Heuristic Scheduling of Serial-Batch Processor System for Cycle Time by mercy2beans111

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									                               007-0780

Heuristic Scheduling of Serial-Batch Processor System for
                 Cycle Time Reduction


                          Abdullah Cerekci
           Department of Industrial and Systems Engineering
                       Texas A&M University
                  College Station, TX 77843-3131
                          cerekci@tamu.edu
                           (979)-845-5467



                          Amarnath Banerjee
           Department of Industrial and Systems Engineering
                       Texas A&M University
                  College Station, TX 77843-3131
                         banerjee@tamu.edu
                           (979)-845-5110




   POMS 18th Annual Conference Dallas, Texas, U.S.A. May 4 to May 7, 2007
Abstract

Control of batch processors is one of the most important issues in semiconductor manufacturing.
Ineffective dispatching policies may cause an increase in overall cycle time. This paper presents a
real-time scheduling heuristic for a production unit consisting of a serial processor feeding a
batch processor. In this multiple product batching problem, our objective is to reduce the average
waiting time in the batch processor’s queue. Our automated policy uses downstream information
to schedule the next lot in the serial processor when the batch processor is busy. When the batch
processor is idle, it uses upstream information to decide whether to start the batch process or wait
for another arrival of any type existing in the serial processor’s buffer. The problem setting allows
the selection of the next arriving lot type to the batch processor out of available types at the serial
processor to reduce the average cycle time. Simulation is used to benchmark our approach with
other policies. Results show that using upstream and downstream information reduces waiting
times in the batch queue.

Keywords: Batch Control, Semiconductor Manufacturing, Serial-Batch System, Cycle Time
Reduction


1. Introduction

Batch process control in a multi-product manufacturing system is the set of decisions

about which product type is batched at what time with how many products. If the batch

processor is available and the number of products ready to be processed is less than the

batch capacity for all product types, the decision is between waiting for future arrivals

and loading a partial batch to the processor. The tradeoff between these two alternative

decisions is the utilization of the batch processor versus the additional delay of the

products currently waiting for processing. The constraints of these decisions are as

follows. (i) Products of different types can not be processed together. (ii) Once a batch

process starts, it can not be interrupted. (iii) Batch processing times are independent of

the number of products that are batched.



Although scheduling and control of batch processor research is encountered in many

manufacturing industries, it has been extensively studied in semiconductor manufacturing

[1]. Batch processors are the main sources of product flow variations in semiconductor
manufacturing systems. The collection of products to the batches results in a non-smooth

product flow, and the existence of re-entrant flow complicates this further. Batch

processor tools are very expensive to purchase so; it is desirable to maintain high

utilization of these equipments. Therefore maintaining an effective batch control policy is

very important to avoid any bottleneck situations. Cycle time is one of the most common

performance measures in semiconductor industry since the due dates are directly related

to the length of the cycle time. Highly competitive market rules make cycle time

reduction the first goal of most semiconductor companies. Shorter cycle times tend to

help in responding to market demands quickly because of lower levels of WIP. Assuming

all of the processing times are deterministic, reducing the queueing times reduces cycle

time.



In a semiconductor manufacturing environment, it is very common that a batch process

operator communicates with the operator at the upstream process to see the arriving

products and subsequently be involved in the decision of next job (as a pull process).

Most manufacturing companies employ computerized shop floor control systems which

can provide data to be used in dynamic scheduling systems. Availability of this real-time

data motivates us to look at the batch control problem from a system-wide perspective by

including a serial processor as the upstream. In this paper, we consider a small multi-

product manufacturing system composed of a serial processor followed by a batch

processor (Figure 1). In this manufacturing system, both processors have infinite size

buffers. We will use “upstream information” to refer to the serial processor’s buffer

information, “upstream control” to refer to the next job decision process of the serial
processor, “downstream information” to refer to the batch processor’s buffer information

and “downstream control” to refer to the batch process control in the rest of this paper.




                              Figure-1 Serial-batch processor system



Upstream and downstream information are assumed to be available for both upstream and

downstream control processes. The objective of this paper is to analyze the performance

of upstream and downstream control policies under the availability of upstream and

downstream information. In section 2, we provide a literature review about existing batch

control and scheduling strategies. In section 3, we describe our downstream control

heuristic which utilizes upstream information. Furthermore, we propose a simple

upstream control policy, and we outline the benchmarking policies. In section 4, we

provide simulation-based experimentation to benchmark the upstream and downstream

control policies. We discuss the simulation results in section 5, and we conclude with

future research directions in section 6.



