2. Literature Review
2.4. Batch Processing Machine Scheduling Problems
In this dissertation, the aging test scheduling problem (ATSP) considers a parallel batch processing machine scheduling problem on the aging test operation in the module assembly process. In recent years, much research has focused on providing solutions to the batch processing machine (BPM) scheduling problems on a single or parallel batch processing machines. A comprehensive literature and a classification scheme on batch processing machine scheduling problems are presented by Potts and Kovalyov [73]. For the batch processing machine scheduling problems in semiconductor manufacturing, Mathirajan and Sivakumar [59] have provided a complete survey.
There are two types of batch processing machine scheduling problem, which are named as incompatible product family and compatible problem family. The former is
that jobs with different product families are mutually incompatible for processing in the same batch; the latter is assumed that jobs belonging to different product families may be simultaneously processed. In this dissertation, the aging test scheduling problem we investigated considers the batch processing of compatible product families. In problems of this type, the batch processing time is computed by the longest job processing time in that batch.
The literature regarding the BPM scheduling problems on a single or parallel batch processing machines with compatible product families is shown in Table 2-3. As presented in Table 2-3, the first researchers to address the batch processing scheduling problem arising in a burn-in oven of the final test in the semiconductor industry are Lee et al. [52]. They used dynamic programming-based algorithms and heuristics for a number of performance measures, such as maximum tardiness (Tmax), the number of tardy jobs (
Ui ), and maximum lateness time (Lmax) on a single batch processing machine. They have also presented heuristics for the parallel batch processing machine scheduling problem with the minimum makespan (Cmax) and maximum lateness time (Lmax) criteria. They have explored the area of scheduling batch processing machines and offered a classification of complexity for the investigated problems. Furthermore, Chandru et al. [12][13], DuPont and Ghazvini [30], Poon and Yu [71], Mönch et al. [63] provided the solutions for the single/parallel batch processing machine scheduling problems with identical job sizes. Although the single batch processing machine scheduling problem (Uzsoy [86], Ghazvini and DuPont [37], Zhang et al. [94], DuPont and Dhaenens- Flipo [29], Melouk et al. [60], ErramilliTable 2-3The literature related to the batch processing machine scheduling problem with compatible product families.
Year Authors and Refs. Shop type Ready time
Job size Performance criterion 1992 Lee et al. [52] single machine/
parallel machines
1993 Chandru et al. [12] single machine equal identical Cmax
1993 Chandru et al. [13] single machine/
parallel machines
equal identical Cmax
1997 DuPont and Ghazvini [30]
single machine equal identical Fi
2004 Poon and Yu [71] single machine equal identical
Ci2006 Mönch et al. [63] single machine equal identical
di Ci1994 Uzsoy [86] single machine equal non-identical Cmax,
Ci1998 Ghazvini and DuPont
[37] single machine equal non-identical Fi
2001 Zhang et al. [94] single machine equal non-identical Cmax
2002 DuPont, and Dhaenens-Flipo [29]
single machine equal non-identical Cmax
2004 Melouk et al. [60] single machine equal non-identical Cmax
2004 Damodaran and Srihari
single machine equal non-identical
w Ti i2006 Kashan et al. [49] single machine equal non-identical Cmax
1999 Lee and Uzsoy [51] single machine unequal identical Cmax
2000 Sung and Choung [82] single machine equal/
unequal identical Cmax
2002 Sung et al. [83] single machine unequal identical Cmax
2002 Wang and Uzsoy [89] single machine unequal identical Lmax
2004 Li and Lee [55] single machine unequal identical Tmax,
Ui2004 Poon and Zhang [70] single machine unequal identical Cmax
2004 Deng et al. [26] single machine unequal identical
w Ci i2005 Deng et al. [27] single machine unequal identical
Ci2005 Poon and Yu [72] single machine unequal identical Cmax
2006 Gupta and Sivakumar [42]
single machine unequal identical Tmax,
Ui ,
T ni2004 Van Der Zee [87] single machine dynamic arrival
identical Fi
2004 Chang and Wang [15] single machine unequal non-identical
Ci2006 Chou et al. [21] single machine unequal non-identical Cmax
2007 Chou [20] single machine unequal non-identical Cmax
2007 Wang et al. [91] single machine unequal non-identical Cmax
2007 Chou and Wang [22] single machine unequal non-identical
w Ti i2004 Chang et al. [14] parallel machines equal non-identical Cmax
2007 Mönch and Unbehaun [64]
parallel machines equal identical
di Ci2007 Van Der Zee [88] parallel machines dynamic
arrival non-identical Fi
2008 ATSP (this dissertation) parallel machines unequal non-identical Cmax
and Mason [31], Kashan et al. [49]) and the two batch processing machines in a flow shop (Damodaran and Srihari [25]) took the non-identical job sizes into consideration to reflect more practical situations, they have assumed that the ready times of jobs for batch processing machines are equal. This assumption prevents the developed procedures from being directly applied to the parallel batch processing machine scheduling problem investigated in this dissertation because the ATSP involves unequal ready times.
