The performance of workload rules for order acceptance in
batch chemical manufacturing
Citation for published version (APA):
Raaymakers, W. H. M., Bertrand, J. W. M., & Fransoo, J. C. (2000). The performance of workload rules for order acceptance in batch chemical manufacturing. Journal of Intelligent Manufacturing, 11(2), 217-228.
https://doi.org/10.1023/A%3A1008999002145, https://doi.org/10.1023/A:1008999002145
DOI:
10.1023/A%3A1008999002145 10.1023/A:1008999002145 Document status and date: Published: 01/01/2000
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The performance of workload rules for order
acceptance in batch chemical manufacturing
W E N N Y H . M . R A AY M A K E R S , J . W I L L M . B E R T R A N D and J A N C . F R A N S O O *
Department of Operations Planning and Control, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
E-mail: w.raaymakers@organon.oss.akzonobel.nl, J.W.M.Bertrand@tm.tue.nl, J.C.Fransoo@tm.tue.nl
We investigate the performance of workload rules used to support customer order acceptance decisions in the hierarchical production control structure of a batch chemical plant. Customer order acceptance decisions need to be made at a point in time when no detailed information is available about the actual shop ¯oor status during execution of the order. These decisions need therefore be based on aggregate models of the shop ¯oor, which predict the feasibility of completing the customer order in time. In practice, workload rules are commonly used to estimate the availability of suf®cient capacity to complete a set of orders in a given planning period. Actual observations in a batch chemical manufacturing plant show that the set of orders accepted needs to be reconsidered later, because the schedule turns out to be infeasible. Analysis of the planning processes used at the plant shows that workload rules can yields reliable results, however at the expense of a rather low capacity utilization. In practice this is often unacceptable. Since, solving a detailed scheduling problem is not feasible at this stage, this creates a dilemma that only can be solved if we can ®nd more detailed aggregate models than workload rules can provide.
Keywords: Batch process industries, workload control, capacity planning, order acceptance
1. Introduction
In this paper, we investigate the appropriateness of workload rules used to support customer order acceptance decisions in the hierarchical production control structure of a batch chemical plant. The plant considered produces active ingredients for the pharmaceutical industry. Production is characterized by long and complex routings, and consequently long throughput times. The plant is a so-called multi-purpose plant (Reklaitis, 1990) in which products may follow different routings, like in a traditional job shop. An important difference with the traditional job shop is that in this situation unstable intermediate products
cause no-wait restrictions between processing steps. At the operational level a schedule needs to be constructed in which these no-wait restrictions are met. At the work order release and customer order acceptance level, an assessment needs to be made regarding the estimated throughput time of a set of orders (i.e., the makespan). Due to the variety in product routings and the no-wait restrictions some capacity slack is required for this higher level decision, since it is not possible to construct a detailed schedule at the time the customer order acceptance decision needs to be made.
There are two main reasons why it is not possible to use detailed scheduling to determine the amount of capacity slack required at higher planning levels. First, detailed scheduling is not useful, since disturbances may occur that in¯uence the shop ¯oor status. Second,
0956-5515 # 2000 Kluwer Academic Publishers *Contact author.
decisions concerning order acceptance need to be made quickly; scheduling is often too time-consuming in that situation. Therefore, aggregate methods for estimating the capacity slack are preferred.
A commonly used aggregation principle is the use of workload rules. These workload rules determine the maximum workload that is allowed per resource type based on empirical information. This is the aggregation principle currently used by this batch chemical plant and many other plants. The main problem resulting from using workload rules in the batch chemical plant, was that many of the released orders cannot be completed in the planned period. This results in low delivery reliability and many re-planning activities. In this paper we investigate the cause of this phenomenon.
