برنامه ریزی در تولید کارگاهی مونتاژ پویا کار برای به حداقل رساندن مجموع زودرسی وزنی، تاخیر ورود وزنی و زمان شناوری وزنی

In many manufacturing systems, jobs that are completed early are held as finished-goods inventory until their due-dates, and hence we incur earliness costs. Similarly, jobs that are completed after their due-dates incur penalty. The objective in such situations would, therefore, be to meet the due-dates of the respective jobs as closely as possible, and consequently minimize the sum of earliness and tardiness of jobs because earliness and tardiness of jobs greatly influence the performance of a schedule with respect to cost. In addition, a job incurs holding cost from the time of its arrival until its completion. Most studies on scheduling in such manufacturing systems assume unit earliness cost, unit tardiness cost and unit holding cost of a job. However, in reality such an assumption need not always hold and it is quite possible that there exist different costs of earliness, tardiness and holding for different jobs. In addition, most studies on job-shop scheduling assume that jobs are independent and that no assembly operations exist. The current study addresses the problem of scheduling in dynamic assembly job-shops (i.e. shops that manufacture multi-level jobs) with the consideration of jobs having different earliness, tardiness and holding costs. An attempt is made in this paper to present dispatching rules by incorporating the relative costs of earliness, tardiness and holding of jobs in the form of scalar weights. In the first phase of the study, relative costs (or weights for) earliness and tardiness of jobs are considered, and the dispatching rules are presented in order to minimize the sum of weighted earliness and weighted tardiness of jobs. In the second phase of the study, the objective considered is the minimization of the sum of weighted earliness, weighted tardiness and weighted flowtime of jobs, and the dispatching rules are presented by incorporating the relative costs of earliness, tardiness and flowtime of jobs. Simulation studies have been conducted separately for both phases of the current study, the performance of the scheduling rules have been observed independently, and the results of the simulation study have been reported. The proposed rules are found to be effective in minimizing the mean and maximum values of the measures of performance.

Most research on scheduling in dynamic manufacturing systems has dealt with the problem of scheduling in dynamic job-shops. A survey of dispatching rules in dynamic shops was presented by Day and Hottenstein, 1970, Blackstone et al., 1982 and Haupt, 1989, and Ramasesh (1990). Of late, efficient dispatching rules in dynamic job-shops and flow-shops have been proposed by Holthaus and Ziegler (1997), Holthaus and Rajendran, 1997, Holthaus and Rajendran, 2000 and Holthaus and Rajendran, 2002, Jayamohan and Rajendran (2000), and Framinan, Ruiz-Usano, and Leisten (2000). Researchers have attempted to evaluate the performance of dispatching rules in an assembly job-shop environment where assembly operations take place. In an assembly job-shop, the operations of an item are carried out serially by following the precedence relationships, while those of another item belonging to the same assembly may be carried out in parallel (unlike non-assembled or serial jobs where all the operations are performed in series). In this context, an item here may refer to a component, a sub-assembly, or a sub-sub-assembly. As a result, in addition to waiting for a resource, an item may wait for the processing of its mating items, before the required assembly can take place. Moreover, the jobs can have a very simple structure involving just one level of assembly, or can be complicated with several levels of assemblies. Irrespective of the nature of the job structure, processing of components, sub-assemblies and sub-sub-assemblies must be completed in such a way to make the schedule and assembly feasible. This makes the scheduling problem in assembly job-shops quite challenging, when compared to the conventional job-shop (Adam, Bertrand, & Surkis, 1987). Unlike the job-shop, the amount of research work done in the assembly job-shop environment is rather limited. The measures of performance, used by most of the researchers in the area of dynamic assembly job-shops, to evaluate the performance of the dispatching rules include job flowtime, tardiness, percentage of tardy jobs and assembly delay. Initially, simple job structures were considered, and the performance of simple and composite rules (with the consideration of information about the shop status, job progress in the form of remaining job-time, and slack) was evaluated with respect to the measures of mean flowtime and mean tardiness (e.g. Maxwell & Mehra, 1968; Sculli, 1980 and Sculli, 1987). The good performance of the job due-date rule (Goodwin & Goodwin, 1982) and the non-performance of the other milestones, namely, the operation and assembly due-dates (Phillipoom, Markland, & Fry, 1989) for complex job structures were reported with respect to the minimization of mean flowtime, mean tardiness and percentage of tardy jobs. New dispatching rules, namely, relative remaining operations (RRO), relative remaining processing time (RRP) and importance ratio (IR), were developed with due consideration given to pacing, acceleration and structural complexity (Adam et al., 1987 and Phillipoom et al., 1991) which resulted in minimizing the staging delay. A tie-breaking rule is used when two or more jobs wait in the queue and have the same priority value. The importance of tie-breaking was observed by Adam et al. (1987) when they used the TWKR (total work content remaining or total processing times of remaining operations on the job) rule with their proposed tie-breaking rules, namely, relative remaining operations (RRO) and relative remaining processing times (RRP). Later, Phillipoom et al. (1991) evaluated the use of the importance ratio (IR) rule for tie-breaking. Recently, Reeja and Rajendran, 2000a and Reeja and Rajendran, 2000b came up with the operation synchronization date (OSD) rule, and found the rule to be better than the RRP and IR rules for tie-breaking when the TWKR rule is the primary one. The effect of product structures on the performance of the dispatching rules (Fry, Oliff, Minor, & Leong, 1989) and