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INT. J. PROD. RES., 2000, VOL. 38, NO. 18, 4743 ± 4761

Master production scheduling in capacitated sequence-dependent process industries JAMES A. HILL{*, WILLIAM L. BERRY{, G. KEONG LEONG{ and DAVID A. SCHILLING{ Traditional approaches to planning and control of manufacturing (MRPII) focus on discrete parts manufacturing industries (e.g. automotive). The chemical industry, however, presents unique challenges. Cross-contamination of production is a key issue among some chemical facilities. A considerable amount of capacity is lost as a result of changeovers which involve performing thorough clean-ups to wash away the impurities which may contaminate the next product to be produced. Therefore, planning for sequence-dependent changeovers becomes crucial and complicates the master production scheduling process. This paper shows how improved master production scheduling performance can be obtained by using a two-level master production schedule (MPS) to focus on key plant processes, and by incorporating a scheduling heuristic which considers sequence-dependent changeovers and capacity constraints. This approach is illustrated using actual operating data from a chemical ® rm typical of many process industry operations. Simulation experiments are reported that test the performance of the proposed master scheduling method in a single-stage sequence-dependent process. The experimental factors include both the introduction of the two-level MPS with the scheduling heuristic, and the eŒect of changes in the MPS batch size. The results demonstrate that important simultaneous improvements in process changeover time and delivery performance can be achieved using the proposed MPS scheduling approach against a more traditional (single-level) MPS approach which does not consider sequence-dependent changeovers. Further, we ® nd that delivery performance is relatively insensitive to adjustments in the MPS batch size when using the two-level MPS approach.

1.

Introduction  C hanging markets are placing new business requirements on companies today, producing the need for a quicker, more accurate response to customer delivery needs and increased product variety (Stalk and Hout 1990, Pine 1993). This is particularly true in process industries because of long, product sequence-dependent changeover times that arise from product contamination and plant design issues; thereby limiting product mix ¯ exibility (Taylor and Bolander 1994, Turek 1994). Frequently, process industry changeover times are large, e.g. as much as 47± 92% of operating capacity (Leschke 1995) and thus need to be addressed when planning for production. However, previous research on capacitated master production scheduling (Chung and Krajewski 1984, Sum and Hill 1993, Kern and Wei 1997) generally do not Revision received May 2000. { Owen Graduate School of Management, Vanderbilt University, Nashville, TN 37203, USA. { Fisher College of Business, The Ohio State University, USA. * To whom correspondence should be addressed. e-mail: [email protected] International Journal of Production Research ISSN 0020± 7543 print/ISSN 1366± 588X online # 2000 Taylor & Francis Ltd http://www.tandf.co.uk/journals

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consider sequence-dependent changeovers. One paper reported by OliŒand Burch (1985) considers the product sequence restrictions and capacity limitations frequently encountered in process industries. They report a mixed integer programming model that determines lot sizes, line assignments and inventory levels, and considers the changeover costs from one product to another. However, because of computation requirements, the applicability of their linear programming approximation is limited to relatively small problems.  T he need for quick delivery in capacitated process industry environments is challenging conventional thinking concerning the design of manufacturing planning and control systems. Some have argued, e.g. that MRPII does not adequately address the planning and scheduling needs in process industry ® rms because they lack the ability to consider plant limitations, e.g. sequence-dependent changeovers in planning and scheduling (Taylor and Bolander 1994, Turek, 1994). Others have proposed ® nite scheduling methods to address these issues (Umble and Srikanth 1995). In this paper we propose the development of a two-level master production schedule for make-to-stock products in capacitated process industries that incorporates sequence-dependent changeovers. The advantage of this approach is that conventional MRPII systems can be used to plan and schedule process industry operations in the same way as in discrete manufacturing applications. The key research questions involve the following. (1) To what extent can manufacturing performance improve by using a twolevel MPS with a sequencing heuristic versus a single-level MPS in process industries with sequence-dependent changeovers? (2) How does a two-level MPS affect trade-offs between changeover time reduction and customer delivery performance in master scheduling sequencedependent processes? (3) How does adjustments in MPS batch size affect performance in scheduling sequence-dependent processes in both a single-level and two-level MPS design? We begin by demonstrating how the master production schedule can be designed to use a two-level MPS approach for process industries, and show how sequencing heuristics can be incorporated into the master production schedule to consider sequence-dependent changeovers. Next, we introduce the research design and experimental factors. Finally, computational experiments are reported that measure the improvement in changeover time and delivery performance obtained using the proposed scheduling approach.

