Customer order acceptance decision models for a process-focused production system.

Lee, Huei ; Deane, Richard H.

INTRODUCTION

The ability to attract customer orders has long been recognized as one of the key success factors for process-focused production or job shops. Scant attention however has been devoted in the literature to the customer order acceptance decision. That is, the decision as to whether a customer order should in fact be accepted once it is received. This decision is part of the firm's demand management function.

Guerrero and Kern (1988) point out the importance of the customer order acceptance decision: "Under any circumstances, accepting orders without considering their possibly costly impact on capacity can lead to paying for the privilege of accepting an order" (p. 59). The need for order acceptance decision rules is also addressed by Matsui (1982, 1985) and others.

Guerrero and Kern (1988) suggest a framework for demand management. From a day-today perspective, a simple demand management system, as shown in Figure 1, includes order entry, order accumulation, establishment of order priority, precapacity allocation, and order acceptance decision. A well developed demand management system offers at least two advantages for the firm. First, shop capacity can be more effectively planned and controlled. Second, realistic customer order due date commitments can be made. Traditionally, managers have a tendency toward accepting all incoming orders. However, some customer orders may in fact not be a good match with current shop capacity. Two specific questions arise:

(a) What is the relationship between system performance and the customer order acceptance decision process?

(b) What types of decision rules might be adopted to assist managers in accepting customer orders in a process-focused production system?

Despite the importance of order control and acceptance in practice, researchers have published very little on the development of effective answers to these questions.

There are several important factors that impact customer order acceptance decisions. These factors include the decision period (the period of time over which orders may be collected before order acceptance decisions must be made), size of the order, due date requirements, current capacity constraints, and order preference (e.g. profit margin, customer credit, etc.).

The production system considered in this research is a make-to-order, non-MRP, process-focused production shop. Process-focused production systems are commonly referred to as job shops or intermittent production because products move from department to department in jobs that are normally determined by customer orders. An order acceptance decision is considered on a "micro" level for each individual order. Fixed capacity is assumed in the shop and due dates are the function of estimated processing time and set-up time. The primary purpose of this research is to test an order acceptance algorithm, the JOA model, for the customer order acceptance decision in a process-focused production system.

REVIEW OF LITERATURE

Little attention and effort has been directly devoted to demand management in the literature. Prior research has addressed demand management primarily in broad terms, for example, as demand forecasting, order entry, due date promising, customer order service, and other customer contact-related terms (Vollmann, Berry, & Whybark, 1988). Most research efforts related to demand management have been directed toward aggregate level decisions in an MRP environment, such as demand forecasting and the interaction between demand management and master production scheduling (MPS). McClelland (1988), for example, provides guidelines for the selection of an appropriate master scheduling method for a make-to-order firm to improve order promising.

Although job shop scheduling has an interactive relationship with demand management, including the individual order acceptance policy, job shop studies do not normally consider demand management decisions. That is, the demand management process is considered as external to most job shop research. Specifically, the literature dealing with order management in the job shop level is sparse and was practically nonexistent before 1970. Melnyk (1988) discussed "order review/releasing" (ORR), in which the process of order management changes from the planned system to the shop floor system. Although order review/releasing and order acceptance control have similar purposes, they are different functions. Order review/releasing concerns the job releasing mechanism, and is based on the assumption of accepting all the incoming jobs.

[FIGURE 1 OMITTED]

Since 1970, there have been a few articles in the Japanese literature concerning aggregate order decision mechanisms (Nomura, 1974; Ikuta, 1975; Ichimura, 1977; Matsui, 1980, 1981, 1982; Nishimura, 1982). This research has been summarized by Matsui (1982, 1985) in an English language article. A number of papers have discussed the effective decision rules in customer order acceptance. Miller (1969), Lippman and Ross (1971), and Balachandran and Schaefer (1981) discussed the aggregate (i.e. not the individual) customer order acceptance decision. Guerrero and Kern (1988) discussed the use of the forward loading and backward finite loading methods in the process of order acceptance decision. Lee and Deane (1991a) devised a mathematical linear programming method for order acceptance decisions in a make-to-order job shop environment. Lee and Deane (1991b) compared two relatively simple order acceptance decision rules, the Workload Rank (WR) heuristic and the Input/Output (I/O) heuristic in a similar environment. Philipoom and Fry (1992) compared three different order review/release strategies to improve manufacturing performance. While the first two different strategies used by Philipoom and Fry are in fact similar to Lee and Deane's WR and I/O heuristics, the third strategy is not to use any decision rule in job order review/releases. Wang, Yang, and Lee (1994) used a neural network solution for multi-criteria order acceptance decision in a over-demand job shop.

