A time-cost based procedure for rescheduling job orders.

ABSTRACT

Rescheduling of open orders has played an important part in manufacturing systems to deal with production uncertainty, such as machine breakdowns or scraps. To be responsive to the needs of customers, rescheduling becomes an essential component in the time-based competition for manufacturing firms. Nevertheless, when production planners are flooded with numerous rescheduling requests, they may have difficulty in deciding which rescheduling requests should be implemented. Previous rescheduling methods have primarily considered only the timing issue, but not the costs of rescheduling. This paper presents a time-cost based procedure to job rescheduling decision by considering both the timing issue and the penalty costs (i.e. out-of-pocket costs and opportunity cost) of rescheduling. Such a procedure has significant implications for cost/management accountants as well as the production engineers.

1. INTRODUCTION

With increasing variability and volatility in customer tastes, rescheduling job orders becomes an essential component in the time-based competition for manufacturing firms. How to satisfy customer's needs in a timely manner while reducing work-in-process inventories and keeping the total product cost down is crucial for the success of a manufacturing firm in this dynamic environment. Cost/management accountants can play a proactive role in this environment in providing relevant cost information for helping production personnel to make correct job rescheduling decisions. Unfortunately, accountants have not been involved in the measurement of the costs of rescheduling as they consider the issue of rescheduling is primarily the responsibilities of production personnel. The objectives of this paper are to develop a time-cost based procedure to help production planners to make rescheduling decisions in a cost effective manner and to show that cost/management accountants can play a significant role in rescheduling decisions.

Several traditional buffering methods such as safety stock or safety lead time may help reduce the need for rescheduling. These buffering methods, however, may result in work-in-process inventories, and may prove to be cost-ineffective. When production planners are flooded with numerous rescheduling requests, they can either use the informal or formal scheduling systems to evaluate each rescheduling requests. Informal system, such as the use of a hot list, may cause production planners to make incorrect decisions based on subjective judgment as it does not consider the timing and the costs of rescheduling. Formal rescheduling systems have been developed but focus primarily on time factor, not the interaction of time and cost factors. In this paper, a time-cost based procedure considering both the time and cost factors of rescheduling is proposed. This procedure can be computerized to automate the rescheduling decision in a job shop environment.

The remaining of this paper is organized as follows. Section 2 provides a brief literature review of the related studies. Currently used rescheduling procedures are discussed and evaluated in Section 3. The time-cost based procedure is presented in Section 4 and is followed by a numerical illustration of the procedure in Section 5. Section 6 discusses the implications of the procedure for the cost/management accountants. Finally, a summary and conclusion of the paper is presented in Section 7. Future research directions which will enhance the understanding of this important area are also discussed.

2. BRIEF LITERATURE REVIEW

The term "frequent rescheduling" has been used interchangeably with the term "system nervousness" in the material requirements planning (MRP) systems. Carlson, Jucker, and Kropp (1979) have defined system nervousness as the shifting of scheduled setups. Blackburn, Kropp, and Millen (1986) viewed system nervousness as the instability in planned orders. This problem is continual for MRP users since instability at one stage in the production process tends to propagate throughout the system. A more detailed definition of rescheduling was provided by Mather (1977, p. 69): "changing the required due date on a related replenishment order for either purchased or manufactured material." Minifie and Davis (1986) defined system nervousness as the degree to which upper-level changes immediately reflect in lower-level exception conditions. System nervousness was also viewed as the adverse effects that arise in scheduling systems that use a dynamic due date maintenance procedure (Penlesky, Berry, and Wemmerlov, 1989). The adverse effects of inadequately handling rescheduling problems may include considerably higher rescheduling costs, fluctuation in capacity utilization, and confusion on the shop floor (Campbell, 1971).