The paper is organized as follows. Section 2 describes the batch chemical plant and the hierarch-ical production planning methods used. Section 3 discusses the aggregation and disaggregation princi-ples proposed in the literature. Section 4 characterizes the hierarchical production control used by Pharmcom in terms of aggregate control and disaggregate control. Section 5 discusses the performance of the customer order acceptance procedure for one of the departments of the plant. Section 6 gives the results of experiments in which the performance of workload rules is tested. Finally, in Section 7 conclusions are drawn and possibilities for further improvement of the aggregation principles proposed.
2. Description of the batch chemical plant Pharmcom is a worldwide producer of active ingredients for pharmaceutical products. In this paper, the production of chemical ingredients at a production site in The Netherlands is considered. In three production departments approximately 140 ®nal products are produced. Routings are divergent, and consist of 4 to 25 operations, with a total throughput time of 3 to 9 months. Each operation results in a stable intermediate product that can be stored. Subsequent operations in a routing are often performed at different production departments.
Each operation consists of one or more processing steps, each of which requires a single resource. Processing steps may be overlapping in time. During an operation, the intermediate product is generally not stable, resulting in no-wait restrictions between
processing steps. Figure 1 presents an example of an operation consisting of three processing steps, for which two vessels and a ®lter are required. The bold lines show when the resources are needed. The time at which vessel 2 and ®lter 1 are required in relation to the start time of the processing step on vessel 1 is given by a ®xed time delay (q).
The three production departments (PDs) are functionally organized. The PDs contain, on average, 30 vessels including some highly speci®c vessels and several general-purpose vessels. For the speci®c vessels, no alternatives are available at the production site. General-purpose vessels are grouped into work centers within the PDs. Each production department can perform a speci®c set of operation types. When an operation type can be performed in more than one PD, the operation is allocated to one of these PDs. That PD then completes all production orders for the operation type.
2.1. Production planning at Pharmcom
Three planning levels are distinguished, namely aggregate planning, material and capacity planning, and shop ¯oor control. Figure 2 gives an overview of the planning levels. The two highest levels are the responsibility of the logistics department (LD). The production departments perform shop ¯oor control (SFC). The complex goods ¯ow between PDs requires close coordination by the LD. In addition, the coordination with sales concerning customer order acceptance is the responsibility of the LD. This is an important function because of the demand uncertainty and the lumpiness of demand.
2.2. Aggregate planning
The coordination between the production, marketing and sales, logistics, and research and development departments is performed at the aggregate planning level. The planning horizon is one year, divided into monthly periods. Generally, customer orders are known over a horizon of three months. Because of the manufacturing throughput times of three to nine months, production often needs to be started before actual customer orders are received. Thus, the ®rst operations in a routing are performed based on the demand forecasts, while the last operations are performed based on actual customer orders. At the aggregate planning level decisions are made
con-cerning both the production to forecast as the production to order. Based on the expected demand and the amount of product in the ``pipeline'' it is decided how many batches of the products need to be produced and when the ®nal products need to become available. Using the average throughput time, the periods in which the ®rst operation of a routing needs to be performed is determined. The subsequent operations in the routing are planned allowing some time-slack between successive operations. The number of batches that need to be produced per operation depend on the batch size used for that operation. Each production order is related to a single batch of a speci®c operation. When customer orders arrive, the products in the ``pipeline'' are allocated to these customer orders. The due dates agreed with
customers may differ from the dates used in the forecasts. In that case production may be accelerated or slowed down by decreasing or increasing the time-slack between two subsequent operations in a routing. To estimate whether suf®cient capacity is available to realize the aggregate production plan, workload rules are used. For each work center, the maximum workload is speci®ed as a percentage of the available capacity of that work center. The workload limits have been determined empirically, based on evalua-tions of the realized production in previous periods. The limits provide the capacity slack that is needed to account for the capacity losses that will be incurred by interaction between production orders and by the disturbances in the production system. Interactions between production orders result from the fact that for
Fig. 1. Example of an operation.
each operation several resources are required, and that no-wait restrictions apply to the processing steps of an operation. The maximum workload allowed deter-mines the maximum utilization of a resource.
