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Economic implications of incorporating job value in dispatching rules.

Efficient processing of jobs is of major importance in job shop management. The efficiency of a job shop depeqnds on how quickly jobs are processed through the most efficient utilization of available machine centers. Improving the efficiency of a job shop results in greater economic value due to reduced work-in-process inventory costs. Many studies have been conducted in order to determine the most appropriate job dispatching rules under different shop conditions.

Although the shorest processing time (SPT) dispatching rule has been argued as the most efficent of available dispatching rules, research has not yet addressed the economic implications that result from incorporating job value into this dispatching rule. The main emphasis of this study was to compare the performance of SPT rule with a modified SPT rule that incorporates economic values of jods (VSPT) in job shop scheduling.

The evaluation criteria in this study was work-in-process (WIP) inventory costs, which directly measures the efficiency of operations in a job shop. Wilson and Mardis argued that the mean value of jobs in the shop is a more useful measure of performance. Using Monte Carlo simulation, they found that the value-added modification did in fact result in lower mean WIP inventory costs for most dispatching rules. They also discovered that the shortest weighted processing time (SWPT rule outperforms SPT in single machine systems and extended this finding to include multidimensional systems.

There is no indication in the literature when the SPT algortithm weighted by value (VSPT outperforms the SPT algorithm. This study utilized a more complex job shop with four machine centers and three types of jobs that had different processing sequences. Eight experimental conditions, not considered by Wilson and Mardis, were simulated. Factors included the two dispatching rules (SPT and VSPT), two levels of shop work load (low, 75 percent; and high, 95 percent) and two scenarios of processing times (deterministic and stochastic).

The job shop developed to test the eight experimental conditions consists of four machine centers. Three types of jobs are processed in this shop, each having a unique processing sequence and different processing times at various machine centers. Job processing sequences are illustrated in Table 1.

Shop work load is varied by setting the interarrival times of jobs entering the shop. Interarrival times are set to ensure that jobs arrive at a rate that will result in achievement of the specified capacity utilization level, either 75 percent or 95 percent. Interarrival time distribution for high workload was modeled as an exponential function with t=8.5, while for low workload t=10.5.

Job processing times were modeled as either deterministic of stochastic. Stochastic processing times were generated as the product of the predetermined job time and a triangular distribution with a mean value of 1.0, low value of 0.7 and high value of 1.6. The predetermined processing times, which were additionally used as the deterministic processing times, are displayed in Table 1.

The value of jobs being processed in the shop were assumed to vary to incorporate differing scenarios. These were modeled as uniform distributions. Parameters of these job value distribution are shown in Table 1.

Other assumptions in this job shop simulation include the following. The dejay in moving a job from one machine center to another is built into the processing times and is not explicitly considered. Storage space of infinite capacity is available at each machine center. No job is rejected, nor is any recycled. These actions are taken outside the job shop.

The simulation model

The job shop was modeled using the network orientation of SLAM II. The network drawing of the shops is illustrated in Figure 1. The three job types were placed into the shop by way of three create nodes (CI-C3). Attributes are assigned at various points in the shops as jobs are routed in the shop. These attributes are described as follows.

* ATR(1) = Job entry time;

* ATR(2) = Job identifier (1,2 or 3);

* [ (3) = Value of the Job;

* ATR(4) = Predetermined processing time for the first machine center visited;

* ATR(S) = Ratio of job value to job processing time; and

* ATR(6) = Work-in-process inventory cost.

Jobs are routed to the queue preceding the first machine center in their processing sequences. When the SPT dispatching rule is used, jobs are selected from the queues based on the lowest processing times. When the VSPT dispatching rule is used, jobs are selected from the queues based on the highest value of the ratio of job value to processing time (ATR(5)). Branches emanating from ythe queue nodes represent service activities at each machine center. Routing of jobs to subsequent machine centers and termination of jobs that have completed processing are functions performed by conditional branching based on the job identifier (ATR(2)).

