Multiple Part Types Research Articles

Optimal average cost manufacturing flow controllers: convexity and differentiability

The authors consider the control of a production facility consisting of a single workstation with multiple failure modes and part types using a continuous flow control model. Technical issues concerning the convexity and differentiability of the differential cost function are investigated. It is proven that under an optimal control policy the differential cost is C/sup 1/ on attractive control switching boundaries.

Scheduling in robotic cells: Complexity and steady state analysis

This paper considers the scheduling of operations in a manufacturing cell that repetitively produces a family of similar parts on several machines served by a robot. The decisions to be made include finding the robot move cycle and the part sequence that jointly minimize the production cycle time, or equivalently maximize the throughput rate. We focus on complexity issues and steady state performance. In a three machine cell producing multiple part-types, we prove that in two out of the six potentially optimal robot move cycles for producing one unit, the recognition version of the part sequencing problem is unary NP-complete. The other four cycles have earlier been shown to define efficiently solvable part 'sequencing problems. The general part sequencing problem not restricted to any robot move cycle in a three machine cell is shown to be unary NP-complete. Finally, we discuss the ways in which a robotic cell converges to a steady state.

Performability of systems based on renewal process models

A system of N statistically identical machines is modeled using renewal theory through a unique architecture and state space. The model is very useful in evaluating flexible manufacturing systems (FMS) in particular. Each machine consists of multiple part types that are subject to individual failure. A multiple stage repair process composed of integrable sojourn time distributions requires access to spare parts to repair down machines. A performability measure is used to gauge system effectiveness for this partially degradable system, and an example is given.

Design for global manufacturing and assembly*

In this paper the author presents and tests new concurrent engineering strategies that focus on manufacturing and assembly operations with a global perspective. Specifically, the focus is upon new design for manufacturability and assembly (DFMA) strategies to support multi-facility, global operations. These DFMA strategies are more holistic than most published techniques in that they focus on total system approaches that explicitly consider product mix, process configuration, and capital procurement strategies, as well as tooling, design, and set-up costs associated with manufacture and assembly. Furthermore, the DFMA strategies presented here consider the cost of transportation logistics in multi-facility, global manufacturing, assembly, and distribution networks., A general mathematical formulation is presented and tested under realistic conditions. It is demonstrated that this model can be used for capacity planning and product sourcing for multiple part types in many facilities. Similarly, it can be used to examine the sensitivity of solutions to changes in various costs, productivity levels, or product configuration and mix assumptions at each facility. Test results demonstrate the efficacy of use of the formulation in general terms. Finally, a research agenda is posited for the future development of the strategies.

Scheduling in Robotic Cells: Classification, Two and Three Machine Cells

This paper considers the scheduling of operations in a manufacturing cell that repetitively produces a family of similar parts on two or three machines served by a robot. We provide a classification scheme for scheduling problems in robotic cells. We discuss finding the robot move cycle and the part sequence that jointly minimize the production cycle time, or equivalently maximize the throughput rate. For multiple part-type problems in a two-machine cell, we provide an efficient algorithm that simultaneously optimizes the robot move and part sequencing problems. This algorithm is tested computationally. For a three-machine cell with general data and identical parts, we address an important conjecture about the optimality of repeating one-unit cycles, and show that such a procedure dominates more complicated cycles producing two units. For a three-machine cell producing multiple part-types, we prove that four out of the six potentially optimal robot move cycles for producing one unit allow efficient identification of the optimal part sequence. Several efficiently solvable special cases with practical relevance are identified, since the general problem of minimizing cycle time is intractable. Finally, we discuss ways in which a robotic cell converges to a steady state.