2. Process industry example 2.1. Incorporating plant restrictions in the MPS In order to incorporate product sequence restrictions in the MPS, the MPS function needs to be designed in a way that re¯ ects the nature of the process structures found in process industries. We use actual operating data from a chemical manufacturing ® rm to illustrate how this can be accomplished, and the resulting impact on master scheduling performance. This involves the use of a two-level master production scheduling design to link the MPS with the process and product structure. This approach is quite general and can be applied in a wide variety of process ¯ ow structures.

MPS in sequence-dependent process industries

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2.2. The master production schedule The function of the MPS is to balance the product demands of customers with the supply of product made available by plant schedules and inventory. The MPS speci® es the anticipated build schedule for end products. This task is illustrated using the process industry example in ® gure 1. The company is a leading chemical manufacturer with branded products sold in both consumer and industrial markets through a variety of channels, including mass merchandisers, independent retailers and manufacturer’ s representatives. The product structure in ® gure 1 has four levels, consisting of purchased ingredients, manufactured chemicals, end product formulas and packaged products. Ingredients are purchased and stored in raw material inventory to be later transformed into a ® nished chemical product. Chemical products are then blended in capacitated storage tanks to be later packaged and stored in full goods inventory. Each family of packaged products is produced on a seven day per week, high-volume linked batch process which has a series of three processing units: chemical manufacturing, formula blending, and product packaging. Inventory is held for raw material ingredients and for ® nished packaged products. This process can be considered a single-stage process as work-in-process inventory is not held because materials are moved automatically from chemical manufacturing to formula blending and ® nally to packaging, and each processing line at this company is scheduled separately. Formula blending is where there are capacity constraints in this process. Its capacity is relatively expensive, the changeovers are longer than those for chemical manufacturing and packaging, and the blending changeovers are sequence dependent as shown in table 1. These changeovers involve substantial cleaning

Figure 1.

Process ¯ ow diagram.

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J. A. Hill et al. To formula

From formula

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5 6 7 8 9 10

100 12 48 8 6 12 12 4 6 6

6 100 48 8 6 12 12 10 12 6

24 48 100 6 4 12 12 8 8 6

6 12 48 100 6 12 12 6 4 6

6 12 48 8 100 8 12 12 6 6

12 16 48 12 12 100 12 12 12 12

6 12 48 10 6 12 100 6 6 6

6 12 48 6 4 12 6 100 12 6

6 12 48 8 6 12 6 4 100 6

6 12 48 6 6 12 12 6 6 100

Table 1.

Formula blending changeover times (h).

