Optimal Production Cycle Time Research Articles

An Internet-of-Things-Based Dynamic Scheduling Optimization Method for Unreliable Flexible Manufacturing Systems under Complex Operational Conditions

The dynamic scheduling problem (DSP) in unreliable flexible manufacturing systems (UFMSs) with concurrency, conflicts, resource sharing, and sequential operations is a complex optimization problem that requires the use of efficient solution methodologies. The effectiveness of scheduling UFMSs relies on the quality of equipment maintenance. Currently, UFMSs with consistently large queues of parts awaiting service employ a repair-after-failure approach as a standard maintenance procedure. This method may require unexpected resources, incur costs, consume time, and potentially disrupt the operations of other UFMSs, either partially or fully. This study suggests using a predictive maintenance (PdM) strategy that utilizes the Internet of Things (IoT) to predict and avoid early mechanical equipment failures before they happen in UFMSs, thereby reducing unplanned downtime and enhancing reliability. Therefore, the objective of this paper is to construct timed Petri net (TPN) models using the IoT for the PdM configuration of mechanical equipment in the dynamic scheduling problem of UFMSs. This necessitates that users represent the specific problem using TPNs. The process of PN modeling requires the utilization of domain knowledge pertaining to the target problems as well as to machine information. However, it is important to note that the modeling rules for PNs are straightforward and limited in number. Consequently, the TPN model is applied to generate and formulate mixed-integer linear programming (MILP) instances accurately. This is done to identify the optimal production cycle time, which may be implemented in real-life scenarios. Several UFMS instances are used to demonstrate the applications and effectiveness of the proposed method. The computational results demonstrate that the proposed method shows superior solution quality, effectively solves instances for a total of 10 parts and 6 machines, and achieves a solution in a reasonable CPU time.

OPTIMAL PRICING AND PRODUCTION LOT SIZE FOR TWO RATES OF PRODUCTION WITH PRICE-SENSITIVE DEMAND, PRICE BREAK-EVEN POINT, AND PROFIT MAXIMISATION IN HIGHER ORDER EQUATION

In the present study, optimal pricing and optimal lot size production policy models with price-sensitive demand of deteriorating products are considered, taking into account two distinct production rates. It is possible to begin production at one rate and then switch to a different rate after a period of time. Such a scenario is appealing, in that a big initial stock of produced goods can be avoided by starting production at a modest pace, thus reducing the initial investment and the holding cost. Further, the fifth-order equation is obtained when the equation for optimal pricing is derived. Maximising the profit is calculated based on a fifth-order equation. Both optimal pricing and production lot size are decision variables, and optimal cycle time is also one of the decision variables for determining price break-even points. As far as information is concerned, no researcher has examined optimal pricing and production lot size policies in two-rates-of-production models for their study.The objective of the present study is to examine the optimal production, optimal pricing, and optimal cycle time to reduce the total cost and to maximise the total profit. Both price break-even point and profit maximisation are considered. An appropriate mathematical model is developed. An illustrative example is provided and numerically validated using a sensitivity analysis. Microsoft Visual Basic 6.0 was used to code the model’s outcome validation.

Determination of epoxy resin usability for mass production of reinforced laminated veneer lumber

This study is part of a comprehensive study on the industrial production of reinforced laminated wood composites. The main aim of the study is to determine the production parameters of reinforced laminated wood composite board under an optimal production cycle time under temperature and pressure, using epoxy resin cured at room temperature for 24 h. For this purpose, 1.2 mm thick Samsun Poplar (Populus Deltoides I-77/51) veneer layers, three different pressing cycle times (15, 20, and 25 min), three different temperatures (100°C, 120°C, and 140°C), and three different amounts of adhesive (100, 150, and 200 g/m²) were used also 200 g/m² density twill woven glass–carbon fiber fabric was used as the reinforcement layer. In order to determine the production quality of reinforced laminated wood composite boards, the adhesion strength between the reinforcement layer and the wood veneer layer was determined according to TS EN 3969 314-1. Considering the adhesion strengths in terms of production parameters, the best results were observed at 100°C press temperature, 20 min press cycle time, 200 g/m² adhesive amount, and the use of glass fiber woven fabrics for reinforcement. Under these conditions, the best adhesion strength was found to be 4.17 N/mm². When the samples were examined, it was seen that almost all of the failures occurred as a result of the fracture in the wood layer. This indicates that sufficient adhesion can be achieved between the reinforcement layer and the wood layer.

