A heuristic algorithm for the loading problem in flexible manufacturing systems

The paper considers the loading problem in flexible manufacturing systems (FMSs). This problem involves the assignment to the machine tools of all operations and associated cutting tools required for part types that have been selected to be produced simultaneously. The loading problem is first formulated as a linear mixed 0–1 program with the objective to minimize the greatest workload assigned to each machine. A heuristic procedure is presented in which an assignment of operations to machine tools is obtained by solving a parameterized generalized assignment problem with an objective function that approximates the use of tool slots required by the operations assigned to the machines. The algorithm is coded in FORTRAN and tested on an IBM-compatible personal computer. Computational results are presented for different test problems to demonstrate the efficiency and effectiveness of the suggested procedure.     

Cyclic Scheduling of Operations for a Part Type in an FMS Handled by a Single Robot: A Parametric Critical-Path Approach

We consider two problems of periodic scheduling of parts in a robotic production system functioning under a given repetitive robot's route. The objective is to determine the starting times and durations of processing operations so as to minimize the cycle length. We reduce the problems to finding parametric critical paths in networks with varying arc lengths. In contrast to previously known methods, which solve these cyclic scheduling problems in cubic time, the parametric network approach solves the problems in time, m being the problem size.     

Simulation optimization for a flexible jobshop scheduling problem using an estimation of distribution algorithm

The flexible jobshop scheduling problem permits the operation of each job to be processed by more than one machine. The idea is to assign the processing sequence of operations on the machines and the assignment of operations on machines such that the system objectives can be optimized. The assignment mentioned is a difficult task to implement on real manufacturing environments because there are many assumptions to satisfy, especially when the amount of work is not constant or sufficient to keep the manufacturing process busy for a long time, causing intermittent idle times. An estimation of distribution algorithm-based approach coupled with a simulation model is developed to solve the problem and implement the solution. Using the proposed approach, the shop performance can be noticeably improved when different machines are assigned to different schedules.     

A geometrical approach to computer-aided process planning for computer-controlled machine tools

This paper documents part of a research program which has been under way at the CIM Centre at Swinburne University of Technology since 1989. The purpose of the research program was to develop an open-architecture machine tool control system and then to see how that system could be used to change the distribution of traditional manufacturing design, planning and control functions. This paper examines one part of that research program and focuses on a methodology which could prove to be useful in the machine tool selection, cutter selection and cutter path generation phases of process planning for cutting operations on workpieces in computer-controlled machine tools.It is suggested that a configuration space transform be used for each cutter/machine tool combination to find the volume that the combination could remove from the uncut workpiece without removing any of the material that will form the final workpiece. A method of comparing these volumes from different combinations is then outlined. The output of this method is a reasonable sequence of machine tools and cutters. Path planning can then be carried out for each of the chosen combinations using a method similar to the one used to find the possible volume to be removed.Possible implementation techniques, and their limitations on existing computer hardware, are discussed and the most promising of these are identified, based upon some properties of configuration space transforms.     

A resource-oriented tolerance representation scheme for the planning of robotic machine tending operations in automated manufacturing systems

In this paper, we define a representation for tolerances associated with robotic machine tending operations. The intent of the representation and analysis presented in the paper is to assess whether a robotic material handler is capable of holding the accuracies required for loading and unloading a machine. This representation and analysis, therefore, provides the basis of a process planning system for robotic operations. This representation is critical for flexible and automated manufacturing because it enables automatic planning of unload and load operations from and to machining centers that are required for discrete part manufacturing. Planners can use this representation along with the specified tolerance criteria to conservatively assess if a given robot resource is capable of using a specific gripper to unload or load a given part from a given fixture on a machining center. For a new part, this assessment allows an automatic material handling operations planner to determine if reconfiguration or procurement of resources is required for the material handing of the new part or if simple reprogramming of the robot and machine resources is sufficient. Also, this representation helps providing flexibility to the manufacturing system control software in the case of the addition of a new machine to the manufacturing system. In this case, the new resource data would be input into the resource model, and the decision on the machine tending operations (loading or unloading) would be carried out in the same manner. This representation was tested successfully using an automatic operations planner at The Pennsylvania State University’s Factory for Advanced Manufacturing Education (FAME) lab.     