A MATHEMATICAL PROGRAMMING MODEL

The primary objective of this study is to improve and evaluate a mathematical programming model, the Job Order Acceptance (JOA) model, for a process-focused production system. A custom order, after entering a production shop, is also referred to as a job. The model described in this paper is based on the early framework of JOA devised by Lee and Deane (1991a). The first section describes this mathematical programming model and its associated implementation issues. The objective function, constraints and model parameters are also discussed.

A mathematical programming approach is used to model the important decision variables and parameters in the customer order acceptance decision. The JOA model employs an integer programming algorithm executed at the end of each decision period. The purpose of the JOA model is to achieve both work-in-process related performance (e.g., minimize work-in-process inventory level, or mean and variance of shop flow time) and due-date related performance (e.g., minimize average tardiness).

With respect to work-in-process related performance, the JOA model seeks to minimize the difference between the current workload and the target workload at each machine. Within a capacity constraint, the JOA model not only maximizes the utilization level of each machine but also controls the work flow to the machines, thereby helping to reduce the average WIP. For due-date related performance, the JOA model seeks to maximize the slack time of accepted customer orders. As such, customer orders with tight due dates are afforded less priority since they increase the possibility of job tardiness. Although order release policy and sequencing rules at each station have an impact on WIP and due-date performance, they are not final solutions for long shop flow time and poor due-date performance in a high congestion shop. Research also indicated that dispatching rule has little impact on shop performance while the I/O control method is used (Ragatz & Mabert, 1988; Philipoom & Fry, 1992).

The JOA model makes an integrated decision as to which customer orders in a decision period should be accepted. The decision is "dis-aggregated" in that the workload of each machine is separately considered. The primary focus of the mathematical programming model is thus to select customer orders that best "fit" the available capacity in the shop, and have the best chance of being completed by their required due date.

Formulation of the JOA Model

The basic variables and parameters in the JOA model are:

k = total number of incoming customer orders during a decision period

i = customer order number (1 .. k)

M = total machine number

j = machine number (1 .. M)

[d.sub.i] = job due date for customer order i

TNOW = time now

[P.sub.ij] = estimated processing (run) time of customer order i on machine j

[S.sub.ij] = estimated set-up time for customer order i on machine j

T = the number of planning periods

t = t-th planning period

T[W.sub.tj] = target workload for machine j for t-th planning period

A[W.sub.tj] = actual workload for machine j for t-th planning period

To formulate the JOA model, the current shop capacity should be expressed for M machines in a process-focused production system. A Forward Finite Loading (FFL) algorithm is used to compute the unfilled capacity ([C.sub.j]) in the JOA model. Under the forward finite loading algorithm, time is divided into T planning periods and a target workload, T[W.sub.tj], in t-th period is assigned for j-th machine.

The target workload, T[W.sub.tj], is the value used to control utilization level. When the value of T[W.sub.tj] is high, more customer orders are accepted to shop and the shop utilization is high. When the value of T[W.sub.tj] is low, fewer customer orders are accepted to the shop and the shop utilization level is low. O[W.sub.tj] denotes actual current workload which is greater than target workload for the machine j during planning period t:

O[W.sub.0j] = 0

O[W.sub.tj] = max [0, ([OW.sub.(t-1)j] + A[W.sub.tj] - T[W.sub.tj])] for t 1 (1)

Unfilled capacity available for machine j (Cj) during the planning period 1 to t is defined as:

[C.sub.j] = 3 [max (0, T[W.sub.tj] - A[W.sub.tj] - O[W.sub.tj])] t (2)

The second factor for this formula involves assigning a priority to each incoming customer order. For due-date related performance, the JOA model seeks to maximize the slack time of accepted customer orders. As such, customer orders with tight due dates have lower chances since they increase the possibility of job tardiness. The estimate slack time for customer order i (S[L.sub.i]) is computed as:

