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© 2001 by CRC Press LLC 7 Scheduling Systems and Techniques in Flexible Manufacturing Systems Preface 7.1 Flexible Manufacturing Systems and Performance Parameters Background • Manufacturing Systems • Transfer Line and Job Shop: Characteristics and Limitations • Flexible Manufacturing System Technology • Flexibility 7.2 Scheduling Issues in FMS Scheduling in FMS Technology • Performance Parameters • Static and Dynamic Scheduling • Static • Constructive Heuristics • Dynamic Approach • Research Trends in Dynamic Scheduling Simulation Approach • Experimental Approach for Simulated Dynamic Scheduling (ESDS) • Input Product-Mix and ESDS in a Random FMS • Data Analysis • Mix-Oriented Manufacturing Control (MOMC) 7.3 Summary Preface In this chapter a number of issues relating to scheduling in the flexible manufacturing system (FMS) domain will be discussed in detail. The chapter is divided into four main areas. First, performance parameters that are appropriate for a FMS will be covered. Here we will look at the background of manufacturing systems along with their characteristics and limitations. FMS technology and the issue of flexibility will also be looked at in this section. In the following section a detailed description of scheduling issues in an FMS will be presented. Here we will cover both static and dynamic scheduling along with a number of methods for dealing with these scheduling problems. The third major section of this chapter will detail a new approach to these issues called mix oriented manufacturing control (MOMC). Research trends and an experimental design approach for simulated dynamic scheduling (ESDS) will be covered in this section along with operational details and examples. Finally, the chapter will close with a summary of the information presented and conclusions. Ernest L. McDuffie Florida State University Marco Cristofari Florida State University Franco Caron Politecnico di Milano Massimo Tronci University of Rome William J. Wolfe University of Colorado at Denver Stephen E. Sorensen Hughes Information Technology Systems © 2001 by CRC Press LLC 7.1 Flexible Manufacturing Systems and Performance Parameters Background In a competitive world market, a product must have high reliability, high standards, customized features, and low price. These challenging requirements have given a new impulse to all industrial departments and in particular, the production department. The need for flexibility has been temporarily satisfied at the assembly level. For example, several similar parts, differing from each other in few characteristics, e.g., color or other small attributes, are produced in great quantities using traditional manufacturing lines, and then are assembled together to produce smoothly different products. Unfortunately, this form of flexibility is unable to satisfy increasingly differentiated market demand. The life cycle of complex products, e.g., cars, motorbikes, etc., has decreased, and the ability to produce a greater range of different parts has become strategic industrial leverage. Manufacturing systems have been evolving from line manufacturing into job-shop manufacturing, arriving eventually at the most advanced expression of the manufacturing system: the FMS. Manufacturing Systems Based on flexibility and through-put considerations, the following manufacturing systems are identifiable 1. Line manufacturing (LM). This structure is formed by several different machines which process parts in rigid sequence into a final product. The main features are high through-put, low variability in the output product-mix (often, only one type of product is processed by a line), short flow time, low work-in-process (WIP), high machine utilization rate, uniform quality, high automation, high investments, high unreliability (risk of production-stops in case of a machine breakdown), and high time to market for developing a new product/process. 2. Job-shop manufacturing (JSM). The workload is characterized by different products concurrently flowing through the system. Each part requires a series of operations which are performed at different work stations according to the related process plan. Some work centers are interchange- able for some operations, even if costs and quality standards are slightly different from machine to machine. This feature greatly increases the flexibility of the system and, at the same time, the cost and quality variability in the resulting output. The manufacturing control system is respon- sible to choose the best option based on the status of the system. In a job-shop, the machines are generally grouped together by technological similarities. On one side, this type of process-oriented layout increases transportation costs due to the higher complexity of the material-handling control. On the other side, manufacturing costs decrease due to the possibility of sharing common resources for different parts. The main features of a job-shop are high flexibility, high variability in the output product-mix, medium/high flow time, high WIP, medium/low machine utilization rate, non-uniform quality, medium/low automation level, medium/low investments, high system reli- ability (low risk of production-stop in case of a machine breakdown), and for developing a new product/process. 