Single Part Type Research Articles

Modelling and analysis of a Markovian Production-Inventory Network

In this paper we model and study a stochastic manufacturing system with two stages in tandem that operates under a push type production control policy. The system produces a single part type and each stage consists of a machine and an output buffer. The machines are subjected to deterioration while operating and this deterioration results in decreased productivity. The production system is modeled as a continuous time Markov chain that describes the transitions between all system states due to the occurrence of demand arrival, deterioration failure, production completion and repair completion events. Solving the Markov chain numerically enables us to determine the steady state probabilities and this facilitates the calculation of useful performance metrics, namely system availability, down time, idle time, utilization and average inventory. We conduct a series of numerical experiments where we examine the behavior of the system for specified parameter set and gain insights on its properties.

Joint production, inventory rationing, and order admission control of a stochastic manufacturing system with setups

In this paper, we examine a single-stage, manufacturing system with setups, which produces a single part type to satisfy demand from two customer classes. We address the problem of coordinating production control, stock rationing, and order admission decisions. The optimal policy, in respect to minimizing holding, backorder, lost sales, and setup costs, is derived by formulating the underlying problem as a Markov Decision Process and solving it by means of Dynamic Programming. The structure of the optimal policy is investigated numerically and, on that basis, a parametric control policy is proposed. The Markov chain model of the single-machine manufacturing system, operating under the proposed policy, is developed. Furthermore, analytical expressions of the steady-state probabilities and of the expected total cost are obtained. The proposed policy is compared to the optimal, as well as to three heuristics, in an extended series of experiments. The numerical results indicate that the proposed policy is a very good approximation of the optimal one, and that it largely outperforms the alternative control policies.

ANÁLISIS DE ESTRATEGIAS DE PRODUCCIÓN Y REEMPLAZO DE SISTEMAS PRODUCTIVOS BAJO UN PROCESO DE DETERIORO

El presente articulo estudia el problema de la determinacion de estrategias de produccion y reemplazo para un sistema de produccion sujeto a un proceso de deterioro. El sistema de manufactura esta compuesto por una unidad productiva, la cual produce un tipo de pieza. Debido al proceso de deterioro, la tasa de fallas del sistema aumenta progresivamente al igual que la tasa de unidades defectuosas. Este articulo propone tres estrategias que controlan simultaneamente la tasa de produccion al igual que la tasa de reemplazo que mitiga los efectos del deterioro del sistema. Las tres estrategias de control propuestas CPR1, CPR2 y CPR3 son analizadas y comparadas en terminos del costo total incurrido. El objetivo de los modelos desarrollados es minimizar el costo total incurrido en un horizonte infinito. Se propone ademas una metodologia basada en el analisis estadistico de modelos de simulacion y su optimizacion, con el objetivo de determinar los parametros de control optimos. A fin de validar los resultados obtenidos, se realiza un extenso analisis de sensibilidad de ambas politicas, el cual muestra el efecto de diversos costos en sus respectivos parametros de control. Los resultados obtenidos, indican que la politica CPR3, la cual necesita un inventario de seguridad para reemplazar el sistema, reporta una reduccion en el costo total comparado con las politicas CPR1 y CPR2. Palabras clave: sistemas de produccion, proceso de deterioro, produccion, reemplazo, simulacion.

Independence of the hedging points in PHP control policy

For the control of single machine and multiple part-types manufacturing systems, the prioritized hedging point (PHP) policy is often used. In this paper, the probability distribution of the system states under this control is analysed. Unlike the work by Shu and Perkins (2001), where the maximum production rates for all part-types are identical, we deal with the situation that the maximum production rates for various part-types are different from each other. For this situation, we obtain the independence property of the PHP policy, that is, the marginal probability density function of the production surplus of a specific part-type only relies on the hedging point of itself, but does not depend on the hedging points of other part-types. On the basis of this property, the problem of optimizing the hedging points of the PHP policy can be solved by dividing the single machine and multiple part-types system into a series of equivalent single machine and single part-type systems, the closed form of whose optimal hedging point is known and can be applied directly to optimize the hedging points of the PHP policy.