This paper focuses on open order rescheduling which has a direct impact on the shop floor performance. Several studies have focused on the impact of schedule disruptions on the system performance (Christy and Kanet, 1988; Ho, 1989; Penlesky, Berry, and Wemmerlov, 1989). Penlesky, Berry and Wemmerlov (1989) compared a static and a dynamic due date maintenance heuristics procedures by the customer service level and the total inventory level. Ho (1989) evaluated the impact of operating environments on MRP system nervousness and concluded that the selection of rescheduling heuristic is rather situation-specific. Examining open order scheduling in a job-shop environment, Christy and Kanet (1988) found that a total decision policy is preferred, i.e., open orders can be revised to either an earlier or later date, in terms of inventory levels and tardiness. However, none of these studies have addressed the cost aspect of rescheduling decisions directly. In this paper, a time-cost based procedure is developed to consider the time required to reschedule and to quantify the cost penalty of rescheduling so as to justify the rescheduling decision economically.

3. RESCHEDULING MECHANISM

There are several rescheduling or dampening mechanisms commonly used in the industry. A dampening procedure can be viewed as a filter which screens out insignificant rescheduling messages. The insignificant rescheduling messages are those which are expected to have little negative impact on the ability of the production scheduling system to meet the desired due date. In contrast, the messages not eliminated by the rescheduling filter are considered significant and should be implemented. The degree of complexity of a rescheduling procedure depends on the criterion used in classifying rescheduling messages. The following two subsections discuss the mechanism of two rescheduling procedures and their limitations.

3.1 Static Dampening Procedure

The static dampening procedures, suggested by Mather (1977) and Peterson (1985), refer to a set of heuristic rules which consider due date changes involving only a few periods as trivial. The magnitude of timing changes in open orders is used as the filtering criterion. For example, Mather (1977) proposed to ignore reschedule-in messages of only one week and reschedule-out messages of less than or equal to two weeks. The rescheduling mechanism is illustrated in Figure 1, which shows a "no rescheduling fence" around a original due date to classify rescheduling messages. The scale represents the magnitude of timing changes in either direction. A reschedule-in of less than a weeks, or reschedule-out of less than b weeks, is to be ignored. It should be noted that "no rescheduling fence" is not necessarily symmetric. That is, the values of a and b can be different because the importance of reschedule-in and reschedule-out may be perceived differently by production planners. Furthermore, the width of "no rescheduling fence" dictates the behavior of this rescheduling procedure. As "no rescheduling fence" widens, the performance of static rescheduling procedure should converge to the procedure that implements all the rescheduling requests.

[FIGURE 1 OMITTED]

The major weakness of this procedure is that the criterion used to classify the rescheduling messages ignores such cost-related information as the cost tradeoffs of rescheduling. As a result, the negative effects of rescheduling may be substantially overlooked. Another operational weakness is the static nature of this procedure. Once the parameters, a and b, used in this procedure are determined, they are rarely revised. Furthermore, this static dampening procedure is applied to all inventory items without regards to lead time, cost, and the interaction of these two factors.

3.2 Automatic Rescheduling Procedure

Jackson (1974) and Orlicky (1976) are proponents of automatic rescheduling in MRP systems, which completely rely on a computer program to reschedule shop orders without manual interventions. All the "feasible" rescheduling messages for shop orders are significant, and thus should be implemented. The criterion used in this procedure is the "feasibility" of rescheduling an open order. Orlicky (1976) defined a "minimum lead time" as the cumulative lead time required to complete a job order with the highest priority. The "minimum lead time" is used to evaluate whether a rescheduling message is feasible. A rescheduling message that reschedules an order inside its minimum lead time is not considered feasible and the system will then reschedule the open order to the date of the minimum lead time. Figure 2 demonstrates the rescheduling mechanism of this procedure.

[FIGURE 2 OMITTED]

In order for this procedure to work effectively, it is necessary to assume that the production systems will be able to accommodate any emergency event if the rescheduled orders requested meet the minimum lead time requirement. This procedure again ignores the cost of rescheduling. Furthermore, this procedure overlooks capacity utilization. If many unexpected events occur at one time and many rescheduling messages are generated, the slack capacity would disappear. Consequently, many orders requested to be rescheduled would be delayed.