3. Cell manufacturing. Following the criteria of group technology, some homogeneous families of parts may be manufactured by the same group of machines. A group of machines can be gathered to form a manufacturing cell. Thus, the manufacturing system can be split into several different cells, each dedicated to a product family. Material-handling cost decreases, while at the same time flexibility decreases and design cost increases. The main features of cell-manufacturing systems range between the two previously mentioned sets of system characteristics. Transfer Line and Job Shop: Characteristics and Limitations A comparison of the first two types of manufacturing systems listed, LM and JSM, can be summarized as follows. The main difference occurs in the production capability for the former and the technological capability for the latter. This is translated into high throughput for LM and high flexibility for JSM. A © 2001 by CRC Press LLC number of scheduling issues become apparent during different phases in these systems. These phases and different issues are: 1. Design phase. In case of LM, great care is to be taken during this phase. LM will operate according to its design features, therefore, if the speed of a machine is lower than the others, it will slow down the entire line, causing a bottleneck. Similar problems will occur in the case of machine breakdowns. Availability and maintenance policies for the machines should be taken into account during the design phase. Higher levels of automation generate further concern during the design phase because of the risk stemming from the high investment and specialization level, e.g., risk of obsoleteness. On the other hand, the JSM is characterized by medium/low initial investment, a modular structure that can be easily upgraded and presents less problems in the design phase. The product-mix that will be produced is generally not completely defined at start-up time, therefore, only the gross system capacity may be estimated on the basis of some assumptions about both processing and set-up time required. The use of simulation models highly improves this analysis. 2. Operating phase. The opposite occurs during the operating phase. In an LM, scheduling problems are solved during the design stage, whereas in a JSM, the complexity of the problem requires the utilization of a production activity control (PAC) system. A PAC manages the transformation of a shop order from the planned state to the completed state by allocating the available resources to the order. PAC governs the very short-term detailed planning, executing, and monitoring activities needed to control the flow of an order. This flow begins the moment an order is released by the planning system for execution, and terminates when the order is filled and its disposition completed. Additionally, a PAC is responsible for making a detailed and final allocation of labor, machine capacity, tools, and materials for all competing orders. Also, a PAC collects data on activities occurring on the shop floor involving order progress and status of resources and makes this information available to an upper level planning system. Finally, PAC is responsible for ensuring that the shop orders released to the shop floor by an upper level planning system, i.e., manufacturing requirement planning (MRP), are completed in a timely and cost effective manner. In fact, PAC determines and controls operation priorities, not order priorities. PAC is responsible for how the available resources are used, but it is not responsible for determining the available level of each resource. In short, PAC depends on an upper level planning system for answers to the following questions • What products to build? • How many of each product to build? • When the products are due? Scheduling in a job-shop is further complicated by the dynamic behavior of the system. The required output product-mix may change over time. Part types and proportion, deadlines, client requirements, raw material quality and arrival time, system status, breakdowns, bottlenecks, maintenance stops, etc., are all factors to be considered. A dynamic environment represents the typical environment in which a JSM operates. The complexity of the job-shop scheduling problem frequently leads to over-dimensioning of the system capacity and/or high levels of WIP. A machine utilization coefficient may range between 15–20% for nonrepetitive production. Some side effects of WIP are longer waiting time in queue and a manufacturing cycle efficiency (MCE) ranging from 1/25–1/30 for the job-shop, compared to approxi- mately one for line manufacturing. MCE is defined as the ratio between the total processing time necessary for the manufacturing of a part and the flow time for that part, which is equal to the sum of total processing, waiting, setup, transporting, inspection, and control times. Flexible Manufacturing System Technology The computer numerical control (CNC) machine was the first stand-alone machine able to process several different operations on the same part without any operator’s intervention. Integration of several machines moving toward an FMSs required the following steps: © 2001 by CRC Press LLC 1. Creation of load/unload automatic device for parts and tools between storage and working positions. 2. Implementation of a software program in the central computer to control the tool-material load/unload automatic devices. 3. Automation of a parts-tools handling system among CNCs for all the cells. 4. Implementation of a software program in the central computer to control the parts-tools trans- portation system such as an automatic guided vehicle (AGV). 