S[L.sub.i] = [d.sub.i] - TNOW - [P.sub.ij] - [S.sub.ij] (3) j j

Based on this slack calculation, customer orders with negative slack times cannot be selected by the algorithm. A "revised" slack time is therefore used to ensure that customer orders with negative slack times are properly considered by the algorithm:

RS[L.sub.i] = S[L.sub.i] + R (4)

The revised slack time, RSLi, for customer order i is computed by adding an adjusting factor, R, to the slack time. The use of the revised slack calculation allows customer orders with negative slack time to be selected. The adjusting constant, R, is added to the slack value to force all the job slack values to be positive:

R = 1-[min (0, S[L.sub.i], .. S[l.sub.k])] (5)

The value of R is computed as: 1-[min (0, Estimated slack time for customer order 1 ([SL.sub.1]), Estimated slack time for customer order 2 ([SL.sub.2]), .., Estimated slack time for customer order k ([SL.sub.k]))] + 1. For example, consider six customer orders with the estimated slack times, S[L.sub.1] = 3, S[L.sub.2] = -4, S[L.sub.3] = -2, S[L.sub.4] = 5, S[L.sub.5] = 7, S[L.sub.6] = 0. Based on these six customer orders, the adjusting constant, R, is 1-(-4) = 5. The revised slack times are S[L.sub.1] = 8, S[L.sub.2] = 1, S[l.sub.3] = 3, S[L.sub.4] = 10, S[L.sub.5] = 12, S[L.sub.6] = 5.

The first constraint, is expressed in the following:

[X.sub.i] = 0 or 1 for all i (6)

This constraint prohibits a "partial" acceptance of an incoming customer order. Each customer order is accepted or rejected in its entirety. Xi is the decision variable for customer order i. When Xi = 1, customer order i is accepted. When Xi = 0, customer order i is rejected. The second constraint, representing the major constraint in the JOA model, is expressed in the following:

[[X.sub.i] * ([P.sub.ij] + [S.sub.ij])] [C.sub.j] for all i,j (7) i

This constraint requires that the total assigned processing time for each machine not be greater than the available machine capacity. This constraint should be examined with the job with revised slack time. A customer order has higher priority in revised slack time will be rejected if it cannot meet this constraint. This constraint shows that the JOA model is based not only on maximizing total revised slack time but also meeting capacity capability.

The final formulation of the JOA model is given as follows:

Maximize:

([X.sub.i] * RSLi) (8)

i

subject to:

[X.sub.i] = 0 or 1 for all i (6)

3 [[X.sub.i] * ([P.sub.ij] + [S.sub.ij])] [C.sub.j] for all i,j (7)

i

Maximizing the objective function, 3i (Xi*RSLi), guarantees that customer orders will be selected and furthermore directs that a preference be given to jobs with larger slack values. Since the objective function is to be maximized, the algorithm favors jobs with large slack time values. A full picture of the object function, constraints and variables of the JOA model is enclosed in Appendix. The decision model described above is appropriate for solution through integer program (IP) since constraint 2 in the formulation of the decision model requires discrete integer values. The decision variables Xi must be either 0 (reject job i) or 1 (accept job i). The solution time is dependent primarily upon the number of incoming jobs, not the number of machines in the shop. A test shows that the time required to solve a JOA integer programming problem is less than 15 seconds on a Pentium 200 computer with 14 incoming jobs in a an eight machine shop.

RESEARCH METHODOLOGY

The purpose of this research is to:

1. improve and evaluate the JOA order acceptance decision model in a make-to-order, process-focused production system, and

2. investigate the impact of target shop utilization levels on different order acceptance decision models.

It is hypothesized that several different decision models exhibit different performance while the JOA model should yield the best performance. It further hypothesized that the JOA model should perform much better than other models in a process-focused production environment under high utilization levels.

A computer simulation experimentation methodology was undertaken to imitate the job shop environment. Primary performance criteria for the study include mean job flow time and the degree to which order due date are met. Independent variables are order acceptance decision model and utilization level. Since the experimental design include two dependent metric variables and two non-metric independent variables, a full factorial fixed effect MANOVA model was used as the primary statistical procedure for analyzing different performance among decision models and utilization levels. There are three different decision models and three different utilization levels which yield 9 different experimental sets (3 * 3). Tables and graphics are used to summarize the experimental results.