time to avoid product contamination as well as the time needed to change ingredient materials and to adjust process control settings. Following basic master scheduling logic this ® rm master schedules at the end product level. It is our goal in this example to demonstrate the di culties when the master schedule is done at the end product level. We demonstrate performance improvements when the master schedule is developed for the formula blending unit shown in ® gure 1. After the master schedule is developed for the blending process, schedules are prepared for the chemical manufacturing and product packaging process units. 2.3. The level 1 and level 2 MPS The diagram shown in ® gure 2 illustrates the steps involved in using a two-level master schedule which includes a level 1 packaged end products MPS, and a level 2 blended product formulas MPS. The level 1 master schedule for individual packaged products uses standard master production scheduling logic and record processing methods commonly used in practice (Vollmann et al. 1997). In this example, individual formula blends are stocked and sold in various types and package sizes. At level 1 the major planning issues involve forecasting, customer order promising and determining a master schedule for individual products that meets customer delivery expectations while conforming to company inventory requirements for individual packaged products. This portion of the master schedule represents a shipment schedule and is referred to as step (1) in ® gure 2. The level 2 master schedule for product blend formulas is derived from the level 1 master schedule by combining the formula requirements for the individual packaged products. This step is accomplished using standard master production scheduling logic and record processing methods (Vollmann et al. 1997). The exploded requirements portion of this master schedule is referred to as step (2) in ® gure 2. Because no ® nished formula blend inventory is held at level 2 in this example, the next task is to adjust the exploded formula blending master schedule developed in step (2) to consider sequence-dependent changeovers. This is noted as step (3) in ® gure 2. Once the formula blend MPS is completed: a product packaging line schedule that is consistent with the formula blending master production schedule (step 4) can be determined, planning for raw material requirements (step 5) can be completed, and a vendor schedule (step 6) can be constructed. The diagram in ® gure 2

MPS in sequence-dependent process industries

Figure 2.

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MRPII systems function.

shows these six steps in terms of the MRPII functions involved (Vollmann et al. 1997). 2.4. Meeting performance requirements The level 1 MPS for packaged products provides a replenishment schedule that meets customer delivery expectations and the shipment objectives of the company. However, because of capacity limitations in the blending process, the exploded level 2 formula blending MPS developed in step (2) may be neither feasible nor acceptable when considering both changeover time and customer requirements. Therefore, step (3), master scheduling the formula blends, has been introduced in ® gure 2. Step (3) involves developing a schedule for the blending process unit that considers the changeover time dependencies between formulas. Once this schedule has been determined, other MRPII functions, e.g. materials planning for end product packaging and raw material ingredients can then be performed. 2.5. Two-level MPS illustration The formula blending master schedule example shown in tables 2 and 3 is provided to illustrate the way in which performance improvements can be obtained using a two-level MPS approach. This example uses actual operating data from the chemical company described earlier. The initial formula master schedule given in table 2 is a result of accomplishing steps (1) and (2) as noted in ® gure 2, and does not re¯ ect product sequence limitations. This

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Formula number 1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

7

8

9

10

11 12

13

14 15

849 1112 1345

1345

1345

1345

925 902

902

902

902

1370 410 550 Table 2.

Formula master production schedule.

schedule is produced by exploding the level 1 individual packaged products master schedule using time-phased make-to-stock master scheduling records with sales forecast data. It implies that the formula blend batches will be processed in the sequence indicated in table 2. The use of ® xed order quantity batch sizes is used to provide an illustration. The MPS orders are based on economic order quantity calculations. The data shown in table 3(A) provide an evaluation of the initial formula blend MPS (shown in table 2) using the process changeover times obtained from the MPS sequence

3

Period due 1 Period complete 1.5 MPS tardiness 0.5 MPS earliness

5

2

3

5

1

4

3

6

5

10

9

3

5

2

4

5

6

8

8

9

9

10

10

11

13

14

3.6 4.2 6.3 8.1 8.9

9.7

10.8

1.6 0.2 1.3 2.1 0.9

1.7

1.8

12.9 13.7 3.9

3.7

14.2 4.3

14.7 15.8

17.6

3.7

2.8

3.6

Average MPS tardiness ˆ 2.3 (periods). Total schedule length= 17.6 (periods). Total changeover time= 316 (h).

Table 3(A). MPS sequence

3

Period due 1 Period complete 1.5 MPS tardiness 0.5 MPS earliness 0.5

Schedule evaluation (initial formula MPS).

2

5

3

5

1

4

3

6

5

9

10

3

5

4

2

5

6

8

8

9

9

10

10

11

14

13

3.5 4.4 5.4 7.2 8.0

8.8

9.8

2.4 0.4 1.2 0.0 0.8

0.9

3.0

12.0 12.8 2.8

2.2

13.2 3.8

13.8 14.8 1.9

Average MPS tardiness ˆ 1.6 (periods). Total schedule length ˆ 16.6 (periods). Total changeover time ˆ 276 (h).

