Solving finite production rate model with scrap and multiple shipments using algebraic approach

This paper solves a finite production rate (FPR) model with scrap and multiple shipments using an algebraic method. Classic FPR model assumes a continuous inventory issuing policy to satisfy demand and perfect quality production for all items produced. However, in real life vendor-buyer integrated production-inventory system, multiple shipment policy is practically used in lieu of a continuous issuing policy and generation of defective items during production run is inevitable. In this study, it is assumed that all defective items are scrap and the perfect quality items can only be delivered to customers if the whole lot is quality assured at the end of the production run. A conventional approach for solving the FPR model is the use of differential calculus on the long-run average cost function with the need to prove optimality first. This paper demonstrates that optimal lot size and its overall costs for the aforementioned FPR model can be derived without derivatives. As a result, it enables students or practitioners who have little knowledge of calculus to understand and to handle with ease the real-life FPR model

Effect of variable shipping frequency on production-distribution policy in a vendor-buyer integrated system

This paper investigates the effect of variable shipping frequency on production-distribution policy in a vendor-buyer integrated system. In a recent article Chiu et al. [1] derived the optimal replenishment lot size for an economic production quantity problem with multi-delivery and quality assurance, based on an assumption that the number of shipment is a given constant. However, in a vendor-buyer integrated system in supply chain environment, joint determination of replenishment lot size and number of shipments may help such a system to gain significant competitive advantage in terms of becoming a low-cost producer as well as having tight linkage to customer. For this reason, the present study extends the work of Chiu et al. [1] by considering shipping frequency as one of the decision variables and incorporating customer’s stock holding cost into system cost analysis. Hessian matrix equations are employed to certify the convexity of cost function that contains two decision variables, and the effect of variable shipping frequency on production-distribution policy is investigated. A numerical example is provided to demonstrate practical usage of the research result

Analysis and Comparison of Fixed-Size Lot and Fixed-Time Lot Batch Production Systems

In high volume automated discrete item batch production systems, the batches or lots are typically fixed quantity (i.e., size), with setups incurred between the different production lots. Processing times for the fixed-size lots are relatively constant when the workstation is operating however, random workstation disruptions cause variability in the lot completion time making the operations of interrelated activities such as material handling and setup crews less efficient. In this dissertation, the long-run average cost performance of fixed-size lot batch production systems is compared to batch production systems where the lot size is defined as a fixed time. In the “fixed-time” lot batch production system, there is ideally no variability in the time length to produce a lot, but the production output in this fixed time length may vary. In this comparison, the batch production systems considered are workstations operating under a continuous review (Q, r) inventory system. The comparison was conducted assuming unmet demands are lost (lost-sales policy), and also when unmet demand can be backordered (backordering policy). One objective of this research was to identify the factors having the largest effect on the long-run average cost differences between fixed-size lot and fixed-time lot systems. Because of the system complexity due to the inclusion of multiple real-world factors, a designed experiment is employed to compare the fixed-sized and fixed-time lot systems using discrete event simulation. For every treatment combination tested the batch sizes and reorder point levels (quantities or time) were optimized, so that differences between systems cannot be attributed to poor batch size and re-order point selection. The experimental results show that for the lost sales policy the factors: interarrival time between demands, and the coefficient of variation of the demand probability distribution have the largest impact on the long-run average cost difference between a fixed-size lot and fixed-time lot batch production systems. For the backordering policy the factors: workstation stand-alone availability, failure and repair frequency, and capacity utilization have the largest impacts Another research objective was to identify functional relationships between the input factors and the output. A feedforward backpropagation neural network with the connection weight approach was applied to the experimental results database to search for relationships between various input factors and the categorical outcomes 1) a fixed-size lot production system has significantly lower cost performance than a fixed-time lot system, 2) a fixed-time lot production system has significantly lower cost performance than a fixed-size lot system, and 3) the cost performance of two systems is not significantly different. The results show that for the lost sales policy the factors: demand coefficient of variation, and stand-alone availability, have the largest relative importance in predicting the outcomes. For the backordering policy the factors: demand coefficient of variation, stand-alone availability, and inventory holding cost have the largest relative importance in predicting the outcomes. In general, at higher stand-alone availability levels and lower demand coefficient of variation the production time to produce a fixed-size lot is low enough that the system can operate in a “just-in-time” manner and a fixed-size lot production system will result in lower costs than a fixed-time lot system. However, as the stand-alone availability reduces and demand coefficient of variation increases, the fixed-time lot system results in significantly lower costs than the fixed-size lot system. The insights developed from this research can be utilized by the decision makers to select which batch production system should be utilized such that the long-run average cost can be minimized