2. Literature Review

Scheduling and control of batch processors has been an interesting research topic for

decades. Mathirajan [1] reviews the literature by classifying the problem configuration as

stochastic and deterministic systems. Furthermore, he groups the researches into single
workstation batch processor, batch processor with upstream and downstream machines

and batch processor with re-entry flow problems. Zee et al. [2] categorize the existing

researches due to the amount of information that is known about the future arrival pattern

of the products. According to this categorization, there are three problem types: problems

with no future information available, problems with full knowledge of future arrivals, and

problems with a limited number of near future arrivals are known. The most famous

strategy for the first category is Minimum Batch Size (MBS) rule developed by Neuts

[3]. In this batching strategy, if the quantity in the queue is less than a specified number,

the decision is to wait till the queue meets the requirement. Duenyas and Neale [4]

extended this approach for multiple product problems and proposed a heuristic that

utilizes estimated arrival pattern. Uzsoy [5] developed efficient algorithms for single

batch workstation problem with full knowledge of the future arrivals. Dynamic real-time

control strategies which are under the third category incorporate the knowledge of future

arrivals. Glassey and Weng [6] developed the first batching strategy of this category for a

single batching processor with single job type. In their Dynamic Batching Heuristic

(DBH), the controller checks the n future arrivals to determine the best arrival epoch at

which loading the batch process minimizes average waiting time in the batch queue.

Fowler et al. [7] extended the idea of look-ahead for single and multiple job types with

their Next Arrival Control Heuristic (NACH). In this heuristic strategy, following a

rolling horizon fashion, the controller considers only the next future arrivals of each job

type. The decision is either to start the batch process with one of the job types or to wait

for the next arrival to repeat the heuristic. They later generalized this heuristic for

multiple batch processors [8]. Weng and Leachman [9] adapted the DBH with the
average queue size objective in their Minimum Cost Rate (MCR) heuristic. Zee et al. [10]

developed an extension of MCR for the multiple batch server problems.



Robinson et al. [11] combined the ideas of MCR and NACH with additional downstream

information. They considered a batch processor followed by a serial processor as their

manufacturing system and proposed a rolling horizon control heuristic for minimizing the

total waiting times spent in batch and serial processor queues. The contributions of

researches on multiple station problems are very significant because of their system-wide

perspective. Multiple station problems include batch-batch, serial-batch, batch-serial and

serial-batch-serial manufacturing systems. With full knowledge of the future arrivals to

the first station, Ahmadi et al. [12], and Kim and Kim [13] developed scheduling

algorithms for multi station manufacturing systems that include batch station. With the

lack of information, Gurnani et al.[14], and Neale and Duenyas [15] developed threshold

policies for the same problems using queueing theory and dynamic programming

respectively. In this paper, we take multiple station batch control problem with limited

future arrival information. The setting of the problem allows the upstream information in

the downstream control and the downstream information in the upstream control. This

two way information sharing helps in finding better heuristics for dynamic control of the

serial-batch manufacturing systems.



3. Serial and Batch Processor Control Policies

The properties of the serial-batch manufacturing system in this paper are as follows. Both

processors are perfectly reliable and serial processor has 100% utilization. Serial
processor’s processing time is deterministic and same for all product types, which

guarantees that the inter-arrival time to the batch processor’s buffer is constant. A

controller is attached to the manufacturing system to make decisions with upstream and

downstream information (Figure 2).




                           Figure-2 Downstream and Upstream Control




In this production flow structure, there are three types of decision epochs for upstream

and downstream control:

   Type-I: The time epoch when there occurs a departure from the serial processor while

   the batch processor is busy. In this decision epoch, the output of the upstream control

   decision is the next job on the serial processor. All of the product types lying in the

   upstream information are considered in the decision process.

   Type-II: The time epoch when there occurs an arrival to the batch processor’s buffer

   while batch processor is idle. In this decision epoch, policies are performed for

   downstream control and upstream control. Only the arriving product type is

   considered for the former, and all of the product types in the upstream information are

   considered for the latter.
   Type-III: The time epoch when the batch processor becomes idle after completing a

   job and there are some products waiting in its buffer. In this decision, downstream

   control is performed using downstream and upstream information. If the decision is to

   wait for future arrivals, upstream control is performed to support the downstream

   control.