A Fuzzy Production Inventory Model for Deteriorating Items with Shortages

In this paper we have developed a supply chain production inventory model for deteriorating items with shortage under Fuzzy environment. The formulae for the optimal average system cost, stock level, backlog level and production cycle time are derived when the deterioration rate is very small. In reality it is seen that we cannot define all parameters precisely due to imprecision or uncertainty in the environment. So, we have defined the inventory parameter deterioration rate as triangular fuzzy numbers. The signed distance method and graded mean integration method have been used for defuzzification. Numerical examples are taken to illustrate the procedure of finding the optimal total inventory cost, stock level and backlog level. Sensitivity analysis is carried out to demonstrate the effects of changing parameter values on the optimal solution of the system.

Pengembangan Model Economic Production Quantity Mengakomodasi Continue dan Discrete Demand serta Kebijakan Rework Secara Simultan

Inventory of finished goods needs to be planned and controlled regularly. Fulfilling customer demand whenever and wherever is the main purpose of the supply. This issue is related to production activities. Many companies use the Economic Production Quantity (EPQ) Model in determining the size of their lot productions. This model is able to show how to minimize total production costs by reducing inventory costs. Customer behavior at PT XYZ makes product delivery divided into 2 types. The first type, finished goods is sent continuously in small amounts called continue demand. The second type, products is sent between certain time intervals in large quantities called discrete demand. Basic EPQ Model’s parameters do not accommodate a system like this. In addition, PT XYZ requires rework for products that do not pass the quality test. Therefore, this research was developed to formulate EPQ model that can accommodate two types of demand, continue and discrete, as well as the existence of rework policy. This study tries to provide another approach in solving the derivation problem using the "Arithmetic-Geometric Mean" method. The results of this study will display a mathematical formulation to find the optimal production cycle time for PT XYZ. Numerical examples are discussed to show practical models.

Investment for process quality improvement and setup cost reduction in an imperfect production process with warranty policy and shortages

Cost reduction for setup and improvement of processes quality are the main target of this research along with free minimal repair warranty for an imperfect production System. This paper deals with the effect of setup cost reduction and process quality improvement on the optimal production cycle time for an imperfect production process with free product minimal repair warranty. Here the production system is subject to a random breakdown from ancontrolledsystem to anout-of-controlstate. Shortages are fully backlogged. The main target to minimize the total cost by simultaneously optimizing the production run time, setup cost, and process quality. A solution algorithm with some numerical experiments are provided such as the proposed model can illustrate briefly. Sensitivity analysis section is decorated for the optimal solution of the model with respect to major cost parameters of the system are carried out, and the implications of the analysis are discussed.

Optimal production cycle time for inventory model with linear time dependent exponential distributed deterioration

We study an inventory system with linear time varying exponential distributed deterioration in which production and demand rates are constant.The mathematical model is developed to obtain the total cost per unit time of an inventory system.The inventory controlling systems in terms of first order differential equations are solved numerically.The optimal cycle time is derived and the results are applied to numerical problems.The effect of changes in the model parameters on decision variables and the average total cost of an inventory system are studied through numerical examples.

Mathematical modeling of a multi-product EMQ model with an enhanced end items issuing policy and failures in rework.