The optimal configuration and workload allocation problem in flexible manufacturing systems

In this article we consider the problem of determining the minimum cost configuration (number of machines and pallets) for a flexible manufacturing system with the constraint of meeting a prespecified throughput, while simultaneously allocating the total workload among the machines (or groups of machines). Our procedure allows consideration of upper and lower bounds on the workload at each machine group. These bounds arise as a consequence of precedence constraints among the various operations and/or limitations on the number or combinations of operations that can be assigned to a machine because of constraints on tool slots or the space required to store assembly components. Earlier work on problems of this nature assumes that the workload allocation is given. For the single-machine-type problem we develop an efficient implicit enumeration procedure that uses fathoming rules to eliminate dominated configurations, and we present computational results. We discuss how this procedure can be used as a building block in solving the problem with multiple machine types.     

Internal energy minimization in biarc interpolation

The problem of scheduling n multioperation jobs on a single machine such as the flexible manufacturing system is considered. Each job comprises up to F operations, which belong to several distinct families, and a sequence-independent setup time is incurred whenever an operation is to be processed following an operation of a different family. A job completes when all of its operations have been processed. Two variants with maximum lateness and total completion time as optimality criterion are considered. The problems are denoted as $1\left| {s_f ,{\text{assembly}},GT} \right|L_{\max } $ and $1\left| {s_f = 1,{\text{assembly}},GT,p_{ij} = 0\,{\text{or}}\,1} \right|\sum {C_j } $ . The decision is to sequence all the families in order to minimize the predefined criterion. This environment has a variety of real world applications such as flexible manufacturing systems scheduling and food industry scheduling. A heuristic is presented and a branch and bound is developed for benchmarking. Experimental results show that the heuristic provides good results and the branch and bound procedure is efficient. These results may narrow down the gap between easy and hard cases of the general problem.     

Optimal Control of a Multistage Machining Operation on a Computer Numerically Controlled Machine

A multistage machining operation ( MMO) model is proposed for a computer numerically controlled (CNC) machine to minimise the production cost of a deterministic order quantity under deadline constraint. Using the Lagrange method, the optimal machining time for each cutting tool is then achieved and the cost-related property of the Lagrange multiplier is also verified. In addition, a computer simulation of a numerical case using the MATLAB program is fully discussed, and the cost function of the machine for machining such operations with respect to the production deadline, is then obtained. Through this study, the project scheduling, production cost estimating, and even the contract negotiating of a deterministic quantity scheduled on the CNC machine can be further accomplished. This paper not only contributes an applicable operational strategy for a machine, but also provides a valuable approach for minimising the production cost for manufacturing engineers. ID="A1"Correspondance and offprint requests to: Chun-Hsiung Lan, 90-2,Nanya W. Road Sec. 2, Panchiao, Taiwan 220. E-mail: clan@mail-iem.tnit.edu.tw     

Alternative optimisation strategies and CAM software for multipass rough turning operations

The development of constrained optimisation analyses and strategies for selecting optimum cutting conditions in multipass rough turning operations based on minimum time per component criterion is outlined and discussed. It is shown that a combination of theoretical economic trends of single and multipass turning as well as numerical search methods are needed to arrive at the optimum solution. Numerical case studies supported the developed solution strategies and demonstrated the economic superiority of multipass strategies over single pass. Alternative approximate multipass optimisation strategies involving equal depth of cut per pass, single pass optimisation strategies and limited search techniques have also been developed and compared with the rigorous optimisation strategies. The approximate strategies have been shown to be useful, preferably for on-line applications such as canned cycles on CNC machine controllers, but recourse to the rigorous multipass strategies should be regarded as the reference for use in assessing alternative approximate strategies or for CAM support usage.Nomenclature d _i depth of cut for theith pass - d _opt optimum depth of cut - d _T total depth of cut to be removed - D _i workpiece diameter before theith pass - D _o,D _m initial and final workpiece diameter (afterm passes) - f _i feed for theith pass - f _max,f _min machine tool maximum and minimum feed - f _opt optimum cutting feed - f _sj, V_sj available feed and speed steps in a conventional machine tool - f _sgl, f_rec optimum and handbook recommended single pass cutting feeds - F _pmax maximum permissible cutting force - L workpiece length of cut - m continuous number of passes - m _H next higher integer number of passes from a givenm - m _HW upper limit to the optimum integer number of passesm _opt - m _L next lower integer number of passes from a givenm - m _LW lower limit to the optimum integer number of passesm _opt - m _o optimum (continuous) number of passes - m _opt optimum integer number of passes - N _a machine tool critical rotational speed whenP _a=P _max - N _max,N _min machine tool maximum and minimum rotational speed - n,n ₁,n ₂,K speed, feed and depth of cut exponents and constant in the extended Taylor's tool-life equation - P _a,P _max machine tool low speed and maximum power constraints - T _i tool-life using the cutting conditions for theith pass - T _L loading and unloading time per component - T _R tool replacement time - T _s tool resetting time per pass - T _T production time per component - T _TDi multi-passT _T equation with workpiece diameter effect - T _TDm, T_TDo multi-passT _T equations with constant diameterD _m andD _o, respectively - T _Topt overall optimum time per component - T _Tsgl optimum time per component for single pass turning - T _{T2re c} handbook recommended time per component - V _i cutting speed for theith pass - V _max,V _min machine tool maximum and minimum cutting speed - V _sgl,V _rec optimum and handbook recommended single pass cutting speeds - V _opt optimum cutting speed - a, E, W empirical constants in theP _a/F _pmax/P _max equations - , , feed, depth and speed exponents inF _pmax andP _max equations     