2.3. Material and capacity planning
At the material and capacity planning level, the aggregate plan is worked out in more detail. The time unit is weeks and the horizon is approximately three months. Two types of manual planning sheets are used as a graphical representation. Routing planning sheets are used for planning the production orders for subsequent operations of one product. In general, a period of two weeks is planned for a production order. Between operations a few weeks of time-slack is planned to cope with production uncertainties. If the subsequent operation is carried out in a different department or if the operation requires a bottleneck resource, more time slack is included in the plan. For products with few operations and/or for products that only require non-bottleneck resources, no routing planning sheets are made. These products are planned by standard MRP, using standard lead time offsets.
Capacity planning sheets are used for planning the bottleneck resources. For each operation at most one resource is considered a bottleneck, and hence, has a capacity planning sheet. Otherwise, coordination between several capacity planning sheets is required, to make them consistent with respect to the no-wait restrictions between processing steps of the same operation. This problem is considered to be too time-consuming to be solved at this level. In practice, this means that several general-purpose resources, which are highly loaded, are not considered as a bottleneck resource. On the capacity planning sheets, the operations of different products that require the same bottleneck resource are planned. The planning on the capacity planning sheets always has to be consistent with the planning on the routing planning sheets. This requires much effort of the planners at the LD.
The start times for operations, according to the routing planning sheets, are integrated with the planning of the MRP planned products by entering them manually into the automated production planning system. Then a production plan is obtained for each production department for a period of three months. This production plan contains the production
orders that have to be carried out, the release dates and due dates of these production orders. Each month a new production plan is provided to the PDs.
2.4. Shop ¯oor control
The PDs construct a detailed schedule with a one-month horizon from the production plan provided by the LD. At this point, the no-wait restrictions between processing steps have to be taken into account. If a feasible schedule cannot be obtained that completes all planned production orders in time, notice is given to the LD. There will be some negotiation on what can be removed from the production plan to realize a feasible schedule. Small disturbances that occur during execution of the schedule are solved by the PD. For major disturbances, the LD is consulted to set priorities.
3. Aggregation principles and hierarchical production planning
The production control structure at Pharmcom clearly shows features of a hierarchical planning and control system. Decisions are made at aggregate and detailed levels, pertained to different time horizons. Hierarchical production planning has been studied from different angles. Hax and Meal (1975), Bitran & Tirupati (1993), and Meal (1978, 1984) published the ®rst results. They considered the problem of deciding for a range of products, consisting of a number of product families, about the amount of product to produce per period. Product families are determined by their similarity of machine set-up. In view of the relationships between the products, due to the shared machine set-up, they designed a hierarchical decision procedure. This procedure ®rst decides about which product families and the total amount of product per family to produce. This is the aggregate decision. Next, for each family, the allocated production is distributed over the individual products in the family. This disaggregation procedure is implemented for the ®rst period only. Thus, the Hax-Meal HPP approach heuristically decides about a complex decision problem, which can be represented in one decision model, in two phases. First, an aggregate problem is solved that generates constraints for a number of detailed problems. Then, the ®rst of the detailed
problems is solved. The Hax-Meal HPP approach, therefore, decomposes the complex overall decision problem into a number of less complex decision problems. AxsaÈter (1981) and AxsaÈter and JoÈnsson (1984) have studied the conditions under which such an approach leads to the optimal solution. In particular, they investigated for which decision problems, an aggregate decision problem can be de®ned that, when solved, leads to a detailed problem that always results in an overall optimal solution. The Hax-Meal approach and the work of AxsaÈter (1981) and AxsaÈter and JoÈnsson (1984) are closely related to the techniques that have been developed for solving complex mathematical programming models (see Graves, 1982). Thus, the approach is applicable to situations where there exists a complex large-scale model that is dif®cult to solve as a single (monolithic) model. The solution proposed by the body of literature that is based on the work done by Hax and Meal is to decompose the model and solve it in two phases. This view on decomposition is therefore called model decomposition.