While the jobs exit the system, each is routed through a collect node (C) to obtain statistics on the performance variable WIP inventory costs. WIP inventory cost is computed as the product of the time spent in the system, the job value and the unit WIP carrying cost:

ATR(6) = WIP INV COST = (TWNOW-ATR(1) *ATR(3)*.05 where, TNOW = Current simulation time;

ATR(1) = Job entry time;

ATR(3) = Value of the job; and

0.5 = The unit WIP carrying cost per year.
JOB VALUE SEQUENCE PROCESSING TIME
 A B C D
1 UNF(15,25) A,B,C,D 3 4 1 2
2 UNF(30,40) B,C,D,A 1 2 8 1
3 UNF(20,30) B,A,D, 4 2 5
TABLE 1. Job Parameter Specifications


Design parameters

The model was simulated for a one year time period. It was assumed that the job shop operated for fifty weeks out of the year, five days per week and eight hous per day for a total of 2,000 hours. The time unit was one hour.

Pilot simulation runs were made in an attempt to establish steady state conditions for the shop. Statistics were obtained from an initial run 300 hours and from subsequent runs in increments of 100 hours. The stability of the length of the queues was used to determine steady state. Queues were observed to stabilize at approximately 640 hours into the simulation. Based on these results, the truncation point for the transient period was assumed to be 640. All arrays were cleared at time 640, and the statistics were collected after this point in time. Every simulation run was conducted for 2,640 hours.

Five runs were executed for of the eight experimental conditions. The decision to make five runs was based on the value of 1 computed as follows:

I = ([sigma.sub.x] /g) * [Z.sub.alpha/2] where, [sigma]sub.x] = population standard deviation of batch means; g = prescribed half-length for the confidence interval; and

Z = standard normal value for alpha/2.

Knowledge of [sigma.sub.x] is required to solve equation (2). A trick here is to specify g in ralative terms of [sigma.sub.x]. Let g = [V.sub.sigma]x for V>0. The value I can be computed without knowledge of [sigma.sub.x]. For the purposes of the current study, V = .70 and alpha = .10 yielded I=5.49.

PROCESSING RUN LOW LOAD HIGH LOAD

TIME
 VSPT SPT VSPT SPT
DETERMINISTIC 1 39.35 43.89 97.05 161.41
 2 63.32 68.56 78.17 157.79
 3 41.56 44.70 91.77 189.64
 4 40.52 42.62 58.73 65.47
 5 31.24 33.11 87.55 130.33
STOCHASTIC 1 90.08 61.51 126.59 130.35
 2 71.56 48.10 96.86 82.33
 3 56.67 62.23 72.43 126.87
 4 90.08 61.51 136.68 126.45
 5 71.56 68.49 99.64 109.31


TABLE 2. Average Annual WIP Inventory Costs

Model verification was performed using three procedures. A trace of 100 time units showed that jobs were flowing through the shop as intended. Entity arrival times were checked in order to verify proper shop loadings. A pilot run was executed to obtain job time in the system statistics. The observation of the histograms of time in the system values demonstrated that items passed through the system in appropriate time.

Results

Average WIP inventory costs are provided in Table 2 for the five observations under each of the eight experimental conditions. The analysis of variance procedure was used as a means to test for significant differences that may exist among treatment combinations.

Under lower shop work load conditions, results indicated no significant differences in the performance of the two dispatching rules. However, a significant difference in total WIP inventory costs (Average annual WIP inventory costs times number of units processed) was discovered when the nature of the processing time specification was varied. The shop with deterministic processing times showed significantly lower WIP inventory cost as compared with the shop in which processing times were assumed to be stochastic in nature. This difference may be due, at least in part, to the skewed tringular distribution employed for determining all of the stochastic processing times.

Implications are that management should pay extra attention to determining accurately the processing times each job takes at each machine center. This may be accomplished through rigorous analysis and planning of activities in a production facility. Through better supervisory control, if management can control production or processing times at pre specified levels standards it can dramatically reduce overall WIP inventory costs.