Scheduling multiple part-types in an unreliable single-machine manufacturing system

Quadratic approximations to the differential cost-to-go function, which yield linear switching curves, have been extensively studied in the literature. In this paper, we provide solutions to the partial differential equations associated with the components of the steady-state probability density function of the buffer levels for two part-type, single-machine flexible manufacturing systems under a linear switching curve (LSC) policy. When there are more than two part-types, we derive the probability density function, under a prioritized hedging point (PHP) policy by decomposing the multiple part-type problem into a sequence of two part-type problems. The analytic expression for the steady-state probability density function is independent of the cost function. Therefore, for average cost functions, we can compute the optimal PHP policy or the more general optimal LSC policy for two part-type problems.

A mathematical modelling approach for the process of part orientation in batch assembly automation

The use of steps as active devices to automatically feed and correctly orient parts has received increased attention in recent years. The work reported so far on determination of the best step sizes for the cases of singlepart and multiple-part types has focused either on experimental evaluation or analytical computation. We present mathematical models for describing the process of correctly orienting parts when steps are used as active devices in batch assembly automation. Two di erent cases-single and multiple-part types-have been considered. Each case is analysed as a single-step active device and as a two-step active device. For the single-part case, the objective function focuses on maximizing the ee ciency, evaluated as the probability of correctly orienting the part. For multiple-part types, the focus is on minimizing the cycle time. This is in line with the current trend in just-in-time manufacturing which requires producing a quantity known as the 'minimum part set'. A series of example problems are solved to illustrate each case. The results obtained further demonstrate how the model can be conveniently used by practitioners in industry to determine the best step size s to use in part-feeder mechanisms.

Design for global manufacturing and assembly

In this paper the author presents and tests new concurrent engineering strategies that focus on manufacturing and assembly operations with a global perspective. Specifically, the focus is upon new design for manufacturability and assembly (DFMA) strategies to support multi-facility, global operations. These DFMA strategies are more holistic than most published techniques in that they focus on total system approaches that explicitly consider product mix, process configuration, and capital procurement strategies, as well as tooling, design, and set-up costs associated with manufacture and assembly. Furthermore, the DFMA strategies presented here consider the cost of transportation logistics in multi-facility, global manufacturing, assembly, and distribution networks. A general mathematical formulation is presented and tested under realistic conditions. It is demonstrated that this model can be used for capacity planning and product sourcing for multiple part types in many facilities. Similarly, it can be used to examine the sensitivity of solutions to changes in various costs, productivity levels, or product configuration and mix assumptions at each facility. Test results demonstrate the efficacy of use of the formulation in general terms. Finally, a research agenda is posited for the future development of the strategies.

Sequencing of robot activities and parts in two-machine robotic cells

This paper deals with the development of analytical methods for determining an optimal sequence of parts and robot activities to minimize cycle time in robotic cells with two machines. A robot is used to feed parts to the two machines or in the absence of machines two robots perform processing operations on parts. Three different types of robotic cellular layouts, namely the robot-centered cell, the mobile robot cell, and the in-line robot cell have been considered in an automated flow line manufacturing system with no storage buffers. Optimal sequences have been established for both single and multiple part types when part production is performed in a repetitive fashion. In order to keep abreast with the current trend toward just-in-time manufacturing, production of a quantity known as the minimum part set (MPS) is considered for multiple part types. The analysis for a single MPS has further been extended to include the cyclic production of multiple MPSs. The problem of determining the optimal sequence of multiple part types has been shown equivalent to a two machines no-wait flow shop problem, and has been solved by Gilmore and Gomory's (1964) algorithm.

A simulation study of container size in two-card kanban systems

Setting container sizes is one of the first decisions that users of kanban systems must address. Yet researchers have largely assumed container sizes to be given. This paper investigates the effect of container size on average inventory and customer service levels in a two-card kanban system processing multiple part types. Container size and the number of kanbans are varied in tandem so that total in-process inventory capacity remains constant. Simulation results show that smaller containers lead to smaller average total inventories. The surprise is that smaller containers do not always lead to poorer average customer service. Smaller container sizes can lead to better average customer service when the costs of greater total setup time are offset by the benefits of more frequent material handling, that is less frequent station material starvation, and improved finished goods part mix. This occurs primarily when container size is larger than average finished-goods order size and when setup times are relati...