Holt et al. (1963), Bertrand and Wortmann (1981), Bertrand, Wortmann and Wijngaard (1990) and Schneeweiû (1995) take a different view on hier-archical production planning. They consider production planning and control as a hierarchy of decision problems with decision variables that each have different effectuation times. The effectuation time of a decision is the time that elapses between the moment that the decision is made and the moment that the impact of the decision on the state of the system has materialized. For instance, if the decision to expand the capacity c0, with a factor a is taken at time
t0, and if the effectuation time of the capacity expansion decision is T time units, then the decision will not be implemented until time tT. However, during the time interval t0, tT unforeseen events may also in¯uence the capacity. Consequently, the actual capacity at tT, may not be ac0, but ac0 e, with e representing the aggregate effects of the other events during t0, tT. Since the decision variables in a decision hierarchy have different effectuation times, and many not modeled factors affect the state of the primary process, it will be clear that a direct ``hard'' relationship between aggregate and detailed decisions cannot exist. In addition, the reason for decomposing the problem into an aggregate and a detailed problem is not necessarily that the overall problem is too hard to solve. The main reason is that at the time the
aggregate decision must be made for a certain period, the detailed decisions for that period need not yet be made and maybe cannot even be made. Furthermore, the necessary information to make the detailed decision may not be available yet. Put in another way, the detailed decisions for a certain period are made within restrictions that are affected by an aggregate decision that was made a number of periods ago. However, this aggregate decision is not the only factor that affects these restrictions. Thus, there exists a rather ``loose'' relationship between the aggregate decision problem and the detailed decision problem. This means that the aggregate decision is one of the factors that constrains the detailed decision problem, but not the only one. This approach to HPP we call problem decomposition.
If the relation between the formulation of the aggregate problem and the formulation of the detailed problem is loose, an abstraction of the detailed and actual state at time tTneeds to be made at time t0. In the case of planning and scheduling problems, this abstraction is usually based on queuing theory results (e.g., Buzacott and Shantikumar, 1993), and the expected workload is used as an abstraction of the detailed state of the primary process. In job shops, this has been researched extensively by Bertrand and Wortmann (1981), Van Ooijen (1996), Wiendahl (1995) and Hopp and Spearman (1996).
4. Hierarchical production planning at pharmcom Also at Pharmcom, workload is used as an abstraction of the expected state of the detailed process. The description in Section 2 shows that the execution of the customer orders requires many operations leading to a long throughput time. The acceptance of customer orders is a decision to deliver the customer orders at a certain future moment in time. Upon acceptance, the materials in the pipeline are allocated to the customer order. Generally, several operations are required before the ®nal product becomes available to the customer. The detailed decisions regarding the scheduling of the production orders associated with these operations are taken later on, within the constraints of the actual capacity available, and the actual customer order due dates. Customer order acceptance takes place for a set of orders, taking into account the material content in the pipeline, the customer orders having been accepted already, and the
available capacity over the customer order lead times. Customer order acceptance at Pharmcom therefore is part of the aggregate decision problem. The aggregate decision regarding the due dates of the customer orders aims at balancing resource utilization and delivery reliability. Further, work orders and due dates are set for the detailed order scheduling and sequencing decisions, which are taken later. The detailed decisions determine the actual resource utilization and the actual delivery performance. In line with the observations made earlier, the aggregate decision needs to be based on a model of the expected performance by the detailed scheduling operation. This expected performance needs to be formulated as a function of the customer order lead times and the capacity slack on the resources. Customer order acceptance and detailed order scheduling are deci-sions that for each order are taken in different periods. At Pharmcom many disturbances in the production process affect the actual progress of the production orders. In view of the previous description of the routing variety and resource requirement structures, we may therefore expect the product mix to have a large impact on the feasibility of the accepted customer order due dates. However, aggregate production planning at Pharmcom is only based on very rough-cut workload rules, while the resource utilization norm is quite high. Considering both factors, we may expect that large differences will exist at Pharmcom between the production orders in the aggregate plan, and the scheduled production orders. Analyzing the planning and production records at Pharmcom we have checked this. The results are reported in the next section.