Analysis of a Serial Production Line with Single Part-Type and Multiple Parallel-Machine Workstations

In this paper, we develop a method of analyzing a serial production line with single part-type and multiple parallel-machine workstations, which has not been paid much attention to in existing literature. At first, we analyze a short line with one parallel-machine workstation and two buffers by constructing its probability balance equation, and evaluating its performances such as throughput and work-in-process level. Then a decomposition-based algorithm is developed for the analysis of a long line with multiple parallel-machine workstations by using the result of short line analysis as building block. Our method is different from traditional decomposition-based method in that our decomposition is workstation-centered while the traditional one is buffer-centered. Numerical experiments shows that result of performance evaluation by using the proposed method is quite close to those obtained by simulation, and our method is much less time-consuming.

Joint assignment of buffer sizes and inspection points in unreliable transfer lines with scrapping of defective parts

An unreliable single part type transfer line with fixed inter machine buffer sizes is considered. In general, imperfect machines operating on imperfect raw material, or partially processed raw material, will result in the production of a mix of conforming and non conforming parts. The problem of optimal joint assignment of buffer sizes and inspection station positions is considered. The performance measure to be optimized is a combination of work in process storage, finished parts shortage, and parts inspection costs. A simplified quality aware machine Markovian model is proposed, and an approximate decomposition scheme for the analysis of the resulting transfer line model is developed, and then validated against detailed Monte Carlo simulations. The decomposition scheme lends to a dynamic programming based buffer size optimization scheme. The latter is implemented; joint buffer and inspections station positioning optimization results are reported.

Cycle time analysis in reentrant robotic cells with swap ability

In this paper, reentrant robotic cells composed of a robot with swap ability for a single part type is studied. In this regard, we restrict our attention to the two-machine reentrant cell scheduling problem. In the cell, a part visits the machines at least once. To minimise the cycle time, the sequence of robot moves must be optimised. Based on our previous study on the optimality of robotic cells, we restrict our investigation to only one-unit cycles. Therefore, all one-unit cycles are generated and their cycle time formulae are developed. Initially, we determine both essential and sufficient conditions for different cycles to be optimal and present the regions of optimality when each part reenters the first machine two times. We determine optimality conditions for different cycles when each part reenters both machines two times. Finally, sensitivity analysis is performed for both cases and the influence of the parameter values in the regions of optimality for each cycle is shown.

Throughput optimization in robotic cells with input and output machine buffers: A comparative study of two key models

We consider the problem of scheduling operations in a robotic cell processing a single part type. Each machine in the cell has a one-unit input buffer and a one-unit output buffer. The machines and buffers are served by one single gripper robot. The domain considered is free-pickup cells with additive inter-machine travel time. The processing constraints specify the cell to be a flow shop. The objective is to find a cyclic sequence of robot moves that minimizes the long-run average time to produce a part or, equivalently, maximizes throughput. Bufferless robotic cells have been studied extensively in the literature. However, the few studies of robotic cells with output buffers at each machine have shown that the throughput can be improved by such a configuration. We show that there is no throughput advantage in providing machine input buffers in addition to output buffers. The equivalence in throughput between the two models has significant practical implications, since the cost of providing additional buffers at each machine is substantial.

Feedback optimal control of dynamic stochastic two-machine flowshop with a finite buffer

Article history: Received 1 May 2010 Received in revised form 6 June 2010 Accepted 7 June 2010 Available online 11 June 2010 This paper examines the optimization of production involving a tandem two-machine system producing a single part type, with each machine being subject to random breakdowns and repairs. An analytical model is formulated with a view to solving an optimal stochastic production problem of the system with machines having up-downtime non-exponential distributions. The model developed is obtained by using a dynamic programming approach and a semi-Markov process. The control problem aims to find the production rates needed by the machines to meet the demand rate, through a minimization of the inventory/shortage cost. Using the Bellman principle, the optimality conditions obtained satisfy the Hamilton-JacobiBellman equation, which depends on time and system states, and ultimately, leads to a feedback control. Consequently, the new model enables us to improve the coefficient of variation (CVup/down) to be less than one while it is equal to one in Markov model. Heuristics methods are used to involve the problem because of the difficulty of the analytical model using several states, and to show what control law should be used in each system state (i.e., including Kanban, feedback and CONWIP control). Numerical methods are used to solve the optimality conditions and to show how a machine should produce. © 2010 Growing Science Ltd. All rights reserved.