N = number of product types
t0 = current decision epoch
ti = ith arrival epoch after t0
Tj = batch processing time of product type j
qj = number of products of type j existing in the batch processor’s buffer
rj = number of product type j existing in the serial processor’s buffer
Q = total number of products in the batch processor’s buffer
Cj = batching capacity for product type of j
B1 = buffer for the serial processor
P1 = serial processor
B2 = buffer for the batch processor
P2 = batch processor
TNj = next arrival time of product type j
Dj = delay caused by decision for product type j
                         Table 1: Notations used in the control heuristics
3.1 Upstream Control Policies

Upstream control policies determine the next job of the serial processor at type-I decision

epochs. These policies utilize the downstream and/or upstream information to help

reduction in average waiting times of products at the batch processor’s buffer. Here we

consider four simple policies:

   •   Myopic Policy loads j* = arg max{r j | j ∈ B1 }
                                         j



   •   Greedy Look-ahead Policy (GLA) loads j* = arg max{q j | j ∈ B1 }
                                                                   j



   •   Weighted Shortest Processing Time Logic (WSPT) loads j* which is found by

       the following simple rule.

       Define the sets A1 and A2 as follows:
              i is in set A1 if product type i exists in B1 and qi<Ci
               i is in set A2 if product type i exists in B1
        If Q=0 or A1 is empty
               j = argmax {r j | j ∈ A2 }
        Else
               j = argmin {(Q − q j ) × T j | j ∈ A1 }
        End if


3.2 Downstream Control Policy

Downstream control policies are used to decide whether to start the batch process of any

product type or to wait for future arrivals. When there exist full batches in B2, waiting for

future arrivals only increase the total waiting time of the products waiting to be

processed. Therefore the trivial decision is to start batch process immediately with one of

the full batches. However, when there are only partial batches in B2, then the decision

requires further analysis of upstream information. We propose a batch control heuristic

that makes use of the upstream information and involves the upstream control if

necessary.


3.2.1   Next Arrival Scheduling based Control Heuristic (NASCH)

As we have mentioned earlier, an operator at a batching station usually communicates

with the upstream station to share upstream information. Furthermore, in order to run the

next batch with a high utilization, the operator may get involved in the upstream control

process to receive a specific product type as the next arrival. In NASCH, we make use of

this knowledge to come up with an efficient automated batch control system. NASCH is

the combination of two decision logics: Arrival Decision Logic that is active at type-II

decision epochs and Departure Decision Logic that is active at type-III decision epochs.
   a) Arrival Decision Logic:

In this downstream control logic, the controller checks for only the arriving product type.

Assume product type j has arrived and it doesn’t complete the full batch. Controller uses

upstream information to see if the serial buffer has any product of type j. If it doesn’t

have any, the trivial decision is to start the batch processor. On the other hand, if

upstream information shows there is at least one product of type j in the buffer then Mj is

calculated for this product type as in (1). Mj is the gain/loss of the total delay time by

waiting for another product of type j. Here TNj is the discrete processing time of the serial

processor by assuming product type j is the next job.

                                                   N
                     M j = {(T j − TN j -t 0 )-(          q i ) × (TN j − t 0 )              (1)
                                                   i =1


Here are the detailed steps of this logic followed by the controller:

Check if there is a full load of type j after this arrival:
If yes,
        Start the batch processing of product type j immediately
Else
        Check if there is any product type j existing in B1
        If yes
                                                                 N
                  Calculate M j = {(T j − TN j -t 0 )-(                 q i ) × (TN j − t 0 ) as assuming the next
                                                                 i =1
                  job on the serial process will be from type j (TNj = t1)

                  If Mj > 0
                          Load the first product type j to P1 and the decision is to wait for
                          the next decision epoch
                  Else
                          Start the batch processing of product type j immediately
                  End If
         Else
                  Start the batch processing of product type j immediately
         End If
End If
    b) Departure Decision Logic

All product types existing in B2 are considered by the controller in this downstream

control logic. Once the batch processor becomes idle the controller checks all product

types within the upstream information. Following a very similar logic to NACH of

Fowler et al. [7], controller checks for every product type whether it is preferable to load

a partial batch or wait for another arrival of that type in the lack of full batches. For those

of which the controller’s decision is to load a partial batch, total delay change that would

be caused by this action is calculated as in (2). Here, different than NACH, we consider

all possible arrivals during the batch process of type j and we normalize this number by

the batch processing time Tj.