dynamic assignment of due-date without the use of parameters (Adam, Bertrand, Morehead, & Surkis, 1993) are other important contributions in the assembly job-shop environment. In real-life situations, since the strength of the relationship between the customer and the firm depends on a variety of factors, it seems appropriate for the manufacturer to reflect these priorities in their scheduling decisions. Accordingly, different tardiness and earliness penalties need to be assigned to different customers. Likewise, the costs of holding different jobs after completion inside the system will also be different. It is therefore important that the scheduling decisions reflect these priorities (or costs) with respect to earliness, tardiness and holding in the process of dispatching jobs in assembly job-shops. In such instances, it is appropriate to associate weights for earliness, tardiness and flowtime of jobs, and gauge the performance of rules by employing the weighted measures of performance (Scudder and Hoffmann, 1987 and Jensen et al., 1995). It also seems appropriate at this juncture to consider briefly the work done in the case of job-shop scheduling with the consideration of weights for earliness/tardiness/flowtime of jobs. Conway et al., 1960 and Rowe, 1960 are perhaps the first to consider the value-based dispatching of jobs in the case of job-shop scheduling. Other studies that are related to job-shop scheduling and those directly use cost based information in developing dispatching priorities include those of Aggarwal and McCarl, 1974 and Hoffmann and Scudder, 1983. Vepsalainen and Morton (1987) first demonstrated the weighted cost over time (COVERT) rule's superiority over the weighted shortest processing time (SPT) rule in the case of dynamic job-shop environment. The authors further developed the average-tardiness-cost (ATC) rule that uses a complex weighted criterion. The ATC rule has been shown to perform better than the weighted SPT and weighted COVERT rules for normalized weighted measures of tardiness. Kutanoglu and Sabuncuoglu (1999) showed that the priority rules which make use of operational information such as operation due-dates and operation processing times perform consistently better than their job-based counterparts and that the weighted SPT rule is more robust to changes in experimental settings. Kanet and Christy (1984), in their work, have stressed the importance of the problem of forbidden early shipment in a manufacturing system. A significant amount of work has been carried out in the area of single-machine scheduling involving early/tardy problem (Baker & Scudder, 1990). However, there appears to be no research work in the environment of multi-machines where serial operations are performed on the job (i.e. job-shops) with the consideration of earliness, tardiness and holding costs. Scudder and Hoffmann (1989), for randomly routed and flow shop environment, developed a two-class active and inactive queue system at each work center with jobs in the active queue having their operations start date reached. The authors found the performance of the time based rules, namely, the critical ratio and operation critical ratio rules, better than the value-based rules. The next important contribution in this area was due to Rohleder and Scudder (1992). The authors used net present value (NPV) and system inventory measures to evaluate a number of rules and found job-based rules performing well for both measures. In another study by the same authors (Rohleder & Scudder, 1993) in a dynamic job-shop environment, a new rule was developed to minimize the early/tardy costs ratio, which is a modified version of the rule (called EXPET rule) proposed by Ow and Morton (1989) for a single machine early/tardy problem. The authors concluded that the proposed rule clearly dominated the WCOVERT, earliest due date (EDD) and first come first served (FCFS) rules with respect to minimizing the early/tardy cost ratio. The importance of total cost criterion for evaluating the performance of the shop floor dispatching rules was highlighted by Yang and Sum (1994). They tested the time-based, value-based and slack-based rules proposed in the prior studies in a job-shop environment and proposed new composite dispatching rules. Their proposed rules are shown to perform better than the earlier rules in environments where early shipment of completed jobs is forbidden. In a recent study, Thiagarajan and Rajendran (2003) proposed dispatching rules with the primary measure of performance being the minimization of the total scheduling cost consisting of the sum of weighted flowtime and weighted tardiness of jobs, and the secondary measures of performance being the minimization of weighted mean flowtime, weighted mean tardiness, maximum weighted flowtime, maximum weighted tardiness and so on, considered separately. Their rules considered the weights for holding and tardiness, apart from considering the factors such as total work content remaining in the job, process time of the imminent operation, job due-date, earliest completion time of the job, and time-in-system. In the current study, the motivation for the development of new dispatching rules that incorporates weights for earliness, tardiness and flowtime has been derived from the findings of the survey on the available literature. Almost all researchers have so far assumed that the cost of earliness, the cost of tardiness and the cost of holding per unit time are the same, whereas in real-life situations, it need not be so. Further, the performance criteria used in a majority of such studies are time-based measures and only a few are cost-based measures of performance. It appears from the literature review that no work has been done with the consideration of earliness, tardiness and flowtime costs in an assembly shop environment where multi-level jobs are processed. Hence the current work is undertaken in two phases. In the first phase, the cost-consideration has included the weighted earliness and weighted tardiness of jobs, while in the second phase, the cost-consideration has included the weighted earliness, weighted tardiness and weighted flowtime of jobs. The current work can therefore be regarded as a follow-up work of Thiagarajan and Rajendran (2003). We first present the details of the first phase of our work, and then the details of the second phase of our work.