Stochastic cycle time analysis in robotic cells

The purpose of this study is to analyse the cycle time in a single part type robotic cell. The robotic cell is made up of several machines and a single gripper robot that loads, unloads the machines and moves the part between machines. The cell can be classified into flow- and open-shops based on the part sequence and robot move. When number of machine is increased, the cycle time analysis in a robotic cell can lead to an NP-complete problem, which remains a challenge in existing literature. In addition, the problem complication rise by having stochastic processing time in the cell. In this study, we have developed a formula for decrease (increase) structure that part processing sequence is based on decrease (increase) order of manufacturing process time. This leads to a virtual robotic cell, which its machines are virtually arranged in order of processing time regardless of their physical location. In addition, using flow-graph concept, a model is developed to calculate the cycle time of a robotic cell where the part processing time element is stochastic. This model provides parametric results for expected value of and variance of the cycle time, which can be used for evaluating the productivity of the scenarios.

A comparative study of pull control mechanisms for unreliable homogenous transfer lines

The problem of tandem production lines composed of multiple unreliable workstations producing a single part type with holding (inventory and storage space) and shortage costs is considered. Given the numerous control mechanisms introduced in recent years, it is a difficult task to evaluate which mechanism is best suited for a specific application. Using simulation, design of experiments and response surface methodology, various homogenous lines controlled by Kanban, CONWIP and the hybrid Kanban/CONWIP control mechanisms are optimized and then compared. It is observed that the hybrid mechanism always outperforms CONWIP and Kanban when storage space and inventory costs are considered explicitly. However, hybrid is equivalent to CONWIP when storage space costs are not considered explicitly but rather aggregated with the inventory costs in the holding costs as usually found in the literature. Furthermore, with the increase of storage space cost and the number of workstations, Kanban outperforms CONWIP.

Productivity analysis in a robotic cell

In this paper, we study the productivity advantage of a variety of scenarios in a robotic cell by comparing their cycle times. The robotic cell is made up of several machines and a single gripper robot in the centre of the cell, which loads, unloads and moves the parts. Considering deterministic robot travelling, loading and unloading time elements and stochastic part process time element, this paper focuses on examining the scenarios composed of the single part type part sequencing methods and the robot moves in a cell. First, the decrease (increase) virtual robotic cell, in which its machines are virtually arranged in order of processing time regardless of their physical location, is introduced to calculate the cycle time. Second, a flow-graph based model is developed to analyse the cycle times for the scenarios when the part processing time element is stochastic. A robotic cell composed of three machines and a robot in the centre of the cell is used as a base example throughout the paper to illustrate the application of the models.

A WIP control policy for tandem lines

The control of manufacturing systems has many similarities with the management of inventories in warehouses. Based on the detailed analysis of these similarities, a new control policy is proposed in this paper. Simulation studies demonstrate that this new policy performs better than several established control policies by providing a higher service level with a lower work in process (WIP). This policy is in its infant stage of development and only single part type tandem lines (transfer lines) are studied in this paper. Studies of re-entrant production systems or multiple part type systems are the focus of future research.

Sequencing of Parts and Robot Moves in a Robotic Cell

In this paper, we deal with the problem of sequencing parts and robot moves in a robotic cell where the robot is used to feed machines in the cell. The robotic cell, which produces a set of parts of the same or different types, is a flow-line manufacturing system. Our objective is to maximize the long-run average throughput of the system subject to the constraint that the parts are to be produced in proportion of their demand. The cycle time formulas are developed and analyzed for this purpose for cells producing a single part type using two or three machines. A state space approach is used to address the problem. Both necessary and sufficient conditions are obtained for various cycles to be optimal. Finally, in the case of many part types, the problem of scheduling parts for a specific sequence of robot moves in a two machine cell is formulated as a solvable case of the traveling salesman problem.