                               N                              N
                   Dj = (           ( qi × T j ) +                (t + T j − t i )) T j
                                                                      0                               (2)
                            i =1,i ≠ j                 i|t0 <ti ≤t0 +T j


For those of which the controller’s decision is to wait for another arrival of this type, total

delay change of this action is calculated as in (3). Same differences mentioned above also

apply for this formulation. In addition to those, TNj is assumed to be the discrete constant

processing time of the serial processor plus the remaining time of the current job on the

processor if the current job is not of type j. In case the current job is of type j, then TNj is

assumed as the remaining time of the current job. The rest of the logic is exactly same as

NACH, except if the decision is to wait for another arrival of product type j, downstream

control requires an upstream control to load product type j at the serial processor.

         N                               N
Dj = (          (qi × TN j ) +                  (T j × qi ) +                      (T + TN j − ti )) (T j + TN j ) (3)
                                                                                         j
         i =1                      i =1,i ≠ j                   i|{t0 <ti ≤T j +TN j &ti ≠TN j }
Following are the steps of this logic in detail:

Check if there are any full loads in B2:
If yes,
        For all j that has full loads in B2, calculate W j = (Q − min (q j ,C j ))T j . Start the
        batch processing of product type j* = arg min{W j } immediately
                                                                   j

Else,
        For all j
                Check if there is any product type j existing in B1
                If yes,
                        calculate M j = {(T j − TN j − t 0 ) − Q(TN j − t 0 ) where,
                                    t1          if the current job in the serial processor is of type j
                         TN j =
                                    t2              o.w

                         If Mj    0,
                                  add j to set S1 (set of product types that the decision is to
                                  start)
                         Else,
                                  add j to set S2 (set of product types that the decision is to
                                  wait for the next arrival of the same type)
                       End If
              Else, add j to set S1
              End If
        End For
              If S1 is empty,
                       the global decision is to wait, load first product type j* on P1
                       where j* = arg max{M j } and wait for the next decision epoch
                                                 j

                Else if S2 is empty,
                        the global decision is to start immediately. Start the batch
                        processing of product type j* = arg min{W j } immediately
                                                                                j

                 Else if there are some product types in S1 and some in S2
                          For j S1, calculate
                                      N                            N
                          Dj = (           ( qi × T j ) +              (t + T j − t i )) T j
                                                                           0
                                   i =1,i ≠ j               i|t0 <ti ≤t0 +T j

                         End For
                         For j S2,
                                 t    if the current job in the serial processor is of type j
                         TN j = 1
                                 t2      o.w.
                         Then, calculate
                          N                          N
                 Dj = (          (qi × TN j ) +                (T j × qi ) +                      (T + TN j − ti )) (T j + TN j )
                                                                                                        j
                          i =1                    i =1,i ≠ j                   i|{t0 <ti ≤T j +TN j & ti ≠TN j }


                End If
         End For
         Then choose j* = arg min{D j }
                                    j

         If j* S1,
                start the batch processing of product type j* immediately
         Else,
                load first product type j* on P1 and wait for the next decision epoch
         End If
End If

4. Simulation Model and Experiments

Simulation is a reliable tool to compare this type of real-time heuristics. The two station

manufacturing model has been simulated using VB.net on an Intel Xeon Processor with a

CPU of 3.60 GHz. Serial station is the arrival station to the system and the batch station

is the departure station. Lots arrive to the serial station with a constant inter-arrival time

that is same as the service time of the serial processor. Besides, there is an initial WIP in

the serial station’s buffer together with the previous property guaranteeing the 100%

utilization for the serial station. Once a lot departs from the serial processor, it arrives

immediately to the batch station’s buffer. We assume, for simplicity, no breakdowns for

the serial and the batch processors. Since the serial processor is always kept busy, the

inter-arrival times of the serial station and the batch station are same and equal to 1/ .



