Variable Lot Sizes Research Articles

Lot streaming of hybrid flowshops with variable lot sizes and eligible machines

Hybrid flowshops are a special type of manufacturing systems, in which a stage may contain identical or unrelated parallel machines. This paper deals with a more practical approach for lot streaming hybrid flowshop in which the sublot sizes of jobs can vary from one stage to the next according to machines' speed. Two models of mixed-integer nonlinear programming are developed to minimise the make-span of two different hybrid flowshop systems. The first model deals with unrelated parallel machines with eligibility, independent setup time, and variable sublot sizes. The second model is a special case of the hybrid flowshop as it consists of multi-stages comprising one machine at the stages preceding the final stage, while the final stage includes unrelated parallel machines. The first model was studied and the data gathered were analysed using ANOVA test to evaluate the factors' effect on system. The factors are number of jobs, maximum number of batches, setup time, and machine's configuration. The analysis revealed that all the factors were effective. The second model was compared to benchmarking published paper and it gets better results.

A two-stage discrete water wave optimization algorithm for the flowshop lot-streaming scheduling problem with intermingling and variable lot sizes

Considering lot-streaming of different orders in the actual production system, this paper examines the lot-streaming scheduling problem in flowshop production system. Given production sublots of the different jobs allowed to be intermingled in the production process, we take a deeper dive into the flowshop lot-streaming scheduling problem with detached setup and transfer batches for production sublots of jobs. And the mathematical model is presented with the objective of makespan. To tackle the complexity of the problem at hand, a two-stage discrete water wave optimization (TSDWWO) algorithm is proposed to optimize the sublots and sequencing. In the algorithm, a double-wave parallel encoding scheme is designed for two kinds of water waves, which are splitting wave and sequencing wave. Besides, considering the operation effect and time of the algorithm, the corresponding operations during the process of wave propagation are improved for these two kinds of waves respectively. Afterward, the parameters of the proposed TSDWWO are calibrated by the design of experiments approach. To evaluate the performance of the proposed TSDWWO, two different types of test sets are utilized in the experiments, which are the test sets in the literature and test sets randomly generated containing instances of variant scales. Compared with other existing algorithms in the literature, the results show the efficiency of this approach for the flowshop lot-streaming scheduling problem.

Lot Streaming of Hybrid Flowshops with Variable Lot Sizes and Eligible Machines

Lot Streaming of Hybrid Flowshops with Variable Lot Sizes and Eligible Machines

A study on lot-size dependence of the energy consumption per unit of production throughput concerning variable lot-size

A study on lot-size dependence of the energy consumption per unit of production throughput concerning variable lot-size

Determination of a new mixed variable lot-size multiple dependent state sampling plan based on the process capability index

ABSTRACTThis article proposes a new mixed variable lot-size multiple dependent state sampling plan in which the attribute sampling plan can be used in the first stage and the variables multiple dependent state sampling plan based on the process capability index will be used in the second stage for the inspection of measurable quality characteristics. The proposed mixed plan is developed for both symmetric and asymmetric fraction non conforming. The optimal plan parameters can be determined by considering the satisfaction levels of the producer and the consumer simultaneously at an acceptable quality level and a limiting quality level, respectively. The performance of the proposed plan over the mixed single sampling plan based on Cpk and the mixed variable lot size plan based on Cpk with respect to the average sample number is also investigated. Tables are constructed for easy selection of plan parameters for both symmetric and asymmetric fraction non conforming and real world examples are also given for the illustration and practical implementation of the proposed mixed variable lot-size plan.

Formularization of Relationship between Energy Consumption Per Production Throughput and Lot size Concerning Variable Lot size in Manufacturing Line

Formularization of Relationship between Energy Consumption Per Production Throughput and Lot size Concerning Variable Lot size in Manufacturing Line

A New Mixed Variable Lot Size Sampling Plan Based on Process Capability Index

Abstract A new mixed sampling plan with a variable lot size plan is developed in this manuscript using the process capability index. The operating characteristic function of the proposed plan is derived and the plan parameters are determined using the non-linear optimization procedure for symmetric and asymmetric fraction non-conforming cases. It is also shown that the proposed plan is more efficient than existing acceptance sampling plans. Industrial data is presented to explain the application of the proposed plan.