4. COST ESTIMATION PROCEDURE

Given the shortcomings of the currently used rescheduling procedures and basing on the concept of "the cost of nervousness" suggested by Carlson, Jucker, and Kropp (1979), this paper presents an alternative rescheduling procedure considering both the time and cost factors in the decision criteria. The term "cost of nervousness" is defined by Carlson, Jucker, and Kropp (1979) as the incremental cost of disrupting previously established schedules. This concept requires the recognition of the economic justification of rescheduling an open order. Ho (1989) first developed a cost-based procedure to screen insignificant rescheduling messages according to the cost trade-offs criterion. This paper further expands this cost estimation procedure which incorporates job-related information such as operation due dates in order to determine the out-of pocket costs and the opportunity costs of rescheduling. Under the proposed time-cost based procedure, each rescheduling decision is made without relying on a subjective perception of system flexibility as used in the static dampening procedure and automatic rescheduling procedure. The focus is on the cost trade-offs of rescheduling. A rescheduling message is viewed as "cost effective" or "significant," if the cost of rescheduling ([COR.sub.i]) of job i is less than that of not rescheduling ([CONR.sub.i]). Otherwise, a rescheduling message is deemed "insignificant" and will not be implemented. In general, [CONR.sub.i] is the late penalty cost of an order requested to be rescheduled but was not being rescheduled. The [COR.sub.i] is defined as the sum of the penalty costs of all jobs that are delayed because job i is rescheduled. To measure the penalty costs, the accountant has to determine the variable costs of carrying inventories (e.g. interest costs, moving, handling, and storing inventories, and also the intangible costs of increase clutter in the plant) and the opportunity costs of not meeting the customers' deadlines.

Two types of rescheduling usually occur in the shop floor: reschedule-in (expediting) and reschedule-out (de-expediting). Consider the following example in Figure 3: five jobs (B, C, D, E, and F) are waiting in the queue and one (job A) is in process at a work center. Using the proposed time-cost based procedure, the following subsections will illustrate how a rescheduling decision can be economically justified in the two rescheduled situations.

[FIGURE 3 OMITTED]

4.1 Reschedule-Out Situation

If there is a rescheduling message to delay the due date of job C, job C would now have a lower priority than job F. The CONR would be the inventory costs (value added and overhead) and the carrying cost of extra inventory for job C if it were to be processed as scheduled. The time period over which this additional inventory would be carried is the sum of the operation and set-up times for jobs D, E, and F.

If job C is rescheduled out as requested, jobs D, E, and F are expected to be completed earlier. Consequently, the COR are the extra inventory costs of jobs D, E, and F which are incurred due to rescheduling. The advantage of freeing up capacity for the emergency orders should, however, be recognized in the reschedule-out situation, Consequently, this advantage may exceed the cost of carrying the extra inventory for jobs D, E, and F. Furthermore, it is not unusual to find that the rearrangement of open order is only a matter of changing the operation due date on the job ticket in the real-world system. The cost of rearranging the affected jobs is usually assumed to be negligible. Hence, the CONR is always greater than the COR for reschedule-out messages and the reschedule-out messages would always be implemented.

4.2 Reschedule-In Situation

The calculation of COR and CONR in reschedule-in situations is quite different from that in reschedule-out situations. Consider job E at the work center illustrated in Figure 3. Suppose that job E is required to reschedule earlier than the original due date. Using a certain due-date-oriented sequencing rule, job E would have a higher priority than jobs C and D. To compute the CONR for job E, we will simply compare the expected completion time of job E with the requested due date to see if there is any delay for this job. The expected completion date is determined by adding all the remaining operation times under the highest priority in the remaining operations to the current date. By rescheduling job E, other jobs will be delayed in the subsequent operations.

The proposed cost-time based procedure focuses mainly on the cost penalty incurred in the current operation. Therefore, the estimation of CONR can be considered as the minimum CONR, which would tilt a rescheduling decision toward implementing a rescheduling request. It is a reasonable assumption in the current operating environment in which quick response technologies have been employed to meet the customer needs. The CONR sets up the minimum cost-threshold for implementing a rescheduling message. The following equation is used to calculate [CONR.sub.i] if we consider rescheduling job i in a work center.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where

[PC.sub.i] = penalty cost per unit per time period delayed for job i, [Q.sub.i] = order quantity of job i, TNOW = current time, ROT = remaining operation time for the job currently being processed, [OT.sub.k] = operation time of job k in front of job i, [RMOT.sub.i] = remaining operation times of job i, [DD.sub.i] = job due for job i, and [[??].sub.i] = number of jobs in front of job i before being rescheduled.