In the experimentation, product mix ratios, P, batch processing times, T, batching

capacities, C and the batch processor’s traffic intensity,                           are used to find the constant

inter-arrival time 1/ using formula (4),
                                                     ρ
                                    λ =        N
                                                     P jT    j
                                                                      (4)
                                              j =1    C j
where j stands for product type j. For the design of experiments, we have seven factors to

create different simulation scenarios which are summarized in Table 2. MBS and

NASCH are the alternatives for batch control strategy. Three serial control policies

mentioned in section 3.1 with the FIFO policy compose the four alternatives of serial

control strategy. We have four alternatives for number of products, two alternatives for

product mix, three alternatives for batch capacity, three alternatives for batch processing

times and three alternatives for the traffic intensity of the batch processor. Using these

combinations, our simulation experiment creates 2x4x4x2x3x3x3 = 1728 scenarios.

No    Factor                           Levels
                                       MBS
1     Batch Control Strategy
                                       NASCH
                                       FIFO
                                       WSPT
2     Serial Control Strategy
                                       MYOPIC
                                       GLA
                                       2
                                       3
3     Number of Products
                                       4
                                       5

                                                      2 Products   3 Products           4 Products                 5 Products
                                        Equal         (0.5, 0.5)   (0.34, 0.33, 0.33)   (0.25, 0.25, 0.25, 0.25)   (0.2, 0.2, 0.2, 0.2, 0.2)
4     Product Mix
                                        Dominant      (0.7, 0.3)   (0.5, 0.4, 0.1)      (0.4, 0.4, 0.1, 0.1)       (0.35, 0.35, 0.1, 0.1, 0.1)
                                        Same          (5, 5)       (5, 5, 5)            (5, 5, 5, 5)               (5, 5, 5, 5, 5)
5     Capacity By Product               High          (7, 2)       (7, 6, 2)            (7, 6, 3, 2)               (7, 6, 3, 2, 1)
                                        Low           (2, 7)       (2, 3, 7)            (2, 3, 6, 7)               (1, 2, 3, 6, 7)
                                        Same          (25, 25)     (25, 25, 25)         (25, 25, 25, 25)           (25, 25, 25, 25, 25)
6      Batch Processing Time By Product High          (40, 10)     (40, 25, 10)         (40, 30, 20, 10)           (40, 30, 25, 20, 10)
                                        Low           (10, 40)     (10, 25, 40)         (10, 20, 30, 40)           (10, 20, 25, 30, 40)
                                        0.5
7     Traffic Intensity                 0.8
                                        0.95
                                Table 2: Design of experiments used in simulation




10 replicates having a run length of 10000 time units with a warm-up of 500 time units

are taken for every scenario. In addition to this, all alternative MBS levels are tested to

find the best performing MBS level for each scenario. The performance measure we use

as the output of the simulation is the normalized average delay time which is found by
normalizing average waiting time of lots in the batch server queue by average processing

time of lots in the batch server.



5. Results and Discussion

All scenarios explained in the previous section are simulated to compare the

performances of upstream control policies and downstream control policies. For

downstream control, Table 3 presents the performance improvement gained by using

NASCH. For a specific scenario, the percentage improvement has been calculated by

comparing the NASCH performance with the best MBS performance. On average,

NASCH improves the average waiting times by 13.8% and 14.6% with WSPT and GLA

respectively. Figure 3a shows the percent of the scenarios that NASCH performed better

than MBS for different upstream control policies and different number of product types.

The success rate of NASCH is 88% on the average. Figure 3b shows the improvement

percentage from the same perspective as Figure 3a.

N u m b er o f Pro d u cts   T raffic In ten sity   F IF O   W SPT    M Y O P IC    G LA

            2                        0.5            14.76%   16.88%      17.83%    12.51%
            2                        0.8             4.14%   10.12%       4.95%    17.10%
            2                       0.95             8.97%   10.66%       9.23%    12.43%
            3                        0.5            12.92%   17.66%      17.40%    12.94%
            3                        0.8             5.86%   17.04%       7.53%    12.73%
            3                       0.95             8.28%   14.66%       9.16%    11.75%
            4                        0.5             6.61%   14.58%       6.94%    14.42%
            4                        0.8             4.43%   14.73%       4.44%    12.85%
            4                       0.95             8.24%   13.54%       8.67%    13.48%
            5                        0.5             6.71%   11.21%       9.23%    21.08%
            5                        0.8            10.31%   14.67%      11.23%    17.17%
            5                       0.95             8.60%    9.43%       9.63%    17.35%
           All                       0.5            10.25%   15.08%      12.85%    15.24%
           All                       0.8             6.19%   14.14%       7.04%    14.97%
           All                      0.95             8.52%   12.07%       9.17%    13.75%
           All                       All             8.32%   13.77%       9.69%    14.65%