5. Implementation of a program-storage central computer, connected to each CNC, to automate the process of loading/unloading software programs necessary to control each manufacturing process. The resulting FMS is a highly automated group of machines, logically organized, and controlled by a central computer (CC), and physically connected with an automated transport system. A CC schedules and provides data, software programs referring to the manufacturing processes to be performed, jobs, and tools to single workstations. Originally, FMS hierarchical-structure was centralized in nature. Typi- cally, a CC was implemented on a mainframe because of the large number of tasks and needed response time. More recently, with the increasing power of mini and personal computers (PCs), the FMS’s hier- archical-structure has become a more decentralized structure. The PCs of each CNC are connected to each other, forming a LAN system. This decentralization of functions across local workstations highly increases both the reliability of the system and, if a dynamic scheduling control is implemented, the flexibility of the system itself. FMS, as an automated job-shop, can be considered as a natural development that originated either from job-shop technology with increased levels of automation, or manufacturing line technology with increased levels of flexibility. Because an FMS’s ability to handle a great variety of products is still being researched, the majority of installed FMS’s produce a finite number of specific families of products. An objective of an FMS is the simultaneous manufacturing of a mix of parts, and at the same time, to be flexible enough to sequentially process different mixes of parts without costly, time consuming changeover requirements between mixes. FMS’s brought managerial innovation from the perspective of machine setup times. Decreasing the tool changing times to negligible values, FMSs eliminate an important job-shop limitation. Because of the significant change in the ratio between working times and setup times, FMSs modify the profit region of highly automated systems. The realization of an FMS is based on an integrated system design which differs from the conventional incremental job-shop approach that adds the machines to the system when needed. Integrated system design requires the dimensioning of all the system components such as machines, buffers, pallets, AGV, managerial/scheduling criteria, etc., in the design phase. Main management leverages for a FMS are: 1. Physical configuration of the system. Number and capacity of the machines, system transportation characteristics, number of pallets, etc. 2. Scheduling policies. Loading, timing, sequencing, routing, dispatching, and priorities. Physical configuration is a medium long-term leverage. The latter is a short-term leverage that allows a system to adapt to changes occurring in short-term. Many different FMS configurations exist, and there is considerable confusion concerning the definition of particular types of FMSs [Liu and MacCarthy, 1996]. From a structural point of view the following types of FMSs can be identified: 1. FMS. A production system capable of producing a variety of part types which consists of CNC or NC machines connected by an automated material handling system. The operation of the whole system is under computer control. 2. Single flexible machine (SFM). A computer controlled production unit which consists of a single CNC or NC machine with tool changing capability, a material handling device, and a part storage buffer. © 2001 by CRC Press LLC 3. Flexible manufacturing cell (FMC). A type of FMS consisting of a group of SFMs sharing one common handling device. 4. Multi-machine flexible manufacturing system (MMFMS). A type of FMS consisting of a number of SFMs connected by an automated material handling system which includes two or more material handling devices, or is otherwise capable of visiting two or more machines at a time. 5. Multi-cell flexible manufacturing system (MCFMS). A type of FMS consisting of a number of FMCs, and possibly a number of SFMs, if necessary, all connected by an automated material handling system. From a functional point of view, the following types of FMSs can be identified: 1. Engineered. Common at the very early stage of FMS development, it was built to process the same set of parts for its entire life cycle. 2. Sequential. This type of FMS can be considered a flexible manufacturing line. It is structured to sequentially manufacture batches of different products. The layout is organized as a flow-shop. 3. Dedicated. The dedicated FMS manufactures the same simultaneous mix of products for an extended period of time. The layout is generally organized as a flow-shop, where each type of job possibly skips one or more machines in accordance with the processing plan. 4. Random. This type of FMS provides the maximum flexibility, manufacturing at any time, any random simultaneous mix of products belonging to a given product range. The layout is organized as a job-shop. 5. Modular. In this FMS, the central computer and the transportation system are so sophisticated that the user can modify the FMS in one of the previous structures according to the problem at hand. Flexibility One of the main features of an FMS is its flexibility. This term, however, is frequently used with scarce attention to current research studies, whereas its characteristics and limits should be clearly defined according to the type of FMS being considered. The following four dimensions of flexibility — always measured in terms of time and costs — can be identified: 1. Long-term flexibility (years/months). A system’s ability to react, at low cost and in short time, to managerial requests for manufacturing a new product not considered in the original product-set considered during the design stage. 