A discrete event simulation model for an eight-machine process-focused production environment was developed using the SIMAN simulation language with a FORTRAN subroutine. The following sections describe details of alternative decision models, the performance criteria, experimental conditions, and data collection method.

Alternative Decision Models

The JOA algorithm is compared with three specific customer order acceptance decision models:

1. Backward Finite Loading (BFL) Approach. The BFL is based on the division of the planning horizon into "planning periods". Incoming customer orders are placed in a "selection pool" and ranked by due date. The BFL approach attempts to fit each operation of each job in the selection pool backward into a planning period from the job's assigned due date, starting with the last operation in the job and working toward the first. If adequate capacity is not available in a time period, the BFL attempts to schedule the operation in the next earliest period that adequate capacity is available. If adequate capacity is available for all operations of an order, the customer order should be accepted and moved from the selection pool to the releasing pool. The workload profile is also updated based on the accepted job order. In contrast, if adequate capacity is not available for a customer order, the customer order is temporarily placed into a holding pool. After a "first pass" attempt is made to fit all the orders in the selection pool into the schedule, a "shop unfilled capacity ratio" (SUCR) is computed by dividing unfilled capacity by target workload. If the shop unfilled ratio is higher than a critical percentage (for example, 15%). An additional customer order from the holding pool will be accepted. The order selected from the holding pool will be the one that creates the least total "overload" for machines in the shop. Additional orders are selected until the shop unfilled capacity ratio falls below the target percentage.

2. Workload Rank (WR) Heuristic. In the WR heuristic algorithm, a priority index is assigned to each customer order based on the projected workload of the machines required in processing the customer order. The WR algorithm computes the unfilled capacity at each machine center and uses it as a base to compute order priority. A job priority is computed based on the estimated unfilled capacity at each machine center on the job's routing. Based on the computed job priorities, orders are accepted by the shop. As each customer order is accepted, the workload of the customer order is added to the "committed workload" for each machine. The addition of the customer order alters the unfilled capacity of one or more machines, and a recalculation of unfilled capacity (Cj) for each machine is made (Lee & Deane, 1991b).

3. I/O Heuristic. The I/O acceptance heuristic is based on the concept that work is accepted to the system when total shop workload falls below a pre-specified level. That is, the input to the system is guided by what is leaving the system as output. A version of this rule for job order releasing was tested by Baker (1984) and suggested earlier by Wright (1979). The I/O acceptance heuristic allows a customer order to be accepted only when the total aggregate workload in the shop is below a pre-specified level.

Performance Criteria

Primary performance criteria include average job flow time and root mean square of tardiness. Average shop flow time ([F.sub.av]) is used as a primary measure of how well jobs move through the shop. Shop flow time is defined as the time between the release of the job to the shop floor and the time when the job completes its last operation. Average shop flow time ([F.sub.av]) is computed as:

([f.sub.i] - [RE.sub.i])

[F.sub.av] = i / n

where

[f.sub.i]: completion time of job i

R[E.sub.i]: releasing time of job i

As an alternative measure of shop congestion, average system flow time is computed as follows:

([f.sub.i]-[A.sub.i])

[S.sub.av] = i / n

where

[A.sub.i] : arrival date of customer order i

Although [S.sub.av] and [F.sub.av] are highly correlated, both have different objectives. General system congestion and customer lead time is measured by [S.sub.av], while work-in-process (WIP) inventory on the shop floor is measured by [F.sub.av]. When utilization level is high, both average system flow time and average shop flow time are high.

Root Mean Square of Tardiness (TRMS) is employed as the measure for due date performance since it is a somewhat "combined" measure of average tardiness and variance of tardiness. TRMS is computed as:

TRMS = [square root of ([[max (0, [f.sub.i]-[d.sub.i])].sup.2] / n i]

where

[f.sub.i]: complete time of job i

[d.sub.i]: due date of job i

n: number of jobs finished

Absolute deviation from due date (| D |) is also reported as a secondary measure of due date performance. Absolute deviation from due date is computed as follows:

| D | = (3 |[f.sub.i] - [d.sub.i] |) / n

Mean and standard deviations (square root of variance) of system flow time, tardiness, lateness, absolute lateness, and earliness are also reported as secondary performance criteria. The percentages of customer orders accepted are also reported for all order acceptance decision models in tabular forms.

