A nonlinearly normalized back propagation network and cloud computing approach for determining cycle time allowance during wafer fabrication

Highlights

• A nonlinearly normalized BPN and cloud computing approach was proposed to establish tight upper bounds on the cycle time estimation.

• A case from a wafer fab was used to evaluate the effectiveness of the proposed method which was compared with various existing methods.

• The proposed methodology was improved by increasing the number of collaborating computing clouds.

• The proposed methodology was much more efficient under a cloud-computing environment than under other environments.

Abstract

This study investigated the determination of the allowance that must be added to the cycle time estimate, which is a critical concern when assigning internal due dates. Because no method for estimating cycle times is completely accurate, producing such estimates remains problematic but has rarely been addressed in the literature. A large allowance postpones the internal due date, diminishing company appeal when a factory manager negotiates with a customer. Therefore, in this study, a nonlinear approach was proposed to normalize the cycle times. After estimating the cycle time of a job by using a back propagation network, the allowance added to the cycle time can be effectively reduced through the collaboration of several computing clouds. Theoretical properties of the proposed method were validated, and a case from a wafer fabrication factory was used to evaluate the effectiveness of the proposed method in comparison with various existing methods. According to the experimental results, the proposed method facilitated establishing tight upper bounds on the cycle times. The proposed method was proven to be very effective.

Introduction

The objective of due date assignment, a critical topic in operations research and production control, is to guarantee a customer when and how an order can be delivered, and depends on the ability of the manager to fulfill an order and negotiate with the customer [21]. A due date can be set by an internal scheduler (i.e., an endogenous due date) or by an external agency (i.e., an exogenous due date) [24]. An internal due date is typically based on the cycle time estimate and used as a basis for negotiating with the customer to determine an external due date that will be met through proper job scheduling [15], [6]. Although the external due date is occasionally specified as the internal due date (as assumed by many previous studies), it often differs from the internal due date [1], [19].

Topics discussed in the relevant literature can be divided into three categories: cycle/completion time estimation [12], [13], [15], [36], [6], [7], [8], [9], due date assignment and factory scheduling [2], [29], [32], [4], and allowance determination [1], [19]. Most literature in this field pertains to estimating the cycle/completion time of a job to determine the internal due date. The cycle time (flow time, manufacturing lead time) equals the total processing time plus the waiting time. Methods used to estimate the cycle time can be classified into four categories: statistical analyses, simulations, soft computing, and hybrid approaches. Table 1 summarizes some examples of these methods.

However, the focus of this study was not on improving the accuracy of cycle time estimation; rather, an allowance was added to the estimated cycle time to determine the due date, which was internal and not directly based on scheduling jobs. If the internal due date had been directly used as the basis for job scheduling, then internal due date assignment and job scheduling would have become interdependent, requiring consideration as a whole, which is easy only in a small factory, but would be impractical for the wafer fab studied in this paper that included hundreds of machines and thousands of jobs. For a large-scale production system, the scheduling problem is recursive, and solving it requires extensive and time-consuming simulation and evaluation.

In addition, existing methods have the following problems:

• Estimating the cycle time of a job in a wafer fab is a nonlinear problem [16]. Adding the same allowance or an allowance that is proportional to the cycle time estimate by using methods such as the constant due date policy (CON), the slack policy (SLK), the total work content policy (TWK) [24], the random allowance policy (RAP), the selective allowance policy (SAP) [19], and the confidence interval method [36], cannot satisfy this requirement.

• Various studies (e.g., [21]) have investigated estimating the cycle time of a job by using a BPN, and subsequently modifying the values of the BPN parameters to establish the cycle time upper bound. However, the resulting nonlinear programming (NLP) problem is difficult to solve.

• Chen and Lin [20] and Chen [16] modified only the threshold on the output node of the BPN, efficiently and effectively establishing the upper bound. However, for some jobs, the upper bounds were not very tight.

To address these problems, in this study, a nonlinearly normalized back propagation network (BPN) and cloud computing approach was proposed and the relationship between the allowance and cycle time of a job was analyzed, enabling the clarification of problems associated with existing allowance determination methods. A nonlinear normalization approach, through which the tightness of the upper bound can be effectively improved, was proposed to normalize the cycle times. Clouds used in the proposed methodology belong to the category – data analysis as a cloud service (DAaaCS) [18], [28], which is particularly useful for small and medium sized enterprises (SMEs) [28]. Table 2 summarizes the differences between the proposed method and some existing methods.

The study objectives included the following:

• To add an allowance to the cycle time estimate used to determine the internal due date so that the completion time is earlier than the internal due date.

• To minimize the allowance that is added when determining the internal due date, enabling the negotiation of the external due date to be based on a favorable basis.

A large allowance can facilitate achieving the first objective (i.e., meeting the due date). However, an allowance that is excessively large is unwelcome; a balance is achieved by optimizing the second objective (Fig. 1).

The remainder of this paper is organized as follows. A literature review is presented in Section 2. Section 3 describes the BPN approach used to estimate the job cycle time in a wafer fab. The approach designed by Chen and Lin [20] was applied to modify the values of the BPN parameters and establish the cycle time upper bound. After the relationship between the allowance and cycle time of a job was regressed, the problem associated with the existing linear normalization method was addressed. Section 4 introduces a nonlinear normalization approach used to resolve the problem. Various theoretical properties of the nonlinear normalization approach were proven, and a cloud computing approach was proposed to improve the effectiveness of the nonlinear normalization approach. A case was used to illustrate the proposed method and compare it with existing allowance determination methods. Section 5 offers a conclusion and directions for future research.