                                 Table 3: Performance improvement by NASCH
It is very clear that NASCH improves the average waiting time performance better with

WSPT and GLA. The main reason of this result is that both WSPT and GLA use

upstream information as a complimentary match for NASCH which uses downstream

information. Finding the best performing MBS level is a big issue in a fab scheduling as

well as in the simulation experiments. In order to give an idea, for 5 product types case

the average simulation times with MBS rule is 249 seconds whereas it is 0.23 seconds

with NASCH.



                                                    NASCH vs MBS                                                                         NASCH vs MBS
                              100.00%                                                                                 20.00%
                                                                                        Percentage improvement with
Success Percentage of NASCH




                                                      MYOPIC




                                                                                                                      18.00%
                                                                       WSPT




                               90.00%
                                          MYOPIC




                                                                               MYOPIC
                                                                                  GLA




                                                                                                                                                                                         GLA
                                             FIFO




                                                       FIFO
                                                      WSPT

                                                       GLA




                                                                                FIFO
                                                                               WSPT
                                                                   MYOPIC
                                                                       GLA




                               80.00%                                                                                 16.00%
                                                                    FIFO




                                                                                                                                                 WSPT
                                        WSPT

                                         GLA




                               70.00%                                                                                 14.00%




                                                                                                                                                                  WSPT
                                                                                                                                       GLA




                                                                                                                                                                           GLA
                                                                                                  NASCH



                               60.00%                                                                                 12.00%




                                                                                                                                                         GLA
                                                                                                                                    WSPT




                                                                                                                                                                                     WSPT
                                                                                                                                                     MYOPIC
                               50.00%                                                                                 10.00%


                                                                                                                               MYOPIC




                                                                                                                                                                                 MYOPIC
                                                                                                                      8.00%     FIFO




                                                                                                                                              FIFO
                               40.00%




                                                                                                                                                                                 FIFO
                                                                                                                      6.00%




                                                                                                                                                                      MYOPIC
                               30.00%




                                                                                                                                                               FIFO
                               20.00%                                                                                 4.00%
                               10.00%                                                                                 2.00%
                                0.00%                                                                                 0.00%
                                            2             3            4         5                                                 2                 3                4              5

                                                     Number of Product Types                                                                 Number of Product Types



                                    Figure-3a Success rate of NASCH                                    Figure-3b Performance improvement by NASCH




For upstream control comparisons, we have observed the performances of the upstream

policies with MBS and NASCH separately. Figures 4a and 4b present these results from

traffic intensity side of view for MBS and NASCH downstream control policies

respectively. The values are the percentage of performance improvements compared to

baseline FIFO policy. Under both MBS and NASCH control policies, the performances

of WSPT and GLA get lower with increasing traffic intensity at the batch processor. For

higher utilization of the batch processor, both policies seem to converge to same
performance level. Myopic policy performs poorly, almost same as FIFO for the high

intensity levels.

                                           Upstream control (MBS)                                                                      Upstream control (NASCH)
                              35.00%                                                                                        40.00%
Percentage improvement from




                                                                                             Percentage improvement from
                              30.00%                                                                                        35.00%

                              25.00%                                                                                        30.00%
        FIFO policy




                                                                                                                            25.00%




                                                                                                      FIFO policy
                              20.00%
                                                                                                                            20.00%
                              15.00%
                                                                                                                            15.00%
                              10.00%
                                                                                                                            10.00%
                               5.00%
                                                                                                                             5.00%
                               0.00%
                                                                                                                             0.00%
                                                0.5                0.8              0.95
                                                                                                                                             0.5                0.8                 0.95
                       WSPT            MYOPIC         GLA    Traffic intensity                                   WSPT               MYOPIC         GLA   Traffic intensity


                        Figure-4a Traffic intensity levels with MBS                                            Figure-4b Traffic intensity levels with NASCH


In figure 5a and 5b the simulation results are grouped by batch capacity alternatives.

Unbalanced batch capacities for different product types decrease the performance of

WSPT and GLA. On average GLA outperforms WSPT by 8% in both batch capacity

levels.