Experimental Conditions

The primary experimental factor is the job order acceptance model. Shop utilization level serves as a secondary experimental factor to compare the different order acceptance decision models.

Shop utilization level is the average "working time" of machines in the shop divided by total machine capacity. The concept of shop utilization levels in this study is not necessarily directly related to customer order arrival rate. Customer order arrival rate is an input, external factor to the job shop model while the actual utilization level is an internal, output level controlled in the shop (through the customer order acceptance process). For example, the utilization level can be controlled by varying the target workload (TWtj) in the JOA model.

Shop utilization level certainly has an impact on the performance of the different decision models. For example, assume that two decision models are evaluated using an incoming job stream that would result in a 100% shop utilization level if all customer orders are accepted. If model A rejects 25% of incoming customer orders and model B rejects 10% of incoming customer orders, then obviously model A would yield better shop flow time and order due date performance. However, model B would result in more total work through the shop (and perhaps higher profits). In order to provide a "fair" comparison of alternative acceptance decision models, each model was evaluated at the same shop utilization level. In this paper, three levels of target shop utilization levels are used to compare decision models: 65%, 75%, and 85%.

In this simulation, arriving orders are accumulated during a "decision period" in order for the manager to make a customer order acceptance decision. That is, the decision period is the period of time over which orders are collected before order acceptance decisions must be made. The decision period may be as short as a few minutes or as long as a few days. The decision period can be an important factor influencing order acceptance performance. A longer decision period normally provides greater flexibility for the demand manager in making order acceptance decisions. Under a longer decision period, the decision process becomes more complex since more customer orders are considered during a decision period. The decision period in this simulation experiment was 6 time units, during which an average of 8 customer orders arrival and were accumulated. Average processing time or job size has a moderate relationship with shop utilization level. Long average processing time requires less setup time such that its utilization level is higher than that of short average processing time. Average total processing time, including setup time, is 6.01 time unit in this experiment.

In the eight-machine simulated shop, customer orders arrive and wait for the acceptance or rejection decision. When a customer order is accepted, it is moved directly to the first machine on its routing. Customer orders are "lost" to the system if rejected. Once in the shop, all jobs are dispatched via the EDD dispatching rule.

The process-focused production system simulated in this study is consistent with those used in previous research and with shops found in industry (Han, 1989; Kim, 1989). The job shop simulation model was validated through the input/output transformation analysis, a set of "snapshot" outputs and graphical animation analysis.

A summary description of the eight-machine shop is provided below:

1. relatively balanced shop (no bottleneck machines),

2. exponential customer order arrivals to the job shop (: = 0.786),

3. deterministic run and setup time (average total processing time, including setup time, is 6.01),

4. batch size is a random variable (following a discrete probability function),

5. operation overlapping and preemption are not allowed,

6. negligible wait time and move time between machines,

7. predetermined job routing through the shop,

8. machine break downs are not considered,

9. alternative job routings are not allowed (average number of job operations = 6),

10. unlimited queues allowed at each machine,

11. the shop is machine constrained, not labor constrained,

12. lot splitting is not allowed.

Data Collection

In order to eliminate initial bias, data from the initial transient period was discarded with the length of the transient period determined by plotting and examining the values of key variables as suggested by Conway (1967). A length of 500 simulation time units of transient period was found to be adequate to yield steady state by observing the plotted output from a pilot run. On average, there are 2486 jobs processed through the shop during each observation period after steady state was achieved.

The "batch means" approach was used for collecting observations in one long simulation run to avoid a run-in period for each observation. One long simulation run was broken down into "batches" (or subruns) so that the end of a simulation batch serves as the starting point for the next batch. Each batch yields one observation for each performance measure. For each experimental setting, twenty "observations" of approximately 2500 jobs, were collected to obtain a sufficient sample to test for differences in performance. The procedure used to determine this batch length was suggested by Fishman (1978). By Fishman's method, a subrun length of 2100 simulation time units was found to be adequate to yield independent observations. In addition, common random number seeds are used as a variance reduction technique to reduce the variances of the performance measures. Each model is therefore tested using exactly the same customer order arrival stream.