2. Medium-term flexibility (months/weeks). Ability of the manufacturing system to react to mana- gerial requests for modifying an old product. 3. Short-term flexibility (days/shifts). Ability of the manufacturing system to react to scheduling changes, i.e., deadlines, product-mix, derived from upper level planning. 4. Instantaneous flexibility (hours/minutes). Ability of the system to react to instantaneous events affecting system status, such as bottlenecks, machine breakdowns, maintenance stops, etc. If alternative routings are available for a simultaneous product-mix flowing through the system, a workload balance is possible concerning the different machines available in the system. It should be noted that production changes generally do not affect the production volume, but instead, the product-mix. In turn, system through-put appears to be a function of product-mix. The maximum system through-put can be expressed as the maximum expected system output per unit time under defined conditions. It is important to identify the conditions or states of a system, and the relation between these states and the corresponding system through-put. These relations are particularly important for the product-mix. In general, each product passes through different machines and interact with each other. System through-put is a function of both the product-mix and any other system parameters, e.g., control policies, transportation speed, queue lengths etc., that may influence system performance. In conclusion, © 2001 by CRC Press LLC system through-put measures can not be defined as a priori because of the high variability of product- mix. Instead, system through-put should be evaluated, i.e., through simulation, for each considered product-mix. 7.2 Scheduling Issues in FMS Considering the high level of automation and cost involved in the development of an FMS, all develop- ment phases of this technology are important in order to achieve the maximum utilization and benefits related to this type of system. However, because the main topic of this chapter is smart scheduling in an FMS, a vast available scientific literature in related areas, i.e., economical considerations, comparisons between FMS and standard technologies, design of an FMS, etc. are only referred to. These main devel- opment phases can be identified as (a) strategic analysis and economic justification, (b) facility design to accomplish long term managerial objectives, (c) intermediate range planning, and (d) dynamic operations scheduling. In multi-stage production systems, scheduling activity takes place after the development of both the master production schedule (MPS) and the material requirements planning (MRP). The goal of these two steps is the translation of product requests (defined as requests for producing a certain amount of products at a specific time) into product orders. A product order is defined as the decision-set that must be accomplished on the shop floor by the different available resources to transform requests into products. In the scheduling process the following phases can be distinguished as (a) allocation of operations to the available resources, (b) allocation of operations for each resource to the scheduling periods, and (c) job sequencing on each machine, for each scheduling period, considering the job-characteristics, shop floor characteristics, and scheduling goals (due dates, utilization rates, through-put, etc.) In an FMS, dynamic scheduling, as opposed to advance sequencing of operations, is usually implemented. This approach implies making routing decisions for a part incrementally, i.e., progres- sively, as the part completes its operations one after another. In other words, the next machine for a part at any stage is chosen only when its current operation is nearly completed. In the same way, a dispatching approach provides a solution for selecting from a queue the job to be transferred to an empty machine. It has been reported that the sequencing approach is more efficient than the dispatching approach in a static environment; however, a rigorous sequencing approach is not appropriate in a dynamic manu- facturing environment, since unanticipated events like small machine breakdowns can at once modify the system status. The complexity of the scheduling problem arises from a number of factors: 1. Large amount of data, jobs, processes, constraints, etc. 2. Tendency of data to change over time. 3. General uncertainty in such items as process, setup, and transportation times. 4. The system is affected by events difficult to forecast, e.g., breakdowns. 