This study uses mathematical modeling to examine a multi-product economic manufacturing quantity (EMQ) model with an enhanced end items issuing policy and rework failures. We assume that a multi-product EMQ model randomly generates nonconforming items. All of the defective are reworked, but a certain portion fails and becomes scraps. When rework process ends and the entire lot of each product is quality assured, a cost reduction n + 1 end items issuing policy is used to transport finished items of each product. As a result, a closed-form optimal production cycle time is obtained. A numerical example demonstrates the practical usage of our result and confirms a significant savings in stock holding and overall production costs as compared to that of a prior work (Chiu et al. in J Sci Ind Res India, 72:435–440 2013) in the literature.

Optimization of a multi-product EPQ model with scrap and an improved multi-delivery policy

This paper considers optimization of a multi-product economic production quantity(EPQ) model with scrap items and an improved multi-delivery policy. We extend thework of Chiu et al. (2013a) by incorporating an improved n + 1 multi-delivery planinto their model with an aim at reducing vendor’s inventory holding cost. Under such aspecific shipment policy, for each product an extra delivery of finished goods is madeduring production uptime to satisfy the product demand for the period of vendor’suptime. Then, when rework process comes to an end (i.e., the rest of the productionlot is quality assured) n fixed quantity installments of finished goods are delivered tobuyers at a fixed time interval. The objectives of this study are to determine the optimalrotation production cycle time that minimizes the long-run average system cost perunit time and reveals the effects of random scrap rate and the improved delivery policyon the optimal production cycle time. With the help of a mathematical model a closedformoptimal common cycle time is derived. Through a numerical example, practicalusages of obtained results and significant savings in vendor’s stock holding cost aredemonstrated.

Multi-Item EPQ Model with Scrap, Rework and Multi-Delivery using Common Cycle Policy

This paper is concerned with determining the optimal common production cycle policy for a multi-item economicproduction quantity (EPQ) model with scrap, rework and multiple deliveries. The classic EPQ model considers theoptimal replenishment quantity of single product under a perfect production assumption and a continuous inventoryissuing policy. However, in real life production planning, manufacturing firms often plan to have multiple productsmade in turn on a single machine in order to maximize the machine utilization. Also, dealing with random defectiveitems during the production run seems to be an inevitable task, and the multi-delivery policy is commonly adopted fordistributing finished items to customers. In this study, we assume a portion of nonconforming items is scrap and theother portion of them can be reworked and repaired in the same production cycle with additional cost. The objective isto determine an optimal common production cycle time that minimizes the long-run average cost per unit time for sucha specific multi-item EPQ model with scrap, rework and multi-delivery policy. Mathematical modeling and analysis isused and a closed-form optimal common cycle time for multi-item production planning is obtained. A numericalexample is provided to demonstrate the practical usage of research result.

On a multi-product lot scheduling problem subject to an imperfect process with standby modules

An Economic Lot Scheduling Problem is considered under the condition that the production process may shift from an in-control state to an out-of-control state due to the deterioration of the facility’s key module. We adopt the Common Cycle policy in two mathematical models depending on whether the key module is repairable or not. Several standby modules are available during a production run. For the model with non-repairable key modules, the active key module, once deteriorated, is disposed of and replaced by a new standby. For the model with repairable key modules, the active one is replaced by a standby as soon as it is deteriorated. The failing module will be restored in a repair shop and rejoin the standbys. The objective is to determine an optimal production cycle time and the economic number of standby modules in order to minimise the long-term average cost including set-up, inventory carrying, standby and defective costs. The convexity of the cost functions is revealed so that efficient algorithms can be developed accordingly to achieve optimal production-inventory policies. It is shown that these policies can be used to significantly improve the system performance.