A note on "Determining the optimal run time for EPQ model with scrap, rework, and stochastic breakdowns"

In a recently published paper by Chiu et al. [Chiu, S.W., Wang, S.-L., Chiu, Y.-S.P., 2007. Determining the optimal run time for EPQ model with scrap, rework and stochastic breakdowns. European Journal of Operational Research 180, 664-676], a theorem on conditional convexity of the integrated total cost function was employed in their solution procedure. We reexamine this theorem and present a direct proof to the convexity of the total cost function. This proof can be used in place of Theorem 1 of Chiu et al.'s paper to enhance quality of their optimization process.Manufacturing Machine breakdown Defective item Rework Production

Contrôle de la production et de la qualité des systèmes manufacturiers non-fiables

RÉSUMÉ Dans les trois dernières décennies, plusieurs politiques de commande optimale stochastique ont été développées pour contrôler les systèmes de production à flux continu sujets aux phénomènes aléatoires. Les opérations après production tel que le transport et l’inspection de la qualité ont toutefois été peu considérées dans ces politiques. Ce mémoire de maîtrise s’intéresse plus particulièrement au problème de commande optimale stochastique des systèmes de production par lots dans un contexte de transport et de contrôle de la qualité par échantillonnage. Ces systèmes sont caractérisés par une dynamique complexe vu les multiples décisions de production et de qualité considérées et par un niveau stochastique élevé où les pannes, les réparations et la qualité effective du processus sont aléatoires. Les systèmes de production par lot dans tels contextes ne peuvent pas être représentés par les modèles de flux continu classiques. Dans la première phase de ce mémoire, nous avons étudié le cas des systèmes de production par lots, non-fiables et parfaits, avec un délai de transport. Le problème est formulé sous forme d’un modèle de programmation dynamique stochastique. Les conditions optimales décrites par les équations Hamilton-Jacobi-Bellman sont résolus numériquement. Ensuite, une loi de commande stochastique sous-optimale basée sur une combinaison de la politique de contrôle à seuil critique modifiée et une politique du lot économique de production est ainsi obtenue. Une approche expérimentale basée sur la simulation est appliquée pour déterminer les valeurs optimales des paramètres de la loi de commande quelque soit la distribution des temps de pannes et de réparation. Dans la deuxième phase de travail, nous avons intégré le contrôle de la qualité en supposant que le système produit un pourcentage aléatoire d’items défectueux. Le problème est décrit par un modèle de programmation dynamique stochastique. Une heuristique de commande est proposée par extension de la politique de commande obtenue dans la première phase en prenant en compte les effets de l’imperfection de la production sur l’inventaire et sur la satisfaction de la demande. Des analyses de sensibilité approfondies permettent d’observer les impacts des différents paramètres de coût et de qualité sur les paramètres optimaux de la politique de commande de la production.----------ABSTRACT In the past three decades, many stochastic optimal control policies have been developed to control the continuous-flow production systems to meet stochastic phenomena. However, operations such as transportation and quality inspection had been little studied in these policies. This master's thesis focuses on the stochastic optimal control problem of batch production systems in the context of transportation and quality control by sampling. These systems are characterized by a complex dynamic due to the many considered decisions of production and quality and by a high stochastic level where all breakdowns, repairs and process imperfection are random. The batch production systems in such contexts cannot be represented by the classical continuous-flow models. In the first part of the master's project, we studied the case of unreliable and perfect batch production systems with a transportation delay. The problem is formulated as a stochastic dynamic programming model. The optimality conditions described by Hamilton-Jacobi-Bellman equations are solved numerically. Then, a suboptimal stochastic control policy based on a combination of a modified hedging point policy and a state dependent economic manufacturing quantity policy is obtained. A simulation-based experimental approach is used to determine the optimal values of the control policy parameters when the failure and repair times follow general distributions. In the second part of the project, we integrated the quality control issue assuming that the system generates a random proportion of defective items. The problem is described by a stochastic dynamic programming model. A heuristic control policy is proposed by extending the control policy obtained in the first part, taking into account the effects of imperfect quality items on the inventory and demand satisfaction. A thorough sensitivity analysis shows interesting behaviours about the impact of various cost and quality parameters on the optimal parameters of the production control policy. Finally, some extensions of the two obtained control policies are proposed by integrating the concept of dynamic lot sizing and a control policy for inspection personnel management. The experiments have shown that these both extensions lead always to economic gains. Other extensions and further research are also discussed