Production-driven opportunistic maintenance for batch production based on MAM–APB scheduling

Nowadays, modern production patterns, such as batch production, have brought new challenges for multi-unit maintenance decision-making. The maintenance scheduling should not only consider individual machine deterioration, but also apply to batch production with variable lot size. An interactive bi-level maintenance strategy is thus proposed in a multi-unit batch production system with degrading machines. In the machine-level scheduling, a multi-attribute model (MAM) is used to obtain maintenance intervals according to individual machine degradation. In the system-level scheduling, a novel production-driven opportunistic maintenance strategy is developed by considering both machine degradation and characteristics of batch production. In this strategy, advance-postpone balancing (APB) utilizes set-up times as opportunities to make real-time schedules for system-level maintenance. The numerical example shows that the proposed MAM–APB methodology can efficiently eliminate unnecessary production breaks, achieve significant cost reduction and overcome complexity of system scheduling.

Low Coherence Interferometry in Selective Laser Melting

Abstract Selective Laser Melting (SLM) is an additive layer manufacturing technology that offers several advantages compared to conven- tional methods of production such as an increased freedom of design and a toolless production suited for variable lot sizes. Despite these attractive aspects today's state of the art SLM machines lack a holistic process monitoring system that detects and records typical defects during production. A novel sensor concept based on the low coherence interferometry (LCI) was integrated into an SLM production setup. The sensor is mounted coaxially to the processing laser beam and is capable of sampling distances along the optical axis. Measurements during and between the processing of powder layers can reveal crucial topology information which is closely related to the final part quality. The overall potential of the sensor in terms of quality assurance and process control is being discussed. Furthermore fundamental experiments were performed to derive the performance of the system.

Catalytic water treatment process

This paper deals with the requirements, present development, and research issues concerning advanced material-handling systems based on programmable manipulators that are commonly called industrial robots.Industrial robots are becoming increasingly important as part of programmable automation systems being developed for the production of batch-produced discrete part goods. As contrasted with hard or fixed automation, programmable systems are designed for flexibility, that is, for ease of set-up for new or changing products in small or variable lot sizes, and adaptively responsive to a variable environment.Material handling entails the controlled manipulation of raw materials, workpieces, assemblies and finished products. Together with inspection and assembly, these functions represent essential parts of the total manufacturing process that are still highly labor-intensive.The great majority of present industrial robots (first generation) are performing relatively simple repetitive material handling tasks in highly constrained or structured environments. They are also increasingly used in spot-welding and paint-spraying operations. Second generation robots which incorporate computer processors or minicomputers have begun to appear in factories, considerably extending rudimentary pick-and-place operations. More advanced robots are being developed which incorporate visual and tactile sensing, all under computer control. These integrated systems begin to emulate human capabilities in coping with relatively unstructured environments.There are two major requirements for advanced material handling systems. The first requirement is for a programmed robot to be able to acquire randomly-positioned and un-oriented workpieces, subassemblies or assemblies from stationery bins or from moving conveyors, in a predetermined manner, and to convey them via a predetermined path, safely, to some desired position and orientation.The second requirement is for the robots to be able to place the acquired workpiece or assembly with a desired orientation in a position with a specified precision.These two requirements share the need for sensor-controlled manipulation to varying degrees. Tactile sensing may be sufficient for a simple task in which the workpieces are already oriented and require crude end-positioning at the destination such as in a palletizing operation. Visual sensing may be required when the workpieces are unoriented originally, are in motion, or when the final position is not precisely determined. In some instances, both tactile and visual sensing would be the most effective method, as when packing an unoriented container with workpieces in a desired order. Finally, in automated assembly processes, visual and/or tactile sensing may be required to bring parts together in fitting operations, or for insertions of shafts or bolts in holes. In the latter cases, the precision requirements for a passive accomodation system, together with the completeness of jigging or fixturing would govern how much sensor control was necessary.The major issues thus are the relative costs of orienting parts, of fixturing to preserve position and orientation, of high-performance robots (speed and precision) and on the trade-off attainable by the use of sensor control to reduce the cost of the other alternatives.