5. Performance analysis of a production department at Pharmcom
In this section, one of the production departments at Pharmcom is considered. In total, 50 types of operations have been allocated to this production department, which consists of 20 resources. The actual utilization of the work centers (April±June 1996) ranges from 43 to 100%, with an average resource utilization of 73%. Work center 1, with 2 resources, is considered as the main bottleneck for this PD. Work centers 2, 3 and 4 contain 3, 3 and 2 resources, respectively. These work centers also have a relatively high utilization. The other work centers
contain speci®c resources with a low or very low utilization level.
We have compared the aggregate production plan of three consecutive months, determined by the LD, with the accepted and scheduled production orders in the same period. Each production order re¯ects one operation in a routing. Based on the workload rules per work center and the information in the capacity planning sheets for bottleneck resources, the LD generates the set of production orders that are planned for a period of one month for each PD (aggregate production plan). At the start of each monthly period, the PD's accept only those production orders they expect can be completed within that month. The PDs then make a detailed schedule that is updated weekly. We assumed that this detailed schedule closely resembles the actual execution of the orders.
Table 1 shows for a number of consecutive months the planned, accepted and scheduled production orders in that month. Table 1 shows that, although the variation is high, on average 68% of the total number of planned production orders for a given month have been accepted for production in that period. Further, 65% of the planned production orders are actually scheduled for execution in that month. In addition to these accepted orders the production department often also processes some orders that had been accepted for the previous month, but have not yet been completed. These orders are not included in the number of production orders accepted and scheduled for that month. Table 1 also gives the difference in workload that has been planned by the LD, accepted by the PD, and actually scheduled (and thus realized). The accepted and scheduled workloads also include production orders that were not planned for the month.
The difference between planned and accepted production orders may result from production dis-turbances, from a plan that is not completely up-to-date or from an incorrect model of the available capacity used at the aggregate level. In situations with a production backlog, the plan should be updated to provide a feasible plan to the PDs. If the plan is not completely up-to-date, this may lead to a relatively low acceptance percentage.
The model used to estimate the availability of suf®cient capacity is mainly based on workload rules. The planners in the LD assume that a feasible schedule can be obtained if the workload per work center does not exceed a speci®ed maximum
work-load. In addition to these workload rules, bottleneck resources are considered in more detail by means of capacity planning sheets. To limit the complexity and the time spent on constructing and updating the capacity planning sheets, only a few resources are considered as bottlenecks. The availability of suf®-cient capacity for other resources with a high workload is evaluated by workload rules only.
Given the large difference between planned and accepted production orders, we may conclude that the LD does not succeed in setting feasible production plans. A possible reason could be that the simple workload rules are insuf®cient predictors of the feasibility of the set of production orders. Another possible reason is that workload rules in itself are a good method for estimating the availability of suf®cient capacity, but that incorrect workload limits are used.
To investigate whether workload rules are an appropriate aggregation principle for estimating the availability of suf®cient capacity for the type of production situations encountered by Pharmcom, we conducted some experiments. In view of the wide-spread use of workload rules in the rough-cut capacity planning in both industry and literature, it is of scienti®c importance to identify the production situations where these rules do not yield satisfactory performance. The investigation has been done by performing a number of experiments with workload rules for the production department studied. These experiments are discussed in the following section.
6. Investigation of workload rules as an aggregation principle
6.1. Customer order acceptance model
We conducted experiments to validate whether the workload rules are appropriate to determine sets of
production orders for which a feasible schedule can be realized. In the situation of Pharmcom, customer orders are not related one by one to production orders. One customer order may result in several production orders. At the same time, several customer orders may be combined into one production order. Furthermore, customer orders may generate production orders for several departments. In our experiments, we limit ourselves to one of the PDs.