To calculate the COR, we need to consider the completion dates of jobs C and D which might be affected by this rescheduling decision. To assess the late penalty cost, we would compare the operation due dates of jobs C and D with their expected completion dates to see if there is a delay for both jobs at this work center. Therefore, operation due dates are considered milestones for a job order involving multiple operations in a job shop environment. Operation due dates are widely established in job tickets which can easily be retrieved in manufacturing firms. If there is a slack capacity in the job shop, the expected completion dates of jobs C and D may be earlier than operation due dates. If jobs C and D are not affected by rescheduling job E earlier, the COR for job E is zero. Otherwise, the COR would be assessed according to how much delay of jobs C and D caused by this rescheduling decision.

[COR.sub.i] = [m.summation over (k=1)][PC.sub.k] * [Q.sub.k] * max. {TNOW + [[gamma]k.summation over (j=1)[OT.sub.j] + ROT - [OPDD.sub.kj], 0 (2)

where

m = m jobs affected by rescheduling job i;

[[gamma].sub.k] = number of jobs in front of job k (including job k) after job i is rescheduled; and [OPDD.sub.kj] = operation due date of the jth stage of operation for job k, which is determined by the following equation. [OPDD.sub.ij] = [OPDD.sub.i,j-1] + [[OT.sub.ij] / [[kappa].summation over (j=1)[OT.sub.ij]] * ([LT.sub.i]) (3)

where

[OPDD.sub.i,j-1] = the order release date for job i when j - 1 = 1, [OT.sub.ij] = operation time for the jth operation for job i, K = the number of operations required for job i, and [LT.sub.i] = the lead time for job i.

Note that only the current operation of jobs C and D are considered in the estimation of COR. The due dates of jobs C and D are not considered here as there may be several subsequent operations for jobs C and D. In addition, there are too many possibilities in the subsequent operations. The delay times of jobs C and D may be made up in the subsequent operations, or they may further delay other jobs in the subsequent operations. This so-called "domino effect" is not considered in this time-cost based procedure. Otherwise, this estimation procedure would become unnecessarily complicated which would serve no value to production planners.

5. ILLUSTRATION OF ESTIMATION PROCEDURE

In the discussion under the reschedule-out situation, any request for rescheduling to a later date would be implemented based on this time-cost based procedure. The following numerical example is used to illustrate the mechanism of this time based procedure for a reschedule-in situation. Consider the same reschedule-in example illustrated in Figure 3. Suppose that job E is requested to be rescheduled to week 5.

Let

[PC.sub.i] = $1.8/unit/week; [Q.sub.i] = 10 units of job E; TNOW = week 3; ROT = 0.5 week of job A; [OT.sub.i] =. 6 week for job B, .8 week for C, .7 week for D, 1 week for E; [RMOT.sub.i] = 1.9 weeks for job E; [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] = 2.1 weeks, total operation time of jobs B, C, and D; [DD.sub.i] = week 5, the requested due date for job E; and [[??].sub.i] = 3, the number of jobs in front of job E, i.e., jobs B, C, and D.

Thus, using equation (1) we obtain the cost of not rescheduling:

[CONR.sub.i] = $1.8 * 10 * max. {3 + 0.5 2.1 + 1.9 - 5, 0} = $45.

If job E is rescheduled, then jobs C and D would be affected. The operation due date of job C is calculated as follows:

[OT.sub.ij]= 0.4 week, operation time for the jth operation for job C; [LT.sub.i] = 4 weeks for job C; [OPDD.sub.i, 1] = the second week, which is the order release date for job C; [kappa] = 3 operations required for job C; and [[kappa].summation over (j=1)][OT.sub.ij] =.8 weeks, the operation time for job C.

Using equation (3), [OPDD.sub.ij] = 2 + [.4/.8] * (4) = week 4

The operation due date for job D is calculated similarly. Suppose that the operation due date for job D is week 5.2. Furthermore, assume that the lot sizes for job C and D are 6 and 8 units, respectively. If the penalty costs of jobs C and D are $2.5/unit/week and $1.5, respectively, then the cost of rescheduling can be computed by using equation (2).

