Transient Analysis of Serial Production Lines With Perishable Products: Bernoulli Reliability Model (original) (raw)
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Production control of unreliable manufacturing systems with perishable inventory
The International Journal of Advanced Manufacturing Technology, 2021
Manufacturing systems with perishable products appears in several industrial branches such as food production, chemical and radioactive material manufacturing, and pharmaceutical industry. Product perishability often results in the disposal of the fraction of products that do not meet the final specifications, after being kept too long within serviceable inventory. The disposal of perishables raises several environmental issues and its minimization together with reduction of other costs related to perishable inventories are most often studied within inventory management framework. The production control problem for the systems with perishable products, especially in case of failure-prone manufacturing facilities, is an important and challenging topic that was only sparsely addressed in the scientific literature. The main difficulty consists in resolving the trade-off between having an inventory level sufficient to fill the demand in case of machine failure, and potential deterioration of products kept too long within inventory. The paper proposes an approach to resolve this trade-off. First, a mathematical model describing the stochastic behavior of such systems is developed. Next, an analytical study of the system is performed, and finally, an optimal production policy that takes the product perishability into account is determined. This policy is shown to be a hedging point-type policy; thus the well-known result about the optimality of hedging point policy (in nonperishable case) is generalized to the class of perishable products with fixed shelf-life. It is shown that under conventional conditions (limited production capacity, Markovian failure/repair processes, constant demand rate), the optimal hedging level does not exceed the cumulative demand along the product shelf-life, and that leads to no disposal of products, known as a zero-waste policy. Numerical simulations allowed to perform the sensitivity analysis and a comparative study of the costs incurred in the systems with and without perishability.
Analytical Solution of Steady-State Behavior of Bernoulli Production Line with Two Finite Buffers
Brodogradnja
Production system engineering is strongly relied on mathematical models of systems under consideration and analytical solution of the problem has an important role in development and validation of more complex numerical tools. Analytical solution of steadystate behavior of serial Bernoulli production line with three machines and two buffers is considered in this paper based on Markov chain approach. Transition matrices in general case, including three machines with different probabilities of failure and arbitrary occupancy of two buffers, are formulated along with equations for performance measures. The developed theory is illustrated using four different serial Bernoulli lines and the obtained results are compared to those determined using semi-analytical approach via aggregation procedure. Finally, the existing discrepancies are analyzed and pointed out for five different levels of buffers occupancy. From general perspective, good agreement has been found for most of the results within the examined space of system states.
Transient analysis of manufacturing systems performance
IEEE Transactions on Robotics and Automation, 1994
Studies in performance evaluation of automated manufacturing systems, us. ing simulation or analytical models, have always emphasized steady-state or equilibrium performance in preference to transient performance. In this study, we present several situations in manufacturing systems where transient analysis is very important. Manufacturing systems and models in which such situations arise include: systems with failure states and deadlocks, unstable queueing systems, and systems with fluctuating or nonstationary workloads. Even in systems where equilibrium exists, transient analysis is important in studying issues such as accumulated performance rewards over finite intervals, first passage times, sensitivity analysis, settling time computation, and deriving the behavior of queueing models as they approach equilibrium. In certain systems, convergence to steady-state is so slow that only transient analysis can throw light on the system performance. After presenting several illustrative manufacturing situations where transient analysis has significance, we discuss two applications: (1) computation of distribution of time to absorption in Markov models of manufacturing systems with deadlocks or failures, and (2) computation of distribution of manufacturing cycle time in a failure-prone manufacturing system operated over a finite shift period. We also briefly discuss computational aspects of transient analysis.
Capacity improvement of an unreliable production line—an analytical approach
Computers & Operations Research, 2006
This paper addresses the problem of capacity estimation and improvement of a multi-stage, multi-product production line where workstations are subject to random failure and repair. The production line can process a variety of products in a batch production environment. Products are processed according to a predefined sequence. A linear programming model is used and modified by taking into account the random behaviour of unreliable stations. Station's downtime is modelled as a fictive product added to the production sequence at appropriate positions. A general procedure for the insertion of fictive products is presented. The procedure considers the states up and down that a station may experience while processing the product mix. It consists of two main steps. Firstly, enumerate the station's states and insert fictive products where appropriate. Secondly, find the best buffer size that minimizes the cycle time. The proposed approach considers more parameters than the Markovian models and the approximation methods where multi-product production lines longer than 2-station 1-buffer can be studied. Numerical examples are presented to show all the steps involved to compute the expected cycle time. Buffer contribution to minimize the cycle time of the production line is also addressed. Simulation is used to validate the results obtained.
