS) have provided job shop-type operations a variety of solutions to their widely documented inefficiencies. FMS come with a wide spectrum of capabilities and are used in a wide variety of manufacturing environments. The present study proposes there are situations where inventory control issues need to be considered during the FMS set-up planning. It has developed a non-linear mathematical programming model, which also has binary variables, to optimize inventory costs during the set-up planning for a sample FMS installation. The solution to the mathematical model is non-trivial. It shows that using this model in conjunction with analytical methods such as constraint propagation and generate-and-test, and sigmoid function approximations, facilitates robust solutions to some of the subproblems of the FMS set-up problem. The study also provides an exchange curve based framework for analysing the implications of inventory policy variables on decisions made at the FMS set-up stage.     

Optimisation for multi-part flow-line configuration of reconfigurable manufacturing system using GA

To facilitate the configuration selection of reconfigurable manufacturing systems (RMS) at the beginning of every demand period, it needs to generate K (predefined number) best configurations as candidates. This paper presents a GA-based approach for optimising multi-part flow-line (MPFL) configurations of RMS for a part family. The parameters of the MPFL configuration comprise the number of workstations, the number of paralleling machines and machine type as well as assigned operation setups (OSs) for each workstation. Input requirements include an operation precedence graph for each part, relationships between operations and OSs as well as machine options for each OS. The objective is to minimise the capital cost of MPFL configurations. A 0-1 nonlinear programming model is developed to handle sharing machine utilisation over consecutive OSs for each part which is ignored in the existing approach. Then a novel GA-based approach is proposed to identify K economical solutions within a refined solution space comprising the optimal configurations associated with all feasible OS assignments. A case study shows that the best solution found by GA is better than the optimum obtained by the existing approach. The solution comparisons between the proposed GA and a particle swarm optimisation algorithm further illustrate the effectiveness and efficiency of the proposed GA approach.     

Investigation of the reconfigurable control system for an agile manufacturing cell

A new type of manufacturing cell, with characteristics of reconfigurability, reusability and scalability, needs to be developed. To achieve the agile reconfiguration of a manufacturing cell, the cell control system must be rapidly and efficiently generated or modified. In this paper, a multi-agent based architecture is defined that supports the design and implementation of highly reconfigurable control systems for agile manufacturing cells, which are comprised of resource agents (material processing agents, material handling agents, and material storage agents), a control agent, and an information agent, in order to reduce costs and increase the control system's agility with respect to the changing environment. Different agents in the cell control system can be organized dynamically, communicate with each other through messages, and cooperate with each other to perform flexibly the task in the cell control system. The structure of the agents is proposed and the message-passing between agents is discussed in detail.