                                           Upstream control (MBS)                                                                     Upstream control (NASCH)
                               35.00%                                                                                      40.00%
Percentage improvement from




                                                                                           Percentage improvement from




                               30.00%                                                                                      35.00%
                                                                                                                           30.00%
                               25.00%
                                                                                                    FIFO policy




                                                                                                                           25.00%
        FIFO policy




                               20.00%
                                                                                                                           20.00%
                               15.00%                                                                                      15.00%

                               10.00%                                                                                      10.00%

                                5.00%                                                                                      5.00%
                                                                                                                           0.00%
                                0.00%
                                                                                                                                             high-low                        same
                                                  high-low                       same
                                                                                                                                                          Batch Capacity
                                                              Batch Capacity
                     WSPT              MYOPIC         GLA                                                         WSPT              MYOPIC         GLA


                              Figure-5a Batch capacity levels with MBS                                             Figure-5b Batch capacity levels with NASCH


Different product-mix levels do not have a significant effect on the performances of both

WSPT and GLA. Figures 6a and 6b present the steady performances for different

product-mix levels. On the other hand, batch processing times have an impact on the
performances. Figures 7a and 7b present the increasing performance of WSPT and GLA

when the batch processing times are equal for different product types.



                                            Upstream control (MBS)                                                                Upstream control (NASCH)
                               35.00%                                                                                 35.00%
Percentage improvement from




                                                                                      Percentage improvement
                               30.00%                                                                                 30.00%




                                                                                          from FIFO policy
                               25.00%                                                                                 25.00%
        FIFO policy




                               20.00%                                                                                 20.00%

                                                                                                                      15.00%
                               15.00%
                                                                                                                      10.00%
                               10.00%
                                                                                                                       5.00%
                                5.00%
                                                                                                                       0.00%
                                0.00%                                                                                                   dominant                         equal
                                                 dominant                 equal                                                                            Product Mix
                                                            Product Mix                                                 WSPT      MYOPIC             GLA
                     WSPT               MYOPIC       GLA


                              Figure-6a Product-mix levels with MBS                                           Figure-6b Product-mix levels with NASCH



                                            Upstream control (MBS)                                                                Upstream control (NASCH)
                               35.00%                                                                                   40.00%
Percentage improvement from




                                                                                        Percentage improvement from




                               30.00%                                                                                   35.00%

                               25.00%                                                                                   30.00%
        FIFO policy




                                                                                                                        25.00%
                                                                                                FIFO policy




                               20.00%
                                                                                                                        20.00%
                               15.00%
                                                                                                                        15.00%
                               10.00%
                                                                                                                        10.00%
                                5.00%
                                                                                                                         5.00%
                                0.00%
                                                                                                                         0.00%
                                              high              low            same
                                                                                                                                        high               low            same
                       WSPT             MYOPIC       GLA    Batch Process Time                                                                         Batch Process Time
                                                                                                            WSPT               MYOPIC          GLA


                              Figure-7a Batch Process Times with MBS                                       Figure-7b Batch Process Times with NASCH


As it is observed, GLA outperforms WSPT from all alternative factors we defined earlier.

However, the patterns they are following are almost same, which explains that the logic

behind these approaches are similar. Both policies use the downstream information, GLA

simplistically utilizes the queue size while WSPT includes batch processing times in

addition.
6. Conclusion and Future Work

In this paper, dynamic batch process control problem has been extended to a serial-batch

production system to utilize the information at serial and batch processors together. A

new batch process control heuristic, NASCH, has been developed which outperformed

best static control policy in most of the scenarios tested. NASCH uses upstream

information and leads the upstream control to improve the average waiting times at the

batch queue. On the other hand, we have discussed the impact of serial control policies

that utilize the downstream information. When the batch processor is busy, upstream

control takes place with the available downstream information at batch process buffer.

We have observed that, these upstream control policies that use downstream information

outperform their benchmarks. And the best performance has been maintained when they

were used as upstream control policies and NASCH was used as downstream control

policy.



This is one of the first studies that introduce the incorporation of upstream control with

downstream control for the batch control problem. We believe that better upstream

control heuristics can be developed to improve the efficiency of the batch processor. Our

assumption on the serial processing times as being same for all product types is one of the

limitations to this model. Our future research will be on this issue with the extension of

this serial-batch production system to multi-server cases.
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