In the experiment, we have generated random production orders for this department based on their actual production frequency in 1996. The production order frequency provides a good re¯ection of the actual demand frequency, because in that year all customer orders were accepted. For some operations, always more than one production order is combined. This is often done because the following operation must be performed with a larger batch size. To allow for this requirement, we generate a number of production orders at the same time for some operations. These production orders are considered as a single group in making the acceptance decision. In generating production orders the relations between production orders for operations that are part of the same routing are not considered, because often successive operations are executed in different production departments. Furthermore, the planned time slack between successive operations is variable. Consequently, it is realistic to assume that there are no precedence relations between different production orders that are planned in the same period for a speci®c production department.
For accepting production orders, periods of 4 weeks in a three shift system T 480 hours are used. This period length is equal to the length of the aggregate planning periods used at Pharmcom. The generated production orders are accepted if the workload on each work center Lmax :: remains below a pre-speci®ed level. This level is expressed as a percentage of the available capacity. If the workload exceeds the
Table 1. Planned versus accepted and scheduled production orders and workload
Number of orders Man hours Machine hours
Plan Acc Sch Plan Acc Sch Plan Acc Sch
July 100% 78% 67% 100% 90% 68% 100% 95% 66%
August 100% 86% 84% 100% 82% 85% 100% 81% 84%
maximum level, orders are rejected. Also, a minimum and maximum total workload (Lmin and Lmax) on the
total capacity over all resources is speci®ed. To ensure a minimum level of overall utilization of resources the minimum total workload is set to 50% in all experiments. As a stopping criterion for generating orders, we use the number of rejected orders after the speci®ed minimum total workload is reached. In each experiment, 10 order sets are generated using these workload rules. For each resulting order set, a near-optimal schedule with respect to makespan Cmax is obtained by simulated annealing. The scheduling algorithm used in the experiments is described in Raaymakers and Hoogeveen (1998).
Some simplifying assumptions have been made for the scheduling phase. Resources that are included in the same work center are considered identical. Resources in different work centers are considered different, and therefore, cannot be used alternatively. Resources are assumed continuously available. Furthermore, the no-wait restrictions between proces-sing steps of an operation are considered ®xed, while in practice there may be some ¯exibility.
6.2. Experimental design
The performance of the workload based customer acceptance rule may depend on the actual workload limits used. Therefore, we evaluated 15 scenarios in which different values for this maximum workload were evaluated. Two types of workload rules were considered. For the ®rst type, the total workload over all resources provides the binding restriction. For the second type, the workload per work center is the binding restriction. Scenarios 1 to 5 use the ®rst type of workload rules. In these scenarios, each individual work center had a workload limit of 100% of its available capacity. The total workload over all resources was limited to 100, 90, 80, 70 and 60% of the available capacity, respectively. Scenarios 6 to 15 use the second type of workload rules. In these scenarios, the workload limits per work center are set at a lower level than 100%. The limit on total workload was set on 100% of the available capacity, which means that total workload did not provide a restriction. This type of workload rule provides more degrees of freedom for modeling the workload, because a speci®c workload limit needs to be de®ned for each work center. We used both equal workload limits for all work centers (scenario 6 to 8) and
unequal workload limits, in which the general-purpose resources have lower workload limits (scenario 9 to 13). These are similar to the workload limits applied by Pharmcom. Finally, we did experiments in which workload limits were higher for the work centers at which more than one resource is available (scenario 14 and 15). We performed these experiments because we expected that the allowed workload on resources could be higher if more parallel resources exist at a work center. The results of the experiments are given in the following subsection.
