A stochastic model of a reconfigurable manufacturing system Part 3: Optimal selection policy

Products required by customers are classified into several product families, each of which is a set of similar products. A reconfigurable manufacturing system (RMS) satisfies customer requirements by ensuring that each family corresponds to one configuration of the RMS. Products belonging to the same family will be produced by the RMS under the corresponding configuration. The manufacturing system is reconfigurable for different families. To utilize the RMS, a selection policy that is an action rule is needed, by which the manufacturer selects a family to produce ordered products belonging to the selected family. Thus, an important issue for an RMS is the optimal selection policy. Based on a stochastic model, an optimization problem stemmed from the issue is formulated. Two solution procedures 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.     

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.     

Delayed reconfigurable manufacturing system

Reconfigurable manufacturing systems (RMS) is a new manufacturing paradigm aiming at providing exactly functionality and capacity needed and exactly when needed. Reconfiguration is the main method to achieve this goal. But, the reconfiguration is an interruption to production activities causing production loss and system ramp-up problem and the ‘exact functionality’ may increase the reconfiguration efforts and aggravate the production loss and the ramp-up time. Therefore, a special RMS – delayed reconfigurable manufacturing system (D-RMS) is proposed to promote the practicality of RMS. Starting from the RMS built around part family with the characteristic of delayed differentiation, whose reconfiguration activities mainly occur in the latter stages of manufacturing system and the former stages have the potential to maintain partial production activities to reduce production loss during reconfiguration. Inspired from this, the basic structure of RMS is divided into two subsystems, subsystem 1 is capable of maintain partial production with a certain more functionality than needed, subsystem 2 reconfigure to provide exactly functionality and capacity of a specific part exactly when needed. And then, the benefits of D-RMS are analysed from inventory and ramp-up time aspects. Finally, a case study is presented to show the implementation process of D-RMS and validates the practicability of D-RMS.     

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.     

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.     

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.     

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.     

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.     

Optimal production control problem in stochastic multiple-product multiple-machine manufacturing systems

This paper deals with the issue of production control in a manufacturing system with multiple machines which are subject to breakdowns and repairs. The control variables considered are the production rates for different products on the machines. Our objective is to minimize the expected total discounted cost due to the finished good inventories and backlogs. Based on the structure of the hedging point policy, a parameterized near-optimal production policy for a multiple-product manufacturing system is proposed. The analytical formalism is combined with simulation-based statistical tools, such as experimental design and response surface methodology. The aim of such a combination is to provide an approximation of the optimal control policy. In the proposed approach, the parameterized near-optimal control policy is used as an input for the simulation model. For each entry consisting of a combination of parameters, the cost incurred is obtained. The significant effects of the control variables are determined by the experimental design. The relationship between the cost and these input factors is obtained through a response surface model. It is from the obtained relationship that the best values of control factors are determined. Extensive computational experience is reported for two-part-type and five-part-type production systems. Finally, simulation experiments on several examples are concentrated on the sensitivities of the control policy obtained.     

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.     

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.     

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.     

Optimal control of a continuum model for single-product re-entrant manufacturing systems

A semiconductor manufacturing system that involves a large number of items and many steps can be modelled through conservation laws for a continuous density variable on a production process. In this paper, the basic hyperbolic partial differential equation (PDE) models for multiple re-entrant manufacturing systems are proposed. However, through numerical examples, the basic continuum models do not perform well for small-scale multiple re-entrant systems, so a new state equation taking into account the re-entrant degree of the product is introduced to improve the basic continuum models. The applicability of the modified continuum model is illustrated through a numerical example. Based on the modified continuous model, this paper studies the optimal control problems for multiple re-entrant manufacturing systems. The gradient of the cost function with respect to the influx is solved by the adjoint approach, and then the optimal influx is computed by the steepest descent method. Finally, numerical examples on optimal influx profiles for steps in demand rate, linear demand rate and periodically varying demand rate are given. The relationships among influx, outflux and demand are also discussed in detail.     

Optimal resource assignment through negotiation in a multi-agent manufacturing system

Research studies on multi-agent systems have been recently boosted by manufacturing and logistics with deep motivations like the presence of independent human deciders with individual goals, the aspiration to dominate the complexity of decision-making in large organizations, the simplicity and robustness of self-reacting distributed systems. After a survey of the multi-agent paradigm and its applications, the paper introduces the notion of hybrid holonic system to study the effect of supervision on a system whose elements negotiate and cooperate in a rule-settled environment to obtain resources for system operation. The supervisor can spur or disincentive agents by assigning/denying resources to them. A simple single-decider optimization model referred to a real application is described, and solution methodologies for optimal resource allocation fitting different scenarios (centralized, distributed, multi-agent) are discussed, identifying ranges of autonomy, quantifying rewarding and defining a negotiation protocol between the agents and the supervisor. Aim of the paper is to describe through an example a general methodology for quantitative decision-making in multi-agent organizations.     

A comprehensive approach to operation sequence similarity based part family formation in the reconfigurable manufacturing system

The industrial sector of the twenty-first century faces a highly volatile market in which manufacturing systems must be capable of responding rapidly to the market changes, while fully exploiting resources. The reconfigurable manufacturing system (RMS) is a state of the art technology offering the exact functionality and capacity needed, which is built around a part family. The configuration of an RMS evolves over a period to justify the needs of upcoming part families. The foundation for the success of an RMS, therefore, lies in the recognition of appropriate sets of part families. In the present work the authors have developed a novel operation sequence based BMIM (bypassing moves and idle machines) similarity coefficient using longest common subsequence (LCS) and the minimum number of bypassing moves and the quantity of idle machines. The effectiveness of the developed similarity coefficient has been compared with the existing best similarity/dissimilarity coefficients available in the existing literature. An example set of parts has been classified using the developed similarity coefficient and average linkage hierarchical clustering algorithm. The developed approach can also be used very effectively for part family formation in the cellular manufacturing system.