Joint optimal lot sizing and production control policy in an unreliable and imperfect manufacturing system (original) (raw)
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In this report we consider a single part-type, single unreliable machine production system with the backlog and the inventory bounded. The part flow into the system is described through a fluid model. The problem is to determine a production control which minimizes an infinite horizon average de- mand loss/backlog/surplus cost. It is well known that, in many interesting cases, if there are no bounds on the inventory and on the backlog of the system, the problem is solved by a hedging point policy, and the hedging point can be analytically computed. In this report we prove that for a bounded inventory/backlog system, the hedging point policy is still optimal and provide an implicit equation to compute the optimal safety stock. The structure of this equation easily allows to determine the optimal safety stock through any numerical method. Using this equation, we analyze the effect of some system parameters (in particular the demand loss cost parameter and the backlog limit) on the com...
International Journal for Numerical Methods in Biomedical Engineering, 2010
This paper employs numerical method for determination of the optimal lot size for a manufacturing system with discontinuous inventory issuing policy and imperfect rework of random defective items. The classic economic manufacturing quantity (EMQ) model assumes a continuous issuing policy for satisfying customer's demands, and perfect quality production for all items produced during a production run. However, in a real-life vendor-buyer integrated system, the discontinuous issuing policy such as multi-shipment policy is practically used in lieu of continuous issuing policy, and it is inevitable to generate defective items during a production run. Imperfect quality items fall into two groups: the scrap and the reworkable. During the rework process, failure in repair exists; a portion of reworked items fails and becomes scrap. The finished items can only be delivered to customers if the whole lot is quality assured at the end of the rework. Mathematical modeling and analysis are used to deal with the proposed model, and the long-run average cost function is derived. Convexity of this cost function is proved and a closed-form optimal batch size solution to the problem is obtained. Two special cases are examined and a numerical example demonstrates its practical usage.
International Journal of Production Research, 2013
Production control policy and economic sampling plan design problems have been studied separately in previous research. This paper considers a joint production control policy and economic single sampling plan design for an unreliable batch manufacturing system. The production is controlled by a modified hedging point policy which consists in building and maintaining a safety stock of finished product to avoid shortages during corrective maintenance. The main objective of this paper is to determine simultaneously the economic production quantity, the optimal safety stock level and the economic sampling plan design which minimize the expected overall cost. A stochastic mathematical model is developed and solved using a simulation optimization approach based on the response surface methodology. Simulation is used to imitate the complex dynamic and stochastic behaviour of processes as in the real-life industrial systems. The obtained results show clearly strong interactions between production quantity, inventory state and sampling plan design which confirm the necessity of jointly considering production and quality control parameters in an integrated model. Moreover, it is shown a significant impact of production system reliability on the economic sampling plan design and therefore on the quality of finished product delivered to consumers. Numerical example and sensitivity analyses are presented for illustrative purposes.
Optimal lot sizing in an unreliable two-stage serial production-inventory system
International Transactions in Operational Research, 2005
This paper deals with a two-stage lot sizing problem in an unreliable production environment in which the machine at the first stage (stage 1) is failure-prone while the machine at the final stage (stage 2) is failurefree. The process goods are obtained in batches by manufacturing and are transferred continuously from stage 1 to stage 2 where the finished goods are produced and then shipped out to customers. If the machine at stage 1 breaks down then the production of the interrupted lot is not resumed. Instead, a new production cycle is initiated after machine repair. The model is formulated assuming that the production rate of the machine at stage 1 is greater than that at stage 2 and the time to machine failure and repair time are arbitrarily distributed. Specific formulation of the model under exponential failure and exponential repair time distributions is derived and a procedure for finding the optimal production policy is presented. The dependence of the optimal production policy on the model parameters is also examined with numerical examples.
This paper considers the problem of production planning of unreliable batch processing manufacturing systems. The finished goods are produced in lots, and are then transported to a storage area in order to continuously meet a constant demand rate. The main objective of this work is to jointly determine the optimal lot sizing and optimal production control policy that minimize the total expected cost of inventory/backlog and transportation, over an infinite time horizon. The decision variables are the lot sizing and the production rate. The problem is formulated with a stochastic dynamic programming model and the impulse control theory is applied to establish the Hamilton-Jacobi-Bellman (HJB) equations. Based on a numerical resolution of the HJB equations, it is shown that the optimal control policy is governed by a base stock policy for production rate control and economic lot size for batch processing. A thorough analysis and practical issues are addressed with a simulation based approach. Thus, a combined discrete-continuous simulation model is developed to determine the optimal parameters of the proposed policy when the failure and repair times follow general distributions. The results are illustrated with numerical examples and confirmed through sensitivity analysis.