RESULTS

The MANOVA technique was used as the primary statistical procedure for analyzing the results from the factorial experimental design of the research because more than one performance criterion is employed in this research. The experimental factors include the customer order acceptance decision model and the utilization level. The full factorial MANOVA, rather than a series of ANOVA, was used to analyze simultaneously the impact of the factors on the multiple criteria. Tukey's test was used to isolate the performance of the specific customer order decision models.

The MANOVA results for total shop performance are provided in Table 1. The results of the ANOVA for each performance criterion are shown in Tables 2 and 3. From these statistical analysis, both experimental factors have significant main effects and there is a significant interaction effect. The main effects of order acceptance models and shop utilization levels must therefore be interpreted jointly considering the interaction effect. From Tables 4 through 6, the results of Tukey's test show that the JOA model is in the best performance category under all utilization levels compared to other order acceptance decision models in terms of both flow time and due date performance. Table 7 and Table 8 summarize the performance of the order acceptance models at various utilization levels in a tabular form.

Figures 2 and 3 depict performance of the order acceptance decision models in a graphical format. From these tables, graphs and Tukey's test, it is clear that the superiority of the JOA model varies with shop utilization level. Under low utilization levels, the differences among the order acceptance decision models may not be practically significant. At higher shop utilization levels, the JOA model is vastly superior to the other decision models in terms of average shop flow time and root mean square of tardiness.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

Table 9 shows secondary performance measures including means and standard deviations for system flow time, tardiness, lateness, absolute lateness, and earliness. The JOA model yields good performance for system flow time, earliness, absolute lateness, and lateness. The BFL model performs well for due date related performance criteria because it uses a structured approach that schedules backward from job due date. Unfortunately the BFL model often requires that jobs remain in the shop for longer time periods so that system flow time is excessive compared to the JOA model.

The general superiority of the JOA model arises from the fact that it jointly and simultaneously considers all incoming customer orders. The other models consider customer order acceptance decisions on a sequential basis. At lower utilization levels, excess capacity is available and work-in-process is small so that order acceptance decision models make relatively little difference in performance. However, higher levels of shop utilization are correlated directly with increased machine/work center loads, queues, and queue waiting time. Under such conditions, the JOA model is effective in considering the dis-aggregated workload on each machine, the available unfilled capacity, and job slack time. As such, the JOA model is able to show much better performance compared with other acceptance decision models. At higher utilization levels, the shop cannot afford to accept any order that does not exactly "fit" existing shop capacity.

Table 10 shows the percentage of incoming customer orders accepted under each model tested. Interestingly, the I/O model tends to accept a greater number of orders but essentially the same workload hours as the other models (i.e., all models yield the same utilization levels). In a decision period when only a relatively small amount of shop capacity is available, the JOA, BFL, and WR models, using a dis-aggregated approach, tend to accept very few orders. These sophisticated models reject more orders since machine capacity must be available for each individual job operation. During a subsequent decision period, additional capacity will likely become available so that larger orders can be accepted by the sophisticated models. However, in situations where available shop capacity is small, the I/O model tends to be able to accept one or more small orders because the acceptance decision is based only on comparing total available shop capacity with the aggregate workload of a job. That is, the I/O model does not match individual operations for arriving orders to individual machine capacities. The use of the I/O customer order acceptance model therefore increases the chances that smaller jobs can be accepted up to the limit of the total available shop capacity. Accepting more small job orders may of course not necessarily the best interest of the shop. The results of this research would seen to support such a generalization.

CONCLUSIONS

This paper attempts to improve and evaluate a model for the order acceptance decision in the process-focused production environment. The statistical analysis indicates that the JOA model is in the superior performance category under all utilization levels tested compared to other order acceptance models. The results also show that there are relatively small differences in performance at lower levels of utilization for the models examined. The implication is that JOA is particularly useful when management elects (and is able to) operate the shop at a higher utilization level. That is, the advantages of the JOA model are more pronounced at higher utilization levels.

A basic implication of this research is that a structured customer order acceptance control mechanism is vastly superior to a random or "naive" control mechanism. That is, the I/O heuristic model (most similar to the situation of naive control), is consistently inferior to other complex order acceptance decision models. Specifically, the research demonstrates that effective customer order acceptance can make a performance difference in terms of job flow time and job tardiness. In practice, managers tend to adopt decision heuristics based on ease of use, simplicity or perhaps because of a lack of knowledge about structured models. However, once a structured model, such as the JOA model, is implemented properly within a computerized information system, difficulty of usage, simplicity or lack of understanding becomes of less concern.