6.3. Results
Table 2 presents the results of the different scenarios. Columns 1 to 5 give the scenario number, the limits used for total workload Lmax and workload per work
center Lmax ::, respectively. Recall that work
centers 1 and 4 each contain two identical resources, and work centers 2 and 3 each contain three identical resources. All other resources are speci®c resources. Work centers 1, 2 and 3 have the highest capacity requirements for the 10 order sets generated under the workload limits. Column 6 and 7 give the mean and variance of the makespan divided by the period length Cmax=T obtained from the scheduling phase. The mean should be close to 1, because then the order set can be completed in time and idle time is relatively small. Also, the smaller the variance the more accurate a prediction that is given of the feasibility of the order set by using the workload rules shown per scenario. The last column in Table 2 gives the average overall workload for each scenario.
Figure 3 gives the makespan divided by the period length Cmax=T for each of the 10 experiments executed for the different scenarios. An order set is feasible if Cmax=T51. That is, the makespan obtained is smaller than or equal to the period length, since, in that situation all orders can be completed before the end of the period. Inspection of the data in Table 2 and Fig. 3 leads to some interesting observations. It is interesting to notice that order acceptance based on total workload limits only, does not provide feasible order sets at all. For lower limits, the performance improves (lower average and lower variance) but even for a low load limit of 60% of total available capacity, all accepted sets of orders have a makespan which is longer then the period length. The ®rst type of workload rule therefore seems not to be very
effective. The implication of this observation is that if workload based order acceptance rules are effective, then load limits should be speci®ed for each work center. This type of workload rule was deployed in scenarios 6±15.
Table 2 shows that there are two scenarios (8 and 11) for which all 10 order sets are feasible. However, the average resource utilization that results from these scenarios is relatively low, 52 and 53%, respectively. Also several other scenarios result in order sets for
Table 2. Workload rules scenarios
Sc. Lmax Lmax 1; 4 Lmax 2; 3 Lmax rest E Cmax=T var Cmax=T E(L)
1 100 100 100 100 1.23 0.007 68 2 90 100 100 100 1.23 0.007 68 3 80 100 100 100 1.23 0.007 68 4 70 100 100 100 1.20 0.006 67 5 60 100 100 100 1.17 0.004 60 6 100 90 90 90 1.09 0.002 62 7 100 80 80 80 1.00 0.002 57 8 100 70 70 70 0.93 0.001 52 9 100 100 70 100 1.02 0.003 57 10 100 90 70 90 0.98 0.002 56 11 100 80 70 80 0.93 0.001 53 12 100 100 80 100 1.10 0.006 60 13 100 90 80 90 1.01 0.003 58 14 100 80 90 70 1.12 0.003 59 15 100 70 80 60 1.01 0.004 53
which the makespan is on average close to the period length. The scenarios 7, 9, 10, 13 and 15 provide order sets that are sometimes feasible. The average total workload accepted for these scenarios is on average 57%. This is 5% higher than for the scenarios that always result in a feasible order set. There is one exception to this, namely scenario 15, which results in an average total workload of only 53%. Study of the detailed data of this scenario revealed that this is mainly due to the relatively low accepted workload for non-bottleneck resources (work center 4 to 11).
Detailed inspections of the data resulting from the difference in resource use show that the workload rules are only restrictive for work centers 1, 2, and 3. All other work centers have a workload that never exceeds 50%. Furthermore, if the maximum workload of work centers 2 and 3 is lower than the maximum workload on work center 1, this automatically limits the accepted workload on work center 1. This is because most products requiring work center 1 also require either work center 2 or 3. This explains why the difference between scenarios 9 and 10 is small. Finally, we see that the results for scenario 8 and 11 not only always yield a realizable set of orders, but also show much less variance than the results for the other scenarios. Therefore, these two scenarios
provide the best workload limits for the PD considered.