A parameterized-dispatching rule for a Logic IC sort in a wafer fabrication

In this paper, a parameterized dispatching rule (PDR) using the response surface method is presented for a Logic IC sort in a wafer fabrication. A broad product mix, variable lot sizes and yields, long and variable set-up times, and limited test equipment capacity can characterize the operations in this wafer probe centre. The objective of this study is to simultaneously optimize the desirability function that is the combination of multiple attributes of the products such as the hot lot or normal lot, critical ratio with good on-time delivery performance, processing time, set-up time, waiting time, and machine flexibility. This is accomplished by combining the multiple attributes together using a linear combination with relative weights. Also, multiple performance measures are considered in this study. Discrete event simulation models based on eM-Plant are developed to implement the proposed rule. The comparison is also made with other rules such as shortest set-up time (SST), shortest processing time (SPT), shortest set-up and processing time (SSPT), smallest critical ratio (SCR), first in first out (FIFO) and least machine flexibility (LMF). Here, two combined performance values are used as the performance measure that both are combined with the multiple performance measures to a single value using the desirability function. The simulation results show that the four proposed PDRs outperform other rules in many different operational conditions.

The effect of discreteness in vendor-buyer relationships

To facilitate integrated vendor-buyer modeling, it has been assumed that the ratio between the lengths of their inventory cycles is integral. This integer-ratio policy has been proven to be optimal for a vendor who is instantly replenished. Unfortunately, the proof is not extendable to a manufacturer who produces at a finite rate. Thus, this case is considered here. First, a proper analytical methodology is developed, which enables us to relax this assumption and characterize the effect of the cycles' ratio on inventory levels. This characteristic fully reveals the effect of discreteness; while the average levels of both the joint inventory and the vendor's inventory follow the general pattern and grow as a function of the production lot-size, both grow in leaps. The average level of both inventories jumps up when the production lot-size reaches an integral multiple of the delivery quantity and decreases between these points. It then follows that once the lower bound of a leap is passed, it is better to round the vendor lot-size up to the next multiple of the delivery quantity. Alternatively, a fractional ratio can be applied as an average of integer ratios by using variable lot sizes. Evidently, this solution reduces inventories but not enough; the associated cost is shown to be higher than the cost associated with either the next or the previous integer ratio.

Capacity-constrained scheduling for a logic IC final test facility

A capacity-constrained scheduling using the concept of the theory of constraints for a semiconductor Logic IC final test operation is presented. The scheduling of the IC final test considers unrelated parallel machines with multiple constraint problems. A broad product mix, variable lot sizes and yields, long and variable set-up times, as well as limited test equipment capacity characterize the operations in this test facility. Discrete event simulation models based on e-M-Plant™ are developed to implement the capacity-constrained scheduling algorithm. A comparison is also made with other rules, which are combinations of the rules such as first come first serve and earliest due date for the order scheduling, and the rules such as minimum set-up time, shortest processing time and shortest set-up time plus processing time for the dispatching test equipment. The simulation results show that the proposed capacity-constrained scheduling outperforms other rules for the committed volume performance in many different operational conditions. Directions for future research are also presented.

Heuristic Approaches for a Scheduling Problem in the Plastic Molding Department of an Audio Company

A production scheduling problem for making plastic molds of hi-fi models is considered. The objective is to minimize the total machine makespan in the presence of due dates, variable lot size, multiple machine types, sequence dependent, machine dependent setup times, and inventory limits. Goal programming and load balancing are applied to select the set of machine types and assign mold types to machines, resulting in a set of single-machine scheduling problems. A mixed-integer program (MIP) is formulated for the general problem but could solve only small instances. A single-machine scheduling heuristic is designed to adopt a production sequence from a travelling salesman solution. The start time of every cycle is determined by a simplified MIP. Production cycles are defined to equalize the stockout times of mold types. A post-processing step reduces the number of setups in the last cycle. Results using real-life data are promising. Characteristics giving rise to high machine utilization are discussed.

A genetic algorithm-based approach to flexible flow-line scheduling with variable lot sizes

Genetic algorithms (GAs) have been used widely for such combinatorial optimization problems as the traveling salesman problem (TSP), the quadratic assignment problem (QAP), and job shop scheduling. In all of these problems there is usually a well defined representation which GA's use to solve the problem. We present a novel approach for solving two related problems-lot sizing and sequencing-concurrently using GAs. The essence of our approach lies in the concept of using a unified representation for the information about both the lot sizes and the sequence and enabling GAs to evolve the chromosome by replacing primitive genes with good building blocks. In addition, a simulated annealing procedure is incorporated to further improve the performance. We evaluate the performance of applying the above approach to flexible flow line scheduling with variable lot sizes for an actual manufacturing facility, comparing it to such alternative approaches as pair wise exchange improvement, tabu search, and simulated annealing procedures. The results show the efficacy of this approach for flexible flow line scheduling.