5. The goals of a good production schedule often change and conflict with each other. Recent trends toward lead time and WIP reduction have increased interest in scheduling methodolo- gies. Such an interest also springs from the need to fully utilize the high productivity and flexibility of expensive FMSs. Furthermore, the high level of automation supports information intensive solutions for the scheduling problem based both on integrated information systems and on-line monitoring systems. Knowledge of machine status and product advancement is necessary to dynamically elaborate and manage scheduling process. Before coping with the scheduling problem, some considerations must be made (a) actual FMSs are numerous, different, and complex. The characteristics of the observed system must be clearly defined, (b) the different types of products produced by a system can not be grouped together during a scheduling © 2001 by CRC Press LLC problem, and (c) decisions on what, how much, and how to produce, are made at the upper planning level. PAC activity can not change these decisions. The following assumptions are generally accepted in scheduling (a) available resources are known, (b) jobs are defined as a sequence of operations or directed graph, (c) when the PAC dispatches a job into the shop floor, that job must be completed, (d) a machine can not process more than one job at a time, (e) a job can not be processed contemporary on more than one machine, and (f) because the scheduling period is short, the stock costs are discarded. Scheduling in FMS Technology Flexibility is a major consideration in the design of manufacturing systems. FMSs have been developed over the last two decades to help the manufacturing industry move towards the goal of greater flexibility. An FMS combines high levels of flexibility, high maximum throughput, and low levels of work-in-progress inventory. This type of system may also allow unsupervised production. In order to achieve these desirable benefits, the control system must be capable of exercising intelligent supervisory management. Scheduling is at the heart of the control system of a FMS. The development of an effective and efficient FMS scheduling system remains an important and active research area. Unlike traditional scheduling research, however, a common language of communication for FMS scheduling has not been properly defined. The definition of a number of terms relevant to FMS scheduling are as follows [Liu and MacCarthy, 1996]: Operation. The processing of a part on a machine over a continuous time period. Job. The collection of all operations needed to complete the processing of a part. Scheduling. The process encompassing all the decisions related to the allocation of resources to operations over the time domain. Dispatching. The process or decision of determining the next operation for a resource when the resource becomes free and the next destination of a part when its current operation has finished. Queuing. The process or decision of determining the next operation for a resource when the resource becomes free. Routing. The process or decision of determining the next destination of a part when its current operation has finished. Sequencing. The decision determining the order in which the operations are performed on machines. Machine set-up. The process or decision of assigning tools on a machine to perform the next opera- tion(s) in case of initial machine set-up or tool change required to accommodate a different operation from the previous one. Tool changing. It has a similar meaning to machine set-up, but often implies the change from one working state to another, rather than from an initial state of the machine. System set-up. The process or decision of allocating tools to machines before the start of a production period with the assumption that the loaded tools will stay on the machine during the production period. All of the above concepts are concerned with two types of decisions (a) assignment of tools, and (b) allocation of operations. These two decisions are interdependent. Loading considers both. Machine set- up or tool changing concentrates on the tool assignment decisions made before the start of the production period or during this period, assuming the allocation of operations is known in advance. Dispatching concentrates on the operation allocation decisions, leaving the tool changing decision to be made later, or assuming tools are already assigned to the machines. Mathematicians, engineers, and production managers have been interested in developing efficient factory operational/control procedures since the beginning of the industrial revolution. Simple decision rules can alter the system output by 30% or more [Barash, 1976]. Unfortunately, the results of these studies are highly © 2001 by CRC Press LLC dependent on manufacturing system details. Even relatively simple single-machine problems are often NP- hard [Garey and Johnson, 1979] and, thus, computationally intractable. The difficulty in solving opera- tional/control problems in job-shop environments is further compounded by the dynamic nature of the environment. Jobs arrive at the system dynamically over time, the times of their arrivals are difficult to predict, machines are subject to failures, and managerial requests change over time. The scheduling problem in an FMS is similar to the one in job-shop technology, particularly in case of the random type. Random FMSs are exposed to sources of random and dynamic perturbations such as machine breakdowns, changes over time in workload, product-mix, due dates, etc. Therefore, a dynamic and probabilistic scheduling approach is strongly advised. Among the different variable sources, changes in WIP play a critical role. This system parameter is linked to all the other major output performance variables, i.e., average flow time, work center utilization coefficients, due dates, setup total time dependence upon job sequences on the machine, etc. Random FMS scheduling differs from job-shop scheduling in the following specific features and are important to note