SXC control chart

This article proposes the SXC (sum of xs with curtailment) control chart. This chart is nearly as simple as the chart for the operators to understand and implement. Meanwhile, it is as effective as the CUSUM chart for detecting the process mean shifts. The SXC chart can be applied to random inspection, as well as its special cases, i.e. uniform and 100% inspections. It is found that the SXC chart can reduce the out-of-control average time to signal (ATS) by 74%, on average, over a wide range of mean shifts compared to the Shewhart chart.     

Workload balance and part-transfer minimization in flexible manufacturing systems

Problems related to the flow management of a flexible manufacturing system (FMS) are here formulated in terms of combinatorial optimization. We consider a system consisting of several multitool automated machines, each one equipped with a possibly different tool set and linked to each other by a transportation system for part moving. The system operates with a given production mix.The focused flow-management problem is that of finding the part routings allowing for an optimal machine workload balancing. The problem is formulated in terms of a particular capacity assignment problem.With the proposed approach, a balanced solution can be achieved by routing parts on a limited number of different paths. Such a balancing routing can be found in polynomial time. We also give polynomial-time and-space algorithms for choosing, among all workload-balancing routings, the ones that minimize the global amount of part transfer among all machines.     

Steady-State Analysis and Scheduling of Cyclic Job Shops with Overtaking

A cyclic shop is a production system that repeatedly produces identical sets of parts of multiple types, called minimal part sets (MPSs), in the same loading and processing sequence. A different part type may have a different machine visit sequence. We consider a version of cyclic job shop where some operations of an MPS instance are processed prior to some operations of the previous MPS instances. We call such a shop an overtaking cyclic job shop (OCJS). The overtaking degree can be specified by how many MPS instances the operations of an MPS instance can overtake. More overtaking results in more work-in-progress, but reduces the cycle time, in general. We prove that for a given processing sequence of the operations at each machine, under some conditions, an OCJS has a stable earliest starting schedule such that each operation starts as soon as its preceding operations are completed, the schedule repeats an identical timing pattern for each MPS instance, and the cycle time is kept to be minimal. To do these, we propose a specialized approach to analyzing steady states for an event graph model of an OCJS that has a cyclic structure, which can keep the MPS-based scheduling concept. Based on the steady-state results, we develop a mixed integer programming model for finding a processing sequence of the operations at each machine and the overtaking degrees, if necessary, that minimize the cycle time.     

Temperature measurement in orthogonal metal cutting

Orthogonal cutting experiments were carried out on steel at different feedrates and cutting speeds. During these experiments the chip temperatures were measured using an infrared camera. The applied technique allows us to determine the chip temperature distribution at the free side of the chip. From this distribution the shear plane temperature at the top of the chip as well as the uniform chip temperature can be found. A finite-difference model was developed to compute the interfacial temperature between chip and tool, using the temperature distribution measured at the top of the chip.Nomenclature contact length with sticking friction behaviour [m] - c specific heat [J kg^–1 K^–1] - contact length with sliding friction behaviour [m] - F _P feed force [N] - F _V main cutting force [N] - h undeformed chip thickness [m] - h _c deformed chip thickness [m] - i,j denote nodal position - k thermal conductivity [W m^–2 K^–1] - L chip-tool contact length [m] - p defines time—space grid, Eq. (11) [s m^–2] - Q _C heat rate entering chip per unit width due to friction at the rake face [W m^–1] - Q _T total heat rate due to friction at the rake face [W m^–1] - Q _% percentage of the friction energy that enters the chip - q ₀ peak value ofq(x) [W m^–2] - q _e heat rate by radiation [W] - q(x) heat flux entering chip [W m^–2] - t time [s] - T temperature [K] - T _C uniform chip temperature [°C] - T _max maximum chip—tool temperature [°C] - T _mean mean chip—tool temperature [°C] - T _S measured shear plane temperature [°C] - x,y Cartesian coordinates [m] - V cutting speed [m s^–1] - V _C chip speed [m/s] - rake angle - ,, control volume lumped thermal diffusivity [m² s^–1] - emmittance for radiation - exponent, Eq. (3) - density [kg m^–3] - Stefan-Boltzmann constant [W m^–2 K⁴] - (x) shear stress distribution [N m^–2] - shear angle     