Hierarchical production planning for complex manufacturing systems

A hierarchical approach to production planning for complex manufacturing systems is presented. A single facility comprising a number of work-centers that produce multiple part types is considered. The planning horizon includes a sequence of time periods, and the demand for all part types is assumed known. The production planning problem consists of minimizing the holding costs for all part types, as well as the work-in-process and the backlogging costs for the end items. We present a two-level hierarchy that is based on aggregating parts to part families, work-centers to manufacturing cells and time periods to aggregate time periods. The solution at the aggregate level is imposed as a constraint to the detailed level problems which are formulated for each manufacturing cell separately. This architecture uses a rolling horizon strategy to perform the production management function. We have employed perturbation analysis techniques to adjust certain parameters of the optimization problems at the detailed level to reach a near-optimal detailed production plan. Numerical results for several realistic example problems are presented and the solutions obtained from the hierarchical and monolithic approaches are compared. The results indicate that the hierarchical approach offers major advantages in computational efficiency, while the loss of optimality is acceptable.

Analysis of flexible manufacturing systems with distinct repeated visits: DrQ

This article examines the performance effects caused by repeated part visits at the workstations of a flexible manufacturing system (FMS). Such repeated part visits to the same workstations are commonly associated with fixture changes for machining complex parts, reclamping, and remounting or reorienting them. Since each of the repeated visits to a workstation may require different processing requirements, the resulting queueing network does not have a product form solution. We therefore develop an approximate mean value analysis model for performance evaluation of an FMS that may produce multiple part types with distinct repeated visits. We provide numerical examples and validate the accuracy of our solution algorithm against simulation. These examples show that the proposed model produces accurate throughput and utilization predictions with minimal computational efforts. These examples reveal that increasing the total pallet population may result in a reduction of the aggregate throughput, and that the FMS's performance could be more sensitive to the mix of pallets and part routes than to the total number of pallets. Our model will be of use, in particular, when managers wish to control individual operations (e.g., to adjust individual operation times to achieve economic savings in tool wear and breakage costs) or to investigate the performance implications of route changes due to alternate assignments of particular manufacturing tasks to certain workstations.

Performability studies of automated manufacturing systems with multiple part types

We consider the transient performance analysis of failure-prone manufacturing systems producing multiple part types. We decompose the exact monolithic model into: 1) a slower time scale structure state process modeling the failure and repair, and 2) a faster time scale performance model describing the part processing and the material movement. We combine the solution of these two models to show that the accumulated reward over a given time interval is a solution of a set of forward or adjoint multidimensional linear hyperbolic partial differential equations. This result generalizes the existing results on composite performance-dependability analysis of manufacturing systems. We also present efficient numerical methods for computing the distribution of the cumulative operational time, and the mean and variance of the cumulative production over a given time interval. Further, we bring out the significance of these results in the manufacturing systems context through several examples.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

DETERMINING THE NUMBER OF KANBANS IN MULTI-ITEM JUST-IN-TIME SYSTEMS

Kanbans (cards) are one means of controlling just-in-time production systems. The Kanbans serve as production authorization orders and essentially become the information system. The presence of a production ordering Kanban for a specific part type constitutes an instruction to the workcenter to produce a “container” of that part. In this chapter we assume workcenters produce multiple part types and address the issue of the number of Kanbans needed for each part type. Our objective is to minimize the sum of inventory holding and backorder cost. A stochastic model is formulated. Steady-state results are derived for several operating environments and results and validated by simulation.