For the single batch processing machine scheduling problem with non-identical job sizes and equal ready times, Uzsoy [86] investigated this type problem to minimize the total completion times (
Ci ) of the jobs and makespan. He has also provided bin-packing-based heuristics for minimizing makespan and has used the branch and bound approach to minimize the total completion times. He also developed effective heuristics for the criteria of minimum makespan and minimum total completion time. Erramilli and Mason [31] have investigated the multiple orders per job (MOJ) problem on a single batch processing machine. They grouped different customer orders into jobs and combined jobs into batches and scheduled them on a single batch processing machine to minimize the total weighted tardiness (
w Ti i ) oforders. Damodaran and Srihari [25] have proposed two mathematical models with the minimum makespan criterion to schedule batches of jobs on two machines in a flow shop. Kashan et al. [49] has addressed the need to minimize makespan by employing two different genetic algorithms (GAs) for scheduling jobs with non-identical sizes on a single batch processing machine. Unfortunately, all the above
models do not consider the unequal ready time that is a common phenomenon in module assembly factories.
Although Lee and Uzsoy [51], Sung and Choung [82], Sung et al. [83], Wang and Uzsoy [89], Li and Lee [55], Poon and Zhang [70], Deng et al. [26], [27], Poon and Yu [72], Gupta and Sivakumar [42], and Van Der Zee [87] have considered the characteristic of unequal ready times, they limited their applications to a single batch processing machine and an identical job size. Lee and Uzsoy [51] have provided efficient heuristics to solve the scheduling problem arising in the final test phase of semiconductor manufacturing. To minimize the maximum completion time on a single batch processing machine with dynamic job arrivals, they designed three algorithms (GRLPT, DELAY, and UPDATE) to find the approximate solutions.
Sung and Choung [82] have presented a branch-and-bound algorithm and several heuristics to solve the static and dynamic cases on a single batch processing machine.
Their objective was also to minimize the makespan of all jobs. Sung et al. [83] have considered a single batch processing machine with job families and dynamic job arrivals. The performance measure used to evaluate a schedule is the minimum makespan. Van Der Zee [87] has also presented the dynamic control of a batch processing machine; his objective was to find the minimum average flow time per product in the presence of compatible product families.
Moreover, in recent years, a series of research papers regarding single batch processing machine scheduling problem with unequal ready times and non-identical job size are provided by Chang, Chou, and Wang [15][20][21][22][91]. First, Chang and Wang [15] investigated the single machine problem of scheduling semiconductor
burn-in operation with non-identical job sizes and unequal ready time. They provided an efficient heuristic algorithm and examine the effect of arrival time and processing time on minimizing the total completion time. Subsequently, Chou et al. [21] changed the objective into minimal makespan and proposed a merge-split procedure to improve the solution obtained by the longest processing time batch first fit (LPT-BFF). Furthermore, two hybrid genetic algorithms (GA) were also provided.
Following that, Chou [20] presented a solution procedure to joint GA and DP (dynamic programming). Wang et al. [91] provided a mix integer programming model to describe problem complexity. Simultaneously, a hybrid forward/backward algorithm is also presented and the computational results showed good performances of this algorithm in term of solution quality within a modest computational time.
Moreover, Chou and Wang [22] took the distinct due date into consideration and investigated the single machine scheduling problem with a minimal total weighted tardiness criterion. They proposed one MIP model and two hybrid heuristics involving a rule-based, GA, and DP algorithms. The computational results indicated GA-based algorithm outperformed the rule-based algorithm in terms of solution quality for small size problems.
More recently, the parallel batch processing machine scheduling problem with compatible product family characteristic is considered by Mönch and Unbehaun [64], Chang et al. [14], and Van Der Zee [88]. Mönch and Unbehaun [64] presented a parallel batch processing machine scheduling problem in which jobs have identical job sizes and equal ready times. The objective is to minimize the sum of the absolute deviations of completion times from the due date of all jobs. They proposed three heuristics based on exact algorithm, genetic algorithm, dynamic programming
techniques. Chang et al. [14] have provided a mathematical model and developed an algorithm based on simulated annealing (SA) approach to minimize makespan for the scheduling problem with equal ready times and non-identical job size. They have not included the unequal ready times in their model. Van Der Zee [88] extended the scheduling problem [87] involved single machine to parallel machines. The objective of the parallel batch scheduling problem is to minimize average flow time per product.
He developed a new look-ahead strategy to solve this problem. However, the processing time in his model is assumed fixed. Their solution procedure cannot be applied to ATSP directly.
At the time this dissertation was being written, the author was not aware of any other studies of the parallel batch processing machine scheduling problem with unequal ready time, non-identical job size, and compatible product family characteristics. Therefore, this dissertation arises from the need in industry to consider jobs with these practical situations, which are processed on identical parallel batch processing machines.