Multiple item batch scheduling model on a batch processor to minimize total actual flowtime parts through the shop

Abstract

This research is to address a problem of scheduling batches consisting of multiple item parts processed on a batch processor where each item requires a certain processing time which may differ from others. A number of parts are defined as a batch and processed simultaneously with sharing a set up time. A batch can be formed of the parts with different type of item and the processing time of batch equals the longest processing time of parts in the batch. It is assumed that an excessive duration of processing the parts will not lead to any defect, but increase the operating cost. The completed part must simultaneously be delivered at common due date, d. The objective is to minimise total actual flowtime of parts through the shop. A solution procedure to solve the problem is proposed and numerical examples are shown.

Multi-items Batch Scheduling Model for a Batch Processor to Minimize Total Actual Flow Time of Parts through the Shop

“…The actual flowtime has been applied to problems of batch scheduling by Halim et al [17,18,19], Sukoyo et al [20] and Zahedi et al [21] but they conduct batch scheduling research for job processors i.e., the machine that processes one job at a time. Hidayat et al [22,23] develop the actual flowtime of parts for batch scheduling problems on batch processors, and adopt it as an objective where parts to be processed are a single item with a common due date. Those model is further developed by Hidayat et al [24] into a condition where the parts should be delivered at different due dates.…”

“…The actual flowtime of batch (denoted by ) states the length of time the batch spends on the shop from its arrival time until its due date (see. equation 2)) (2A concept of the actual flowtime for parts of single item demanded on a common due date have been developed in Hidayat, et al [22]. Figure 1 shows the sequence of the N batches processed on a single batch processor.…”

“…The first model was developed for multiple items of parts with a common due date problem (MICD). The MICD is a development of a single item with common due date problem (abbreviated as SICD) in Hidayat, et al [22]. The difference between those two lies in the number of item type of parts, while simultaneously on a common due date.…”

“…Constraint (14) is the value of the binary variable. It is apparent that if index is eliminated, model M1 becomes SICD model in Hidayat, et al [22] The second model is developed for MIMD problem, which is the development of a single item with multi due dates problem (abbreviated as SIMD) in Hidayat, et al [24]. The ideal condition is when the entire parts can be processed within intervals , but if it can not be met then the part can be processed in other intervals before .…”

“…If the index is eliminated model M2 becomes model M1. Subsequently, if the index and are eliminated, model M2 becomes SICD model in Hidayat, et al [22].…”