We investigate the simultaneous production planning and quality control problem for an unreliable single machine manufacturing system responding to a single product type demand. The machine is subject to deteriorations, and their effect is observed mainly on the rate of defectives, which increases continuously over time. Due to the uncertainty caused by failures, the machine may not meet long-term demand, and an overhaul can be conducted in order to counter the effect of the deterioration. The main objective of this study is to simultaneously determine the optimal production plan and overhaul schedule for the analyzed manufacturing system, in order to minimize the total cost, comprising the inventory, backlog, repair and overhaul cost, over an infinite planning horizon. A stochastic dynamic programming model is proposed, in which a numerical scheme is adopted to solve the optimality condition equations. It is observed that the optimal control policy is described by a machine deterioration-dependent hedging point policy (MDDHPP). To accurately approximate the related control parameters, a simulation optimization approach based on design of experiments, simulation modeling and response surface methodology is applied. The results obtained provide a better understanding about the influence of the deterioration of quality in the production and overhaul policies. A numerical example and an extensive sensitivity analysis are conducted, and show the robust behavior and usefulness of the policy obtained.
Applied Mathematics, 2014
This paper deals with the production-dependent failure rates for a hybrid manufacturing/remanufacturing system subject to random failures and repairs. The failure rate of the manufacturing machine depends on its production rate, while the failure rate of the remanufacturing machine is constant. In the proposed model, the manufacturing machine is characterized by a higher production rate. The machines produce one type of final product and unmet demand is backlogged. At the expected end of their usage, products are collected from the market and kept in recoverable inventory for future remanufacturing, or disposed of. The objective of the system is to find the production rates of the manufacturing and the remanufacturing machines that would minimize a discounted overall cost consisting of serviceable inventory cost, backlog cost and holding cost for returns. A computational algorithm, based on numerical methods, is used for solving the optimality conditions obtained from the application of the stochastic dynamic pro-gramming approach. Finally, a numerical example and sensitivity analyses are presented to illustrate the usefulness of the proposed approach. Our results clearly show that the optimal control policy of the system is obtained when the failure rates of the machine depend on its production rate.
This paper presents the optimal flow control for a one-machine, two-product manufacturing system subject to random failures and repairs. The machine capacity process is assumed to be a finite state Markov chain. The problem is to choose the production rates so as to minimize the expected discounted cost of inventory/backlog over an infinite horizon. We first show that for constant demand rates and exponential failure and repair time distributions of the machine, the hedging point policy is optimal. Next, the hedging point policy is extended to nonexponential failure and repair time distributions models. The structure of the hedging point policy is parameterized by two factors representing the thresholds of involved products. With such a policy, simulation experiments are coupled with experimental design and response surface methodology to estimate the optimal control policy. Our results reveal that the hedging point policy is also applicable to a wide variety of complex problems (i.e. nonexponential failure and repair time distributions) where analytical solutions may not be easily obtained. q
ECONOMIC LOT SIZING FOR UNRELIABLE PRODUCTION SYSTEM WITH SHORTAGES
Interscience Publisher
The purpose of present study is to analyze the optimal lot size in an unreliable single-machine production system with shortages. The production system is subject to failure due to machine breakdown. Breakdown times are considered to be according to Weibull distribution. It is assumed that the shortages are allowed and backlogged. During each production, the set-up preventive (regular) maintenance is performed. The corrective (i.e. emergency) maintenance is carried out immediately after breakdown. For the illustration purpose, numerical results are provided for the special cases. To obtain the optimal cost per unit time, we also employ the artificial neuro-fuzzy inference system (ANFIS) approach which has the learning capability of neural network as well as advantages of rule-base fuzzy system. It is noted that the results obtained by neuro-fuzzy technique are at par with the results computed by the analytical techniques.
Lot sizing in case of defective items with investments to increase the speed of quality control
2014
In many cases the quality of each item in a lot is checked. Speeding up the quality checking process increases the responsiveness of the system and saves cost. The percentage of defective items is a random variable and two models are proposed. In one of the models the system remains always at the same state, while in the other one after each order cycle, the state of the system may change, thus the percentage of defective items may be different in consecutive periods. In both cases the speed of the quality checking is a variable, and procedures are provided to find the optimal lot sizes and screening speed for general and specific investment cost functions. The characteristics of the two model settings will largely be different when the percentage of defective items is high. Among the important managerial insights gained is that a high unit backlogging cost, especially spurs the system to invest more intensively into improving the quality checking process.