In the model configuration with high shop work loads, the difference in total WIP inventory costs for the two dispatching rules was significant. Total WIP inventory costs for the shop that considered the value added approach, VSPT, were significantly lower than those costs for the shop using the SPT dispatching rule at the .025 level. Average costs of $56,975 were realized in the VSPT shop as compared to costs of $97,562 for the SPT shop.

Under conditions of high workloads, incorporating value of the job can greatly reduce WIP inventory costs. This implies that management should have the ability to predict capacity utilizations and determine in advance the most economical way of dispatching jobs through busy job shops. Under conditions of high capacity utilization, meeting production schedules becomes more critical. Therefore, through careful planning as well as control of processing times at each production facility and by predicting utilization levels in advance, management is able to create economic value by not only meeting their production schedules, but also by minimizing the WIP inventory costs.

In general, the value oriented shortest processing time dispatching rule outperformed the conventional rule. Explicit consideration of job value in dispatching rules can greatly aid reducing WIP inventory costs. Various situations, such as customer requirements and special orders, can change value of each job. Management should continuously evaluate the value of each job, and they must incorporate these modifications in appropriate algorithms employed in the job shops.

Conclusions

Job shop workload varies with demand. Consistency in efficiently processing jobs is a concern management. Keeping WIP inventory costs low is one of the major concerns. Through good planning and control, management can better accomplish production schedules. Different production conditions may require special modifications of conventional techniques to create economic value. Experimentation may allow managers to determine in advance the most optimal technique to be employed in speqcial production conditions.

The experiment discussed in this paper compared the SPT dispatching rule with a value added dispatching rule, VSPT, under four shop conditions to determine the most appropriate rule for each of these conditions. the rules were found to be comparable in the lower shop workload case. In the high shop workload configuration, the value added approach proved beneficial in lowering WIP inventory costs.

Through the simple experiment discussed in this study, we demonstrated how competing algorithms can be evaluated in advance through inexpensive simulations. Simulation techniques can provide managers with better insights into managing and optimizing operations in production facilities.

Extensions of current research include comparison of VSPT with other dispatching rules. Considering combinations of performance criteria, such as WIP inventory costs and due dates met, would be logical. Effects of different shop workloads could be studied. Specification of the stochastic processing times may be a pertinent question as well.

For further reading

Elvers, D.A., "Job Shop Dispatching Rules Using Various Delivery Due Date Setting Criteria," Production Inventory Management, Vol. 14, No. 4.

Elvers, D.A., "The Sensitivity of the Relative Effectiveness of Shop Dispatching Rules With Respect to Various Arrival Distribution," AIIE Transactions, Vol. 6, No. 1.

Elvers, D.A., and Taube, L.R., "Time Completion for Various Dispatching Rules in Job Shops." OMEGA The Int. Jl of Mgmt Sct, No. 1 (1981).

Goodwin, J.C., Elvers, D.A., and Goodwin, J.S., "Overtime Usage in a Job Shop Environment," OMEGA Vol. 6, No. 6.

Holloway, C.A., and Nelson, R.T., "Job Shop Scheduling With Due Dates and Variable Processing Times," Management Science, Vol. 20 (1973).

Pritsker, A.B., Introduction to Simulation and SLAM II, 2nd ed. (West Lafayette: Systems Publishing, 1984). Weeks, J.R., "A Simulation Study of Predictable Due Dates," Management Science, Vol. 24, No. 4 (1977).

Weeks, J.R., and Fryer, J.S., "Methodology for Assigning Minimum Cost Due Dates," Management Science, Vol. 23, No. 8 (1976).

Wilbrecht, J.I., and Prescott, W.B., "The Influence of Set Up Time on Job Performance," Management Science, Vol. 16 (1969).

Wilson, H.G., and Mardis, Barbara J., "Modifying Job Sequencing Rules for Work-In-Process Inventory Reduction," IIE Transactions, Vol. 15, No. 4 (1983).
COPYRIGHT 1993 Institute of Industrial Engineers, Inc. (IIE)
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Author:Srivastava, Alok; Prabhu, Suresh
Publication:Industrial Management
Date:Sep 1, 1993
Words:2263
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