AMHS capacity determination model for wafer fabrication based on production performance optimization

Automatic material handling system (AMHS) is becoming more important in 300 mm wafer fabrication factories (fab). Effective and efficient design and control of AMHS has become more critical particularly in capacity planning. The major concept of the AMHS capacity determination model is to maintain the originally designed optimal production throughput or cycle time of products. In order to maintain fab’s throughput or cycle time of products, WIP (work in process) portfolio of the constraint or the fastest workstation should be kept. Based on this concept, a GI/G/m queuing model based on FCFS (First-come-first-serve) dispatching rule of AMHS is applied to determine the required number of vehicles. Basically, products should be transported to the specific workstation (constraint or fastest workstation) before the workstation finishes the existing process; therefore, sufficient WIP in front of this specific workstation should be kept. Under this condition, the probability that transportation time exceeds product processing time under a certain transportation capacity level can be calculated by the proposed model. Hence, we can get the required capacity of AMHS to achieve the probability target set in advance. Due to the capacity of AMHS can be set according to the acceptable probability of non-exceeding the processing time of the constraint or fastest workstation, the level of WIP in front of this workstation can be kept. It also can be ensured that AMHS will not affect the production performance as well as keep the reasonable investment level.

Random Scrap Rate Effect on Multi-Item Finite Production Rate Model with Multi-Shipment Policy

This study investigates the effect of random scrap rate on multi-item Finite Production Rate (FPR) model with multi-shipment policy. The classic FPR model considers production planning for single product, a perfect condition during the production run and a continuous inventory issuing policy. However, in real life manufacturing environments, in order to maximize machine utilization, vendors often make plan to produce m products in turn on a single machine. Also, in any given production run due to various different factors, generation of nonconforming items is inevitable. In this study, it is assumed that these defective items cannot be repaired, thus they must be scrapped with an additional cost and delivery of finished products is under a practical multiple shipment policy. Our objective is to determine an optimal common production cycle time that minimizes the long-run average cost per unit time and to investigate the effect of random scrap rate on the optimal common cycle time. Mathematical modeling is employed and renewal reward theorem is used to cope with the variable cycle length. The expected system cost for the proposed multi-item FPR model is derived and its convexity is proved. A closed-form optimal common production cycle time is obtained. A numerical example and sensitivity analysis is provided to demonstrate the practical use of the obtained results.

Shortening cycle times in multi-product, capacitated production environments through quality level improvements and setup reduction

This paper addresses the issue of investing in reduced setup times and defect rates for a manufacturer of several products operating in a JIT environment. Production cycle times can be shortened by investing in setup time and defect rate reductions, respectively. The objective is to determine optimal levels of setup time and defect rate reductions along with the corresponding optimal levels of investments respectively, and the optimal production cycle time for each product. The problem is constrained by demand requirements, process improvement budget limitations, and manufacturing and warehousing capacity constraints. We consider the cases of product-specific quality improvements and joint-product quality improvements. A general nonlinear optimization models of these problems are formulated. A convex geometric programming approximation of these models is developed respectively, in order to solve them. The approximation can be made to any desired degree of accuracy. Our empirical findings provide insights into a number of managerial issues surrounding investment decisions in product-specific quality improvements and setup reductions due to a product redesign as well as in joint-product improvements due to a process redesign.

Solving a Multi-Item Finite Production Rate Model with Scrap and Multi-Shipment Policy without Derivatives

In real life manufacturing environments, production managers often make plan to produce m products in turn on a single machine in order to maximize the machine utilization. This study focuses on determining an optimal common production cycle time for a multi-item Finite Production Rate (FPR) model with random scrap rate and multi-shipment plan without using the derivatives. We assume that <em>m</em> products are manufactured in turn based on a common cycle policy on a single machine and during the processes some nonconforming items are generated randomly. These defective items cannot be reworked, thus they are scrapped at additional costs in the end of each production cycle. After the entire lot is quality assured, the delivery of finished items is under a practical multiple shipments plan. The objective is to determine an optimal common cycle time that minimizes the long-run average cost per unit time using an algebraic approach. Conventional method for solving such a problem is by the use of differential calculus on system cost function to derive the optimal policy, whereas the proposed approach is a straightforward method. It helps practitioners, who may not have sufficient knowledge of calculus, to understand and manage the real-life multi-item production systems more effectively.