before developing new scheduling methodologies [Rachamadugu and Stecke, 1994]: 1. Machine set-up time. System programmability, robots, automatic pallets, numerical controlled AGVs, etc., decrease the machine set-up times to negligible values for the different operations performed in an FMS. The main effect of this characteristic is the ability to change the manufac- turing approach from batch production to single item production. This has the benefit of allowing each single item the ability to choose its own route according to the different available alternative machines and system status. In a job-shop, because of the large set up time required for each operation, the production is usually performed in batch. Due to the contemporary presence of several batches in the system, the amount of WIP in a job-shop is generally higher than in an analogous FMS. 2. Machine processing time. Due to the high level of automation in an FMS, the machine processing times and the set up times can often be considered deterministic in nature, except for randomly occurring failures . In a job-shop, due to the direct labor required both during the set up and the operation process, the set up and processing times must be considered random in nature. 3. Transportation time. In a job-shop, due to large batches and high storage capacity, the transpor- tation time can be dismissed if it is less than the average waiting time in a queue. In an FMS, because of low WIP values, the transportation time must be generally considered to evaluate the overall system behavior. The AGV speed can be an important FMS process parameters, particularly in those cases in which the available storage facilities are of low capacity. 4. Buffer, pallet, fixture capacity. In an FMS, the material handling and storage facilities are auto- mated, and therefore specifically built for the characteristics of the handled materials. For this reason the material handling facilities in an FMS are more expensive than in a job-shop, and economic constraints limit the actual number of facilities available. Therefore, physical constraints of WIP and queue lengths must be considered in FMS scheduling, whereas these constraints can be relaxed in job-shop scheduling. 5. Transportation capacity. AGVs and transportation facilities must be generally considered as a restricted resource in an FMS due to the low volume of WIP and storage facilities that generally characterized these systems. 6. Instantaneous flexibility — alternative routing. The high level of computerized control typical in an FMS makes available a large amount of real-time data on the status of the system, which in turn allows for timely decision making on a best routing option to occur. In a job-shop, routing flexibility is theoretically available, but actually difficult to implement due to the lack of timely information on the system status. Performance Parameters The scheduling process refers to the assignment and timing of operations on machines on the shop floor. Scheduling goals are generally difficult to formulate into a well defined objective function that focuses on costs for the following reasons: © 2001 by CRC Press LLC 1. Translation of system parameters, i.e., machine utilization coefficient, delivery delays, etc., whose values are important to the evaluation of the fitness of a schedule into cost parameters is problematic. 2. Significant changes in some parameters, such as stock level, in the short-term bring only a small difference to the cost evaluation of a schedule. 3. Some factors derived from medium-term planning can have a great influence on scheduling costs, but can not be modified in short-term programming. 4. Conflicting targets must be considered simultaneously. Because scheduling alternatives must be compared on the basis of conflicting performance parameters, a main goal is identified as a parameter to be either minimized or maximized, while the remaining parameters are formulated as constraints. For instance, the number of delayed jobs represents an objective function to be minimized under the constraint that all jobs meet their due dates. The job attributes generally given as inputs to a scheduling problem are (a) processing time, where j ϭ job, i ϭ machine, k ϭ operation, (b) possible starting date for job j , s j , and (c) due date for job j , d j . Possible scheduling output variables that can be defined are (a) job entry time, E j , (b) job completion time, C j , (c) lateness, L j ϭ C j Ϫ d j , (d) tardiness, T j ϭ max ( 0 , L j ), and (e) flow time, F j ϭ C j Ϫ E j . Flow time represents a fraction of the total lead time. When an order is received, all the management procedures that allow the order to be processed on the shop floor are activated. Between the date the order is received and the possible starting date s j , a period of time which is equal to the sum of procedural time and waiting time passes (both being difficult to quantify due to uncontrollable external elements, e.g., new order arrival time). At time s j the job is ready to enter the shop-floor and therefore belongs to a set of jobs that can be scheduled by PAC. However, time s j and time E j do not necessarily coincide because PAC can determine the optimal order release to optimize system performance. Flow time is equal to the sum of the processing time on each machine, included in the process plan for the considered part, and the waiting time in queues. The waiting time in queue depends on both the set-up time and the interference of