We may conclude that, apparently, detailed work-load rules can result in feasible sets of work orders. However, this goes at the cost of a rather low overall capacity utilization. In fact, it turns out that there exists a linear relationship between the average Cmax=T value and the planned overall resource utilization obtained for the 15 scenarios. Figure 4 shows a plot of the relationship between the makespan of the accepted order set and the planned overall capacity utilization. Note that the realized overall capacity utilization is only equal to the planned capacity utilization in a speci®c period, if the makespan realized is equal to or shorter than the period length. Now recall from the planning and scheduling process at Pharmcom that 65% of the planned orders for a period are actually scheduled in that period. This indicates that it would take approximately 1.5 times the period length to complete all the planned orders. Hence, the value for Cmax=T for the production department of Pharmcom will be approximately 1.5. In Fig. 4 we can see that this will correspond to a planned capacity utilization of approximately 80%. This is not surprising due to the high capacity utilization targets set at Pharmcom.
The results in Figs. 3 and 4 reveal that order
acceptance based on workload rules does not simultaneously result in accepted production order sets with reliable due dates and a high capacity utilization. Now the question is whether the perfor-mance could be improved by constructing a detailed schedule to support the customer order acceptance decision. This would most likely result in a better performance if short term scheduling assumptions (such as the availability of detailed data) would be valid at the time the order acceptance decision needs to be made. However, order acceptance for a speci®c period takes place a number of period earlier. At that time, resource availability and operation processing times are not known with suf®cient accuracy and reliability. Therefore, also in that case re-planning at the scheduling level would be inevitable, resulting again in a poor delivery performance.
Based on these observations, we conclude that a procedure is needed that is able to predict the future scheduling performance for a given set of work orders, without making a detailed schedule. Such a procedure would base its predictions on the char-acteristics of the order set and the resource structure that are known at the time of order acceptance and that remain valid until the time of execution. An approach like this requires a model at the aggregate (customer order acceptance) level that is not directly related to the detailed scheduling model. In this sense, the hierarchical approach underlying such a procedure would be in line with the problem decomposition methodologies as they were discussed in Section 3.
7. Conclusions
In this paper, we have studied the use of workload rules for customer order acceptance in a batch chemical plant. We have analyzed the production control problem of the plant and concluded that the plant employs a hierarchical control structure that is based on problem decomposition, in line with the work of Bertrand et al. (1990) and Schneeweiû (1995). The reason for decomposing the problem into an aggregate and a detailed problem is not primarily because the overall problem is hard to solve, but because at the time that the aggregate decision is made, the detailed decisions for the same period cannot and need not yet be made. Several production and demand disturbances may occur during the time
between the aggregate and detailed decision making, that in¯uence the detailed decision.
At Pharmcom customer order acceptance is performed using aggregate information about orders. This is because upon acceptance of a customer order the detailed situation at the shop ¯oor at the time of execution of the production orders is unknown. The availability of suf®cient capacity for a certain set of orders is checked by determining the expected workload on the resources. Production orders are planned in a period as long as the workload on the resources remains below a speci®ed level. Sets of production orders that meet these restrictions are assumed feasible. Analysis of the real-life data of the plant showed only 66% of the production orders accepted for a period by the customer acceptance decision can actually be scheduled and executed in that period. One third of the orders need to be rescheduled. This results in a lot of re-planning and makes it dif®cult to set short and reliable due dates.
To test whether these large deviations are due to the aggregation rule based on workload, we have investigated a model of this hierarchical control structure. In a simulation experiment, randomly generated production orders were accepted as long as the resulting workload per work center or totaled over all work centers did not exceed certain values. Different scenarios have been investigated. The research showed that reliable accepted order sets could be obtained, but only when restricting the workload per work center. However, the reliability goes at the cost of a rather low capacity utilization, namely 53% instead of 73% actually realized at Pharmcom. We therefore concluded that workload rules are inadequate to obtain both reliable accepted order sets and a high capacity utilization.
We also concluded that detailed scheduling will also not lead to more reliable accepted orders. Therefore, research is needed for performance prediction models, which contain more information on the characteristics of the order set and the resource structure than workload rules, but do not assume full and detailed knowledge order processing times and resource availability.
Acknowledgments
This research has been made possible through the cooperation of Pharmcom and a grant from the Baan Company.
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