Optimal cycle production of a manufacturing system subject to deterioration

A single part type, single machine, fluid model manufacturing system is considered. The machine is subject to a deterministic deterioration process, which depends on the operation rate. The objective is to minimize a long term average cost index which penalizes inventory surplus and backlog. The optimal policy determined presents some similarities with the policy conjectured optimal in the past for a similar Markovian formulation. The considered problem can be applied to several real contexts, and not just from the manufacturing domain, as briefly discussed in the paper.

Scheduling of coupled tasks and one-machine no-wait robotic cells

Coupled task scheduling problems have been known for more than 25 years. Several complexity results have been established in the meantime, but the status of the identical task case remains still unsettled. We describe a new class of equivalent one-machine no-wait robotic cell problems. It turns out that scheduling of identical coupled tasks corresponds to the production of a single part type in the robotic cell. We shall describe new algorithmic procedures to solve this robotic cell problem, allowing lower and upper bounds on the production time and discussing in particular cyclic production plans.

Optimality of a Two-Threshold Feedback Control for a Manufacturing System With a Production Dependent Failure Rate

We consider a Markovian, failure prone, single machine, single part-type, fluid flow, manufacturing system. The failure rate depends on the production rate through a non decreasing, piecewise constant function which may assume two values. The problem is to minimize a long term average expected cost which penalizes both the presence of waiting customers and the inventory surplus. We derive and prove the optimality of a policy which depends on two thresholds. The expression of these thresholds and of the optimal cost is also included in this note together with some numerical examples.

Optimal safety stocks and preventive maintenance periods in unreliable manufacturing systems

We consider a manufacturing system with preventive maintenance that produces a single part type. An inventory is maintained according to a machine-age-dependant hedging point policy. We conjecture that, for such a system, the failure frequencies can be reduced through preventive maintenance resulting in possible increase in system performance. Traditional preventive maintenance policies, such as age replacement, periodic replacement, are usually studied without finished goods inventories. In the cases where the finished goods inventories are considered, restrictive assumptions are used, such as not allowing breakdown during the stock build up period and during backlog situations due to the complexity of the mathematical model. In order to solve this problem, we develop a more realistic mathematical model of the system, and derive expressions of the overall incurred cost used as the basis for optimal determination of the jointly production and preventive maintenance policies (i.e. production rates and preventive maintenance frequency, depending on inventory levels of the produced parts). Such a cost consists of inventory, backlog, corrective and preventive maintenance costs. The work reported here has a significant practical application (no restriction on failures occurrence and backlog situations) in the context of production planning of manufacturing systems. Numerical examples are included to illustrate the importance and the effectiveness of the proposed methodology.

SCHEDULING OF COUPLED TASKS AND ONE-MACHINE NO-WAIT ROBOTIC CELLS

Coupled task scheduling problems are known since more than 25 years. Several complexity results have been established in the meantime, but the status of the identical task case remains still unsettled. We describe a new class of equivalent 1-machine no-wait robotic cell problems. It turns out that scheduling of identical coupled tasks corresponds to the production of a single part type in the robotic cell. We shall describe new algorithmic procedures to solve this robotic cell problem, allowing lower and upper bounds on the production time and discussing in particular cyclic production plans.

Optimal control for a class of manufacturing systems with production rate dependent failure rates

In this paper we consider a failure prone, single part type, single machine manufacturing system. The failure repair process of the machine is characterized by a non-homogeneous Markov chain, with a constant repair rate and a failure rate which is a non decreasing function qd(u) of the production rate. The stability issue is discussed with respect to the failure rate function considered. For a piecewise constant, two value function qd(u), the optimal policy is characterized and it is completely derived for a set of examples. This optimal policy is not a hedging point policy, which is known to be optimal only for particular failure rate functions qd(u).