jobs competing for the same machine. In the short-term, waiting time can be reduced because both of its components depend on good scheduling, whereas the processing time can not be lessened. Given a set of N jobs, the scheduling performance parameters are: Average lateness (7.1) Average tardiness (7.2) Average flow time (7.3) t jik LM L j j=1 N Α N ϭ TM T j j=1 N Α N ϭ FM F j j=1 N Α N ϭ © 2001 by CRC Press LLC Number of job delays (7.4) where, ␦ ( T j ) ϭ 1 se T j Ͼ 0; and ␦ ( T j ) ϭ 0 se T j ϭ 0. Makespan (7.5) Machine i utilization coefficient (7.6) where, t ji ϭ processing time of job j at machine i. Average system utilization coefficient (7.7) where M ϭ number of machines in the system. Work-in-progress (7.8) where, WIP ( t ) ϭ number of jobs in the system at time t ; a ϭ min j ( E j ); and b ϭ max j ( C j ) Total set-up time (7.9) where, SU i ϭ set-up time on machine i to process the assigned set of jobs. ND ␦ T j () jϭ1 N Α ϭ MAK max j C j {}minϪ E j {}ϭ TU i t ij j=1 N Α MAK ϭ TUM t ji j=1 M Α i =1 M Α MAK M ϭ WIP 1 baϪ WIP t()dt a b Ύ ϭ SUT SU i jϭ1 M Α ϭ [...]... against low inventories, short lead times, and high due date performance Static and Dynamic Scheduling Almost all types of scheduling can be divided into two large families, static scheduling and dynamic scheduling Static Scheduling Static scheduling problems consist of a fixed set of jobs to be run Typically, the static scheduling approach (SSA) assumes that the entire set of jobs arrive simultaneously, that... necessitates dynamic updating of scheduling rules in order to maintain system performance Some of the above mentioned conditions are relaxed in some optimization/heuristic approaches, but still the major limitation of these approaches is that they are static in perspective All the information for a scheduling period is known in advance and no changes are allowed during the scheduling period In most optimization/heuristic... prediction of task duration for future scheduling when little historical information is available, and the representation of temporal relationships among scheduled tasks Both of these areas are important in that they deal with time at a fundamental level How time is represented is critical to any scheduling methodology One concept that has been proposed call smart scheduling deals with these areas by... Methods (BM) This method [Vollman, 1986; Lundrigan, 1986; Meleton, 1986; Fry, Cox, and Blackstone, 1992] is representative of other current finite scheduling systems such as Q-Control and NUMETRIX Both programs are capable of finding clever approximate solutions to scheduling models Briefly, BM identifies the bottleneck resource and then sets priorities on jobs in the rest of the system in an attempt to control/reduce... product-mix, which will prove to be a very important system parameter when dynamic scheduling is needed Experimental Approach for Simulated Dynamic Scheduling (ESDS) The proposed ESDS associates appropriate and powerful mathematical-experimental-statistical methodologies with the computer simulation approach to solve a dynamic scheduling problem in a random FMS ESDS deals with the dynamic and stochastic... requirements plan (MRP) IPM can be defined at the scheduling level by the production active control (PAC) IOM is the actual outcome of the planning and scheduling activities IPM can be utilized by PAC as a system parameter to dynamically control and schedule a FMS effectively To generate a robust schedule, continuous feed-back between the planning stage and the scheduling stage is necessary If assumptions... scheduling period In most optimization/heuristic approaches, processing/setup/transportation times are fixed and no stochastic events occur These methodologies are also deterministic in nature Dynamic Scheduling Dynamic scheduling problems are characterized by jobs continually entering the system The parts are not assumed to be available before the starting time and are assumed to enter the system at random,... a job, or the actual operation to be performed in real-time — when the job or the machine is actually available — and not ahead-of-time, as occurs in other types of scheduling approach For this reason, dispatching rules ensure dynamic scheduling of an observed system Dispatching rules must be transparent, meaningful, and particularly consistent with the objectives of the planning system [Pritsker,... technological environment is highly dynamic and probabilistic Research Trends in Dynamic Scheduling Simulation Approach During the 1980s, in the increasingly competitive world of manufacturing, Stochastic discrete event simulation (SDES) was accepted as a very powerful tool for planning, design, and control of complex production systems [Huq et al., 1994; Law, 1991; Pritsker, 1986; Tang Ling et al., 1992a-b]... strategy determine the scheduling objective If jobs do not have the same importance, a weighted average for the corresponding jobs can be applied instead of a single parameter, i.e., average lateness, average tardiness, or average flow time Besides the average flow time, its standard deviation can be observed Similar considerations can be made for the other parameters In several cases the scheduling goal could . Dynamic Scheduling Almost all types of scheduling can be divided into two large families, static scheduling and dynamic scheduling. Static Scheduling . by CRC Press LLC 7 Scheduling Systems and Techniques in Flexible Manufacturing Systems Preface 7.1 Flexible Manufacturing Systems and Performance