Dynamic flexibility metrics for capability and capacity

In production environments, such as Flexible Manufacturing Systems (FMSs), the schedule can be disturbed by the occurrence of unplanned events. Machines stop for major failures, maintenance, tool changes due to wear, or tool reassignments. The rescheduling process, however, can be costly. In this study, a dynamic measure of flexibility which helps to determine an appropriate time for rescheduling an FMS has been defined and investigated. Flexibility is defined as a function of Capability and Capacity. Accordingly, two metrics have been developed to monitor the capability and capacity efficiency of each machine in the system for responding to the dynamic system status. The value of each metric falls between 0 and 1 at all times. Higher values in the capability metric mean better machine selection and part distribution strategies among the machines. Higher values for the capacity metric mean higher machine utilization in the production plan. Based on the interaction between the metrics and their respective behavior in the system, four states have been identified and characterized. Simulations of various scenarios can be used to demonstrate the use of these metrics for monitoring FMS operations and determining appropriate times for rescheduling and tool reassignment.

Solving multi-objective SDST flexible flow shop using GRASP algorithm

This paper deals with the hybrid flow shop scheduling problems in which there are sequence-dependent setup times, commonly known as the SDST hybrid flow shops. This paper describes a Greedy Randomized Adaptive Search Procedure (GRASP) version for scheduling of a SDST hybrid flow shop, in which each stage (work center) consists of parallel identical machines. In this problem, each job has a different release date and consists of ordered operations that have to be processed on machines from different centers in the same order. In addition, the processing times of the operations on some machine centers may vary between a minimum and a maximum value depending on the use of a continuously divisible resource. We consider a non-regular optimization criterion based on due dates which are not a priori given or fixed but can be assigned by a decision maker. A due-date assignment cost is included into the objective function. Finally, the results obtained using GRASP are analyzed in order to find the preferred parameter settings and the features of the algorithms that have a strong influence on the solution quality.     

Using target costing concept in loss function and process capability indices to set up goal control limits

This paper depicts the relationship among the loss function, process capability indices and control charts to establish goal control limits by extending the target costing concept. The specification limits derived from the reflected normal loss function is linked through the C _pm value, computed either directly from the raw data or given by management or engineers, to conventional control charts to obtain goal control limits. The target value can be taken into consideration directly. The advantages of applying the target costing philosophy are also discussed. This paper explains, from a quantitative approach, that reducing process variation is not enough to solve quality problems. In fact, reducing process variation should be used along with bringing the process mean to the target value.A list of symbols K: The maximum-loss parameter in the reflected normal loss function - : The shape parameter in the reflected normal loss function, /4 - T: The target value - : The distance from the target value to the point where K first occurs (tolerance or specification limit) - E(L(y)): The expected loss associated with the reflected normal loss function - : The average value (mean) of a population - : The standard deviation of a population - _T : The standard deviation from the target value of a population - : The estimated standard deviation of - : The new process standard deviation when 2 are applied - n: The sample size of the subgroup - d ₂: The parameter used to estimate , determined by n - D ₄, D ₃, and A ₂: The parameters in and R control charts, determined by n - c ₄: the parameter used to estimate , determined by n - B ₄, B ₃, and A ₃: The parameters in and S control charts, determined by n - L(y): The general loss function - L ₁(y): The general loss function when the quality improvement is implemented - h: The parameter used to determine L ₁(y), where L ₁(y)=hK - f(y): The probability density function     

Making decision to evaluate process capability index C p with fuzzy numbers

The process capability index C _p has wide applications in the manufacturing industry. This paper extends those applications to a fuzzy environment, with a methodology for testing the index C _p of fuzzy numbers. A pair of nonlinear functions is formulated to find the α-cut of index . From various values of α, the membership function of index is constructed, and the probability of rejecting the null hypothesis is calculated based on this membership function. Different from classical tests, the statistical decision proposed in this paper shows a grade of acceptability of the null hypothesis and the alternative hypothesis, respectively. With crisp values, the developed approach not only can boil down to the classical formula for calculating Ĉ _p , but also lead to a binary decision: to reject or to accept the null hypothesis. An example is used to illustrate the performance of the proposed approach.     