Production scheduling algorithms for a semiconductor test facility

The authors develop production scheduling algorithms for semiconductor test operations. The operations in the facility under study are characterized by a broad product mix, variable lot sizes and yields, long and variable setup times, and limited test equipment capacity. The approach presented starts by dividing the facility or job shop into a number of work centers. The method then proceeds to sequence one work center at a time. A disjunctive graph representation of the entire facility is used to capture interactions between work centers. The introduction of different management objectives leads to different work center problems and different production scheduling algorithms. The authors present algorithms for two different work center problems. Direction for future research are discussed. >

Multi-stage lot sizing in a serial production system

SUMMARY This paper summarizes the development and implementation of a large-scale, multi-objective, lot-sizing model for scheduling tablet pharmaceuticals in a serial production system. The model places multiple resource capacity constraints on production at various stages of the manufacturing process and explicitly considers resource set-up times to ensure the generation of a feasible schedule. The multi-period model uniquely allows for variable lot sizes by stage and by period, subject to integrality restrictions arising from the technological nature of the multi-stage process. An integer goal programming approach is used for determining non-dominated solutions to the multi-item problem. The implementation and utilization of the model by an international manufacturer of pharmaceuticals is described, and model results are presented and discussed.

Multi-stage production with variable lot sizes and transportation of partial lots

This paper describes a model for a multi-stage production/inventory system where lots may be of different sizes. In addition, either completed lots or partial lots, called batches, may be transported to succeeding stages. The model incorporates constraints on lot and batch-sizes and thus provides a rather comprehensive set of possibilities for organizing a production/inventory system. A heuristic solution procedure is developed and is shown to be ‘close to optimal’ by bounding.

A Cost Model for Skip-lot Non-destructive Sampling

This paper investigates economic design of a sampling plan using skip-lot approach when sampling is non-destructive. A skip-lot cost model is developed by considering production, appraisal, and failure costs. The optimal sampling plan is characterized by the sample size, the acceptance number, and the inspection interval. Two alternate policies are considered in the design of sampling plan; constant and variable lot size. Model sensitivity is discussed.

Material-Handling Robots for Programmable Automation

This paper deals with the requirements, present development, and research issues concerning advanced material-handling systems based on programmable manipulators that are commonly called industrial robots.Industrial robots are becoming increasingly important as part of programmable automation systems being developed for the production of batch-produced discrete part goods. As contrasted with hard or fixed automation, programmable systems are designed for flexibility, that is, for ease of set-up for new or changing products in small or variable lot sizes, and adaptively responsive to a variable environment.Material handling entails the controlled manipulation of raw materials, workpieces, assemblies and finished products. Together with inspection and assembly, these functions represent essential parts of the total manufacturing process that are still highly labor-intensive.The great majority of present industrial robots (first generation) are performing relatively simple repetitive material handling tasks in highly constrained or structured environments. They are also increasingly used in spot-welding and paint-spraying operations. Second generation robots which incorporate computer processors or minicomputers have begun to appear in factories, considerably extending rudimentary pick-and-place operations. More advanced robots are being developed which incorporate visual and tactile sensing, all under computer control. These integrated systems begin to emulate human capabilities in coping with relatively unstructured environments.There are two major requirements for advanced material handling systems. The first requirement is for a programmed robot to be able to acquire randomly-positioned and un-oriented workpieces, subassemblies or assemblies from stationery bins or from moving conveyors, in a predetermined manner, and to convey them via a predetermined path, safely, to some desired position and orientation.The second requirement is for the robots to be able to place the acquired workpiece or assembly with a desired orientation in a position with a specified precision.These two requirements share the need for sensor-controlled manipulation to varying degrees. Tactile sensing may be sufficient for a simple task in which the workpieces are already oriented and require crude end-positioning at the destination such as in a palletizing operation. Visual sensing may be required when the workpieces are unoriented originally, are in motion, or when the final position is not precisely determined. In some instances, both tactile and visual sensing would be the most effective method, as when packing an unoriented container with workpieces in a desired order. Finally, in automated assembly processes, visual and/or tactile sensing may be required to bring parts together in fitting operations, or for insertions of shafts or bolts in holes. In the latter cases, the precision requirements for a passive accomodation system, together with the completeness of jigging or fixturing would govern how much sensor control was necessary.The major issues thus are the relative costs of orienting parts, of fixturing to preserve position and orientation, of high-performance robots (speed and precision) and on the trade-off attainable by the use of sensor control to reduce the cost of the other alternatives.