Future sensitivity testing of the JOA model is necessary. The impact of other factors, such as the length of decision period, due date tightness, or customer order arrival rate on the customer order acceptance process, should be investigated.

One possible drawback of the JOA model is its computation complexity in practice. The development of a more sophisticated heuristic based on the JOA principle may be possible. This paper was based on the assumption of a relatively balanced job shop with all job orders generating the same profit. An unbalanced job shop should be considered in future research.

Appendix B. Formulation of the JOA Model

The specific formulation of the JOA model is given as follows: Maximize:

([X.sub.i] * RS[L.sub.i]) (8)

i

subject to:

Xi = 0 or 1 for all i (6)

[Xi * (Pij +Sij)] # Cj for all i,j (7)

i

where:

k = total number of incoming customer orders during a decision period

i = customer order number (1 .. k)

M = total machine number

j = machine number (1 .. M)

Xi: decision variable for customer order i

Xi = 1, accept customer order i

Xi = 0, do not accept customer order i,

SLi = di-TNOW-3 Pij--3 [S.sub.ij] (3)

j j

[d.sub.i] = job due date for customer order i

RS[L.sub.i] = S[L.sub.i] + R (4)

R = the value for adjusting the slack time value in a decision period

R = 1 - [min (0, S[L.sub.i], .. S[l.sub.k])] (5)

TNOW = time now

[P.sub.ij] = estimated processing (run) time of customer order i on machine j

[S.sub.ij] = estimated set-up time for customer order i on machine j

T = the number of planning periods

t = t-th planning period

T[W.sub.tj] = target workload for machine j for t-th planning period

A[W.sub.tj] = actual workload for machine j for t-th planning period

O[W.sub.tj] = actual current workload which is greater than target workload for the machine j during

planning period t

O[W.sub.0j] = 0

O[W.sub.tj] = max [0, (O[W.sub.(t-1)j] + A[W.sub.tj]-T[W.sub.tj])]

for t 1 (1)

[C.sub.j] = unfilled capacity available for machine j during the planning period 1 to t

[C.sub.j] = 3 [max (0, T[W.sub.tj]-A[W.sub.tj]-O[w.sub.tj])] (2)

t

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Huei Lee, Lamar University

Richard H. Deane, Georgia State University

Table 1: Multivariate Analysis of Variance Table

Dependent Variables: Average Shop Flow Time ([f.sub.av]) and
Root Mean Square of Tardiness (TRMS)
Root Mean Square of Tardiness ([T.sub.RMS])

 Wilks' DF
Source of Variance Criterion F value N * D ** PR > F

Decision Model 0.01478003 546.73 6 454 0
 (DM) ***
Utilization Level 0.00055338 4711.37 4 454 0

DM x UL 0.02118589 222.09 12 454 0

* Numerator's degree of freedom for critical F value

** Denominator's degrees of freedom for critical F value

*** Decision model refers to order acceptance decision models:
JOA, BFL, WR, and I/O

Table 2. Analysis of Variance Table--Average Shop Flow Time (Fav)

Dependent Variable: [F.sub.AV]

 Sum of Mean
Source of Variance DF Squares Square F Value PR > F

MODEL 11 15263.01 1387.5 1266.38 0.0001

Decision Model (DM) 3 441.63 134.54 0

Utilization Level (UL) 2 14638.46 6690.62 0.0001

DM x UL 6 182.91 27.87 0.0001

RESIDUAL 228 249.42 1.09

TOTAL 239 15512.43

R-squared = 0.983921

Table 3. Analysis of Variance Table--Root Mean Square
of Tardiness (TRMS)

Dependent Variable: [T.sub.RMS]

 Sum of Mean
Source of Variance DF Squares Square F Value PR > F

MODEL 11 4920175.5 447288.7 10874.4 0

Decision Model (DM) 3 285252.6 2311.7 0

Utilization Level (UL) 2 4312100.9 52417.4 0

DM x UL 6 322822.9 1308.1 0

RESIDUAL 228 9378.2 41.1

TOTAL 239 4929553.7

R-squared = 0.998098

Table 4. Turkey's Range Test for Decision Model Under 65%
Utilization Level [alpha] = 0.01