A heuristic for a batch processing machine scheduled to minimise total completion time with non-identical job sizes

This paper studies the problem of scheduling semiconductor burn-in operations, where each job has non-identical lot sizes and an oven (a batch processing machine) that processes several jobs within its capacity limit simultaneously. We present some properties of the problem and an efficient heuristic algorithm. In a computational experiment, pairs of burning operations (,) were presented with the arrival time r_i and processing time p_i for different (,) pairs to examine the effect of arrival time and the processing time on minimising the total completion time. The result shows that a ratio of to greater than 1 was superior to other ratios, which can be a guide for schedule planners of burn-in operations. The heuristic obtains a satisfactory average performance rapidly. This revised version was published online in October 2004 with a correction to the issue number.     

Analysis of the diamond sawing process

There are three methods in use for separating diamonds, i.e. by cleaving, by laser beam and by sawing. Sawing is one of the main methods used for this purpose. This operation is carried out on special sawing machines equipped with a sawing disk blade, 0.04–0.14 mm thick and 76 mm initial diameter. The rotational velocity (n) of the disk is between 6000 and 12 000 r.p.m. Diamond powder is embedded in the periphery of the disk. The outcome surface of a diamond after the sawing operation must be flat and smooth, Whenever such a surface is actually obtained, the polishing time and the loss in size and weight of the diamonds are reduced.In the present work, the positioning of the diamond to be sawed, with respect to an embedded particle in the disk, to create a favourable cutting angle is discussed. This would make it possible to reduce the rake angle () to near-zero, and thereby the cutting forces. Furthermore, a method to control the morphology and grain size of the diamond powder to be used in the cutting was developed.In the diamond industry, two modes of sawing operations are in practice. One uses the periphery of the disk for the sawing while the other employs a circular hole in the centre of the disk. Analysis of the two modes showed that the hole mode is more promising, as the design in that case requires tensioning of the disk and makes for better lateral stability during the sawing process. In addition the tangential and the radial stresses, developed in both sawing methods, were calculated. To support the above, data was obtained from existing literature and analysed.Nomenclature n rotational velocity of the disk, r.p.m. - rake angle, degrees - back clearance angle, degrees - cutting angle, degrees - m relative frequency - f feed - b disk radius, mm - a disk hole radius, mm - r current disk radiusb>r>a, mm - density of disk material, kg m^–3 - angular velocity - Poisson ratio of disk material - g acceleration of gravity, m s^–2 - _r radial stress, kg cm^–2 - _{r max} highest radial stress, kg cm^–2 - _t tangential stress, kg cm^–2 - tangential stress at outside circumference, kg cm^–2 - tangential stress at inside circumference, kg cm^–2     

Chatter stability analysis for end milling via convolution modelling

This research discusses the methodology of developing a symbolic closed form solution that describes the dynamic stability of multiflute end milling. A solution of this nature facilitates machine tool design, machining parameter planning, process monitoring, diagnostics, and control. This study establishes a compliance feedback model that describes the dynamic behavior of regenerative chatter for multiflute tool-work interaction. The model formulates the machining dynamics based upon the interconnecting relationship of the tool geometry and the machining system compliance. The tool geometry characterises the cutting forces as a function of the process parameters and the material properties, while two independent vibratory modules, the milling tool and the workpiece, represent the machining system compliance. The compliance feedback model allows the development of a corresponding characteristic equation. By investigating the roots of the characteristic equation, this research symbolically expresses the stability of the system as a function of the cutting parameters, the tool geometry, the workpiece geometry, and the vibrational characteristics of the machine tool. Machining experimentation examining the fidelity of the regenerative chatter model is discussed. The dynamic cutting forces, cutting vibration, and surface finish of the machining process confirm the validity of the analytical prediction.Nomenclature b damping coefficient: mass-spring-damper representation - b _e equivalent damping coefficient: mass-spring-damper representation - C compliance element - CWD chip with density function - D diameter of cutter - d _a axial depth of cut - d _r radial depth of cut - average total cutting force - K _r radial specific cutting pressure constant - K _t tangential specific cutting pressure constant - k spring constant - k _e equivalent spring constant - m mass: mass-spring-damper representation - m _e equivalent mass: mass-spring-damper representation - n number of flutes on the cutter - p _x,y elemental cutting forces - P _1,2 elemental cutting force functions - R cutter radius - s Laplace variable - TS tooth sequencing function - chip thickness - t _c average chip thickness - t _x feed per tooth - helix angle - _x actual displacement of cutter tip - unit impulse function - _d damped circular frequency of vibration - damping ratio - spindle speed