On real-time scheduling policies for flexible manufacturing systems

The authors consider a model proposed by J.R. Perkins and P.R. Kumar (ibid., vol.34, no.2, pp. 139-148, Feb. 1989) for real-time control of flexible manufacturing systems. In this model, a machine can process a finite number of part types at specified rates, but only one part type can be processed at any given time. To process multiple part types, the machine uses a feedback rule to switch, from time to time, from one part type to another. Such switches incur a setup time of delta time units during which no parts are processed. By introducing the notion of idling, the authors derive a lower bound on the performance, as measured by average buffer size, of any stable feedback scheduling policy for a single machine. >

Quality control of an unreliable flexible manufacturing system with scrapping and infinite buffer capacity

Manufacturing multiple part types on a flexible manufacturing system (FMS) is increasingly becoming a rule rather than an exception. In such systems, attention has been drawn to the application of zero-defect technologies. However, in practice, this goal has remained elusive and costly. As a result, even though FMSs may be more reliable, producing fewer defective parts, system complexity and more stringent quality standards are rendering quality control in FMSs potentially useful. The goals of this article are threefold. First, we introduce a procedure for measuring and managing the in-process quality control of an FMS, which is described by an Open Queueing Network (OQN), bridging thereby a gap between queueing theory and quality control. Second, by focusing attention on the potential unreliabilities of FMSs, we provide some managerial insights regarding the role, position, and distribution of the quality control effort in an FMS. Finally, we stress the intricate relations between an FMS's operating characteristics and the manufactured quality and its control. Using numerical analyses, we draw some inferences regarding the design of such FMSs when both quality and quantity issues in the FMSs are considered. These simultaneous considerations of quantity and quality flows in an FMS have not been previously considered in the study of FMSs.

The Optimal Input Rates To A System Of Manufacturing Cells

AbstractA manufacturing system capable of processing multiple part types generates input, at a given rate, R, to a set of m cells. Each cell processes a certain type of parts and has its own production and buffer capacities. We study the problem of aEocating the production rate, R, among the m cells, such that the total throughput (over all m cells) will be maximised, while the blocking probabilities willl be kept below a given set of limits. An optimisation problem is formulated, which maximises a concave function over a convex set. An algorithm is developed, which fuUy exploits the problem structure and efficiently generates the optimal solution. Several extensions of the model are also discussed.

Formulation and Solution of Nonlinear Integer Production Planning Problems for Flexible Manufacturing Systems

A flexible manufacturing system (FMS) is an integrated, computer-controlled complex of automated material handling devices and numerically controlled machine tools that can simultaneously process medium-sized volumes of a variety of part types. FMSs are becoming an attractive substitute for the conventional means of batch manufacturing, especially in the metal-cutting industry. This new production technology has been designed to attain the efficiency of well-balanced, machine-paced transfer lines, while utilizing the flexibility that job shops have to simultaneously machine multiple part types. Some properties and constraints of these systems are similar to those of flow and job shops, while others are different. This technology creates the need to develop new and appropriate planning and control procedures that take advantage of the system's capabilities for higher production rates. This paper defines a set of five production planning problems that must be solved for efficient use of an FMS, and addresses specifically the grouping and loading problems. These two problems are first formulated in detail as nonlinear 0-1 mixed integer programs. In an effort to develop solution methodologies for these two planning problems, several linearization methods are examined and applied to data from an existing FMS. To decrease computational time, the constraint size of the linearized integer problems is reduced according to various methods. Several real world problems are solved in very reasonable time using the linearization that results in the fewest additional constraints and/or variables. The problem characteristics that determine which linearization to use, and the application of the linearized models in the solution of actual planning problems, are also discussed.

Optimizing Field Repair Kits Based on Job Completion Rate

A formulation is presented for obtaining the optimal kit of parts and tools for on-site equipment repairs, based on the fraction of jobs which can be completed from the contents of the kit. This formulation generalizes previous approaches in that part demands need not be independent and various numbers of parts as well as multiple part types per job may be required. It is shown that the formulation is a special case of Balinski's “selection problem” and thus can be solved by maximal flow/minimal cut network algorithms.