[COR.sub.i] = $2.5 * 8 * max. {3 + 2.4 + 0.5 - 4.0, 0} +

$1.5 * 6 * max. {3 + 3.1 + 0.5 - 5.2, 0} + $50.6

Since [COR.sub.i] > [CONR.sub.i], this rescheduling message will not be implemented. Note that the cost of rescheduling calculated is only the "reference cost" for making rescheduling decisions, and it may not actually be incurred. Furthermore, the rescheduling decision is sensitive to the relative penalty costs for the items involved in a rescheduling decision (jobs C, D, and E in this example). For instance, if the penalty costs of jobs C and D are both $1.8/unit/week, then the cost of rescheduling can be recalculated as $42.48. Since [COR.sub.i] < [CONR.sub.i], this rescheduling message should be implemented. Therefore, in order to develop an effective rescheduling procedure, it is important to estimate the late penalty for the incoming job orders accurately.

6. MANAGERIAL IMPLICATIONS FOR COST MANAGEMENT

In recent years, there is increasing pressure on management accountants to take a more proactive role and to be part of the production team. They should remove the image of bean counters by getting involved in developing information and decision support systems which can improve the efficiency of decision making. Providing cost information to enable planning engineers to make accurate job scheduling decisions is an area that accountants can help significantly.

Activity based costing (ABC) system focuses on tracing costs to the activities required to produce products or provide services. With the implementation of ABC system, it would be possible to provide shop floor personnel with detailed breakdowns of cost incurrences. This costing system can complement the proposed time-cost based procedure as it provides the cost information required for job rescheduling decisions. For instance, an activity or an operation in the shop floor needs to be rescheduled due to an emergency order from a field component/part warehouse. Traditionally, the price of this emergency order would be the cost plus the express shipment expenses. In reality, in order to meet the deadline, some existing set-ups may need to be preempted or torn down to process this emergency order. All these could affect completion times of other items in the same waiting line of the work center. To cost the emergency order accurately, the rescheduling costs, both out-of-pocket and opportunity costs, should be considered and should be accurately reflected in pricing this kind of emergency orders.

Additionally, the proposed time-cost based procedure establishes an evaluation mechanism to justify the need for rescheduling. The cost of not rescheduling can be easily calculated as the penalty of missing requested due dates of existing orders. While the cost of rescheduling can be obtained from the estimation procedure, it can be compared with the cost of not rescheduling to determine whether a certain rescheduling request should be implemented. The economic justification of rescheduling tends to reduce the total cost of operations, which may include carrying costs, set-up costs, shortage costs, and rescheduling costs. At the time of pressing reengineering processes in production systems, cost reductions can be a very important yardstick for benchmarking. Implementing this time-cost based procedure could help accountants in achieving the cost-reduction objective.

7. SUMMARY AND CONCLUSIONS

In this paper, we have presented a time-cost based procedure that helps production planners to automate rescheduling decisions in a job shop environment. This procedure can be incorporated with MRP systems to deal with frequent rescheduling problems. The goal in development of this procedure is to free up production planners to work on more urgent operational problems. It should also help shop floor personnel establish a credible priority planning system instead of turning to informal expediting methods.

In the future, a comprehensive study will be conducted to evaluate the performance of the proposed time-cost based procedure under a variety of operating environments such as MRP or just-in-time (JIT) manufacturing systems. A general guideline can then be drawn to help production professionals implement this procedure effectively in their operating environments. This is an important research area as it supplements the current trend of adopting quick-response technologies in manufacturing firms and service industries. These technologies typically involve rescheduling orders to meet the urgent demand. We should realize that there could be a significant cost penalty associated with the implementation of this quick-response strategy. A trade-off analysis appears to be a logical step when considering the employment of quick-response technologies.

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Chrwan-jyh Ho, Oklahoma State University, Oklahoma, USA

Meihua Koo, College of Business, University of Nevada, Las Vegas, Nevada, USA

Amy H. Lau, School of Business, University of Hong Kong, CHINA