An optimal common production cycle time for imperfect production processes with scrap

This paper considers the effects of imperfect production processes and the decision on whether and when to implement a screening process for defective items generated during a production run on the Economic Lot Scheduling Problem (ELSP). It is assumed that a process is in control at the beginning of a production run. After a period of production, the process may shift to an out-of-control state at a random time, and consequently produces a fixed percentage of defective items. These defective items cannot be repaired or reworked, and thus must be scrapped with an additional cost. The objective is to determine an optimal common production cycle time that minimizes the expected average cost per unit of time. The bisection method is employed to obtain a near-optimal solution. A closed-form solution is also derived after using an approximation to an exponential function involved in the objective function. Numerical examples are provided to illustrate the derivation of the optimal common production cycle time.

Optimal joint replenishment decisions for a central factory with multiple satellite factories

This study investigates the joint replenishment decisions for a central factory and its satellite factories on a Just in Time (JIT) basis. A joint replenishment program involves combining different materials/components from several satellite factories to form a large shipment delivered to the central factory, which provides an opportunity to take advantage of the strong economies of scale present in the freight cost. The program requires closely coordinating the inventory control across satellite factories of multiple materials/components. A decision model with a solution procedure is provided to find the optimal common replenishment cycle time of a group of materials/components for the central factory and the optimal production cycle time as well as the number of shipments per production cycle for each satellite factory. Based on the presented solution procedure, a decision support system has been implemented on a personal computer for the proposed decision. Numerical experiments were conducted to illustrate the application of the model.

AN INTEGRATED PRODUCTION-INVENTORY MODEL FOR DETERIORATING PRODUCTION WITH DEFECTIVE ITEM REWORK AND JOINT MATERIAL REPLENISHMENT POLICY

ABSTRACT This paper considers an integrated production-inventory model which determines an optimal production cycle time and economic joint replenishment quantity of raw materials in a batch production system. The production process is assumed to be imperfect, and thus certain amount of item produced become defective. The defective items are assumed to be reworked immediately after the regular production ends and rework efforts are assumed to be performed under perfect condition. The objective is to minimize the expected total cost for the system over an infinite horizon. An algorithm to obtain an optimal or near optimal solution is presented. To demonstrate the model's fidelity, a numerical example is provided to illustrate the model. Sensitivity analysis is also performed and discussed. This deterministic model attempts to provide mangers with guidelines to evaluate the proper production cycle time and the purchase quantity of raw materials of an imperfect production process simultaneously under defective item rework and joint material replenishment policy.

The optimal production cycle time in an integrated production-inventory model for decaying raw materials

In 1983, Park presented an integrated production-inventory model for decaying raw materials. This paper discusses the same model as that of Park. The main purpose is threefold: This paper shows that the total cost function per unit time is convex by a rigorous proof. This paper derives the closed forms for the upper and lower bounds on the optimal cycle time of the total cost function per unit time, thereby enabling straightforward application of the standard bisection algorithm to numerically compute the optimal cycle time. This paper compares optimal solutions obtained by using our approach (the bisection algorithm) and Park’s approach. Numerical examples show that our approach is better.

Determining a common production cycle time for an economic lot scheduling problem with deteriorating items

This paper considers the economic lot scheduling problem (ELSP) for a production-inventory system where items produced are subject to continuous deterioration. The problem is to schedule multiple products to be manufactured on a single machine repetitively over an infinite planning horizon. Each product is assumed to have a significant rate of deterioration. Only one product can be manufactured at a time. The demand rate for each product is constant, but an exponential distribution is used to represent the distribution of the time to deterioration. A common cycle time policy is assumed in the production process. A near optimal production cycle time is derived under conditions of continuous review, deterministic demand, and no shortage.