 Turkey Grouping Mean Value Decision Model

[F.sub.av] A 14.34 I/O
 B 13.99 BFL
 B 13.95 WR
 B 12.91 JOA

 Turkey Grouping Mean Value Decision Model

[T.sub.RMS] A 16.29 I/O
 B 8.42 BFL
 B 7.31 WR
 B 7.25 JOA

Note: Means with the same letter are not significantly different

Table 5. Turkey's Range Test for Decision Model Under 75% Utilization
Level [alpha] 0.01

 Turkey Grouping Mean Value Decision Model

[F.sub.av] A 22.09 I/O
 A 21.21 BFL
 B 19.77 WR
 C 17.90 JOA

 Turkey Grouping Mean Value Decision Model

[T.sub.RMS] A 60.92 I/O
 A 42.39 BFL
 B 32.40 WR
 B 31.30 JOA

Note: Means with the same letter are not significantly different

Table 6. Turkey's Range Test for Decision Model Under 85%
Utilization Level [alpha] =0.01

 Turkey Grouping Mean Value Decision Model

[F.sub.av] A 35.58 I/O
 B 33.91 BFL
 C 31.50 WR
 D 29.12 JOA

 Turkey Grouping Mean Value Decision Model

[T.sub.RMS] A 452.80 I/O
 B 281.66 BFL
 C 251.43 WR
 C 247.56 JOA

Note: Means with the same letter are not significantly different

Table 7. Average Shop Flow Time *

 Decision Model

Utilization Level JOA BFL WR I/O

65% 12.91 13.99 13.95 14.34
75% 17.90 21.21 19.77 22.09
85% 29.12 33.91 31.50 35.58

* Decision period = 6 time units; Job order arrival rate = exponential
distribution with a mean of 0.786

Table 8. Root Mean Square of Tardiness *

 Decision Model

Utilization Level JOA BFL WR I/O

65% 7.25 7.31 8.42 16.29
75% 31.30 32.40 42.39 60.92
85% 247.56 251.43 281.66 452.80

* Decision period = 6 time units; Job order arrival rate = exponential
distribution with a mean of 0.786

Table 9. Secondary Performance Measurements

 Utilization JOA BFL
 Level
 Mean SD Mean SD

System 65% 15.87 6.18 16.09 6.16
Flow 75% 20.01 7.83 21.84 8.73
Time 85% 31.64 12.88 35.21 14.56

Tardiness 65% 1.11 2.44 1.15 2.51
 75% 3.09 4.66 3.19 4.79
 85% 11.07 11.53 11.98 11.32

Lateness 65% -4.39 7.23 -4.37 7.24
 75% -2.20 8.22 -1.13 8.25
 85% 11.07 11.53 11.09 10.72

Absolute 65% 6.19 5.28 6.22 5.08
Lateness 75% 6.40 5.16 6.27 5.19
 85% 12.79 9.58 12.88 9.64

Earliness 65% 5.48 5.84 5.5 6.01
 75% 3.30 5.04 3.1 4.98
 85% 0.86 2.67 0.87 2.75

 Utilization WR I/O
 Level
 Mean SD Mean SD

System 65% 16.01 6.12 16.16 6.13
Flow 75% 21.35 8.56 22.05 8.75
Time 85% 32.08 12.98 36.31 15.09

Tardiness 65% 1.22 2.63 1.93 3.49
 75% 3.88 5.22 4.84 6.12
 85% 12.37 10.45 16.88 12.94

Lateness 65% -4.39 7.75 -1.63 6.85
 75% 0.9 8.58 2.73 8.55
 85% 12.35 10.45 16.39 13.72

Absolute 65% 8.89 4.73 9.99 5.24
Lateness 75% 6.86 5.21 6.96 5.68
 85% 13.24 9.74 17.37 12.46

Earliness 65% 5.61 6.29 3.56 4.58
 75% 2.98 4.8 2.11 3.91
 85% 0.90 2.82 0.49 2.01

Table 10. The Percentage of Number of Job Orders Accepted

Utilization Level JOA BFL WR I/O

65% 74% 73% 73% 82%

75% 82% 82% 82% 89%

85% 92% 92% 92% 95%