Modeling and exact analysis of a production line with unreliable batch machines and finite buffers
2005
This paper considers a production line with two unreliable batch machines and a finite buffer. Batch machines process a set of parts simultaneously; the maximum number in the set is the size of the machine. The purpose of this paper is twofold: (i) to present a model of this system and its exact analysis; (ii) to present new qualitative insights and interpretations of system behavior. We demonstrate new generalized conservation of flow and flow rate-idle time relationships. We also present various performance measures of interest such as production rate, machine efficiencies, probabilities of blocking and starvation, and expected in-process inventory. We demonstrate an equivalence property and describe deadlock behavior. The effect of the sizes of machines on the performance measures is examined, new phenomena and insights are established, and possible interpretations are presented. *
Simulation modelling and analysis of a production line
International Journal of Simulation and Process Modelling, 2017
Production lines modelling has many problems that are difficult to be solved using analytical solutions, due to uncertainty and/or variability in variables and parameters. This paper is targeting unreliable production lines with finite buffers for the objective of evaluating and analysing the current situation and identifying bottlenecks. We use discrete event simulation to model a real production line based on one-year historical data about the breakdowns of all the production line's machinery. This data is used to find appropriate probability distributions to represent each machinery downtime and uptime. The simulation model is built using AnyLogic software to abstract the actual production line, and the model is validated using the actual data and information about the production line. Improvement scenarios are proposed to resolve the observed bottlenecks, and therefore give managerial insights to increase the throughput according to the increasing demand. Finally, production plans are set for different demands along the year.
Research Article, 2019
This paper analyzes a single product stochastic inventory model with two different production rates where demand follows Poisson distribution and product has a finite lifetime which is level dependent. It is assumed that the system is reached on a predetermined level, the system is converted to ON mode from OFF mode with a significant switching time with an exponential parameter. During switching time no demand will be served, the demand during switching time is lost forever. Here backlogs are allowed and during backlogs, the Production rate is higher than that of normal production time. We assume that the product will decay for the time under consideration. Some system characteristics are displayed with time variation.
Simulation Modeling of Automatic Production Lines with Intermediate Buffers
International Journal of Scientific and Engineering Research
A production line is an important class of manufacturing system when large quantities of identical or similar products are to be produced. The performance of a production line is highly influenced by machine failures. When a machine fails, it is then be unavailable during a certain amount of time required to repair it. Analysis of production lines divides into three types: analytical, approximation and simulation models. The analytical and approximation models have assumptions which make these models unrealistic such as reliable workstations, certain processing distribution, the first workstation cannot be starved and the last workstation cannot be blocked. The main problems in production lines treatment are the calculation of throughput and average levels of buffers because of the great size of state space. An analytical model is reviewed to clarify the limitations to use such treatment in real production lines. Simulation modeling of production lines is considered very important f...
2005
This paper considers a production line with two unreliable batch machines and a finite buffer. Batch machines process a set of parts simultaneously; the maximum number in the set is the size of the machine. The purpose of this paper is twofold: (i) to present a model of this system and its exact analysis; (ii) to present new qualitative insights and interpretations of system behavior. We demonstrate new generalized conservation of flow and flow rate-idle time relationships. We also present various performance measures of interest such as production rate, machine efficiencies, probabilities of blocking and starvation, and expected in-process inventory. We demonstrate an equivalence property and describe deadlock behavior. The effect of the sizes of machines on the performance measures is examined, new phenomena and insights are established, and possible interpretations are presented. *
Simulation of The Production Line Repair Time Via Dynamic Systems
The major aims of this study are to analyze and study the optimal repair time of the production line of a manufacturing company. The relationship between timing failure, downtime, repair time, machine performance, sales and profit status of a dynamic system is also analyzed. It utilizes simulations (“Vensim Software”) and dynamic systems in a vegetable oil manufacturing firm in Iran. At first, the cause and effect diagrams of the model are shown via “Delphi techniques”, and then the statistical distribution of different factors affecting various parts of the model is determined by the “Arena Software”. Consequently the effect of different parts of the model on other parts is analyzed via the dynamic system. Then, by obtaining financial data relating to a digital generator, the cost- benefit of the model is determined from profit status views. The results of this study exhibit that the designated simulation model is potent and was able to indentify 5 factors influencing the repair time. The power disconnection (C.V=1.48), is indeed the most negative factor affecting the system. In addition, the profitability of the model can be enhanced 8.66% by investing in a digital generator.