Table 3(B). Schedule evaluation (revised two-level formula MPS).

2.7

16.6

MPS in sequence-dependent process industries

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company which are shown in table 1. A large value, i.e. M ˆ 100 has been placed on the diagonal in table 1. This is to preclude the combining of MPS orders for like items as the trade-oŒbetween changeover cost and inventory carrying cost has been considered in determining the economic order quantity for the MPS items. Several observations can be made from these data. First, 17.6 scheduling periods are required to complete the 15-period MPS. Second, delivery performance, i.e. meeting the MPS due dates, is poor as none of the formula batches is completed on time. The average order tardiness isÐ 2.3 periods and the latest order is completed 4.3 periods after the MPS due date. Finally, the process changeover time represents 44% of the total schedule length. 2.6. MPS improvement Both changeover time and delivery performance can be improved by using a sequence-dependent scheduling heuristic to improve the initial formula blend MPS. In this illustration we have used the SWAP heuristic described below. The performance of a revised schedule sequence, shown in table 3(B), indicates that the process changeover time can be reduced by 13% , or by 40 h. Further, the average tardiness was reduced by ¹ 30% . The results in table 3(B) illustrate the potential for improvement in plant performance by considering product sequence and capacity restrictions in the MPS. 3.

Development of heuristic The pair-wise swap heuristic used in this paper represents a diŒerent approach in developing a sequence-dependent scheduling heuristic than that taken in previous research. The SWAP heuristic applies the logic used by Clarke and Wright (1964) in vehicle scheduling (also see Laporte 1992) for use in two-level master production scheduling. The SWAP heuristic is a simple local search heuristic which is computationally e cient when applied to large problems, and has been tested extensively in the vehicle scheduling literature (Christo® des et al. 1975). However, the focus here is on improvement in performance of the MPS rather than on the heuristic itself. For master production scheduling we have adapted this approach to sequence a series of MPS production orders in the formula blending operation, beginning with the product formula currently setup on the process and ending with the shortest changeover time to run any other product formula. The notation for the heuristic is shown in the Appendix. This method accommodates the large problem sizes typically encountered in master scheduling, and the need for computationally e cient methods. It uses a neighborhood search approach similar to that used by Gupta and Darrow (1986) to obtain improved solution quality in sequencedependent schedules. All of the research on sequence-dependent scheduling heuristics except that of De Matta and Guignard (1994) has been applied in the context of the scheduling of job shops. De Matta and Guignard (1994) report heuristic Lagrangean methods for small process industry problems, involving two± four products per machine, which averages ¹ 5.95% above the schedule length lower bound. None of the work has been focused on methods for incorporating sequence-dependent scheduling heuristics into systems for master production scheduling which are appropriate for the types of operations found in process industries. Outside of the context of master production scheduling other research has been reported on scheduling individual orders for sequence-dependent processes. Gavett

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(1965), Haynes et al. (1973), White and Wilson (1977), and Lockett and Muhlemann (1972) report heuristics designed to minimize schedule length and changeover time in sequence-dependent single-machine scheduling involving ® ve± 20 jobs. Guinet (1993) uses an assignment algorithm which averages 5.53% over the lower bound value on schedule length in scheduling sequence-dependent jobs on parallel single-machine processors, using 25± 150 jobs. With the exception of the work reported by Guinet (1993) none of the research on sequence-dependent scheduling heuristics has reported computationally e cient methods that can be applied in large-scale problems such as those confronting process industry ® rms. This research extends the applications of sequence-dependent scheduling heuristics by incorporating them with master production scheduling of large-scale problems. 4.

Research design This research design is focused on determining the extent to which a two-level MPS augmented with the SWAP scheduling heuristic can improve manufacturing performance in terms of both changeover time and delivery performance in sequence-dependent processes. It recognizes that changeover time improvement can be achieved in two very diŒerent ways: through the use of improved scheduling methods or through larger MPS batch sizes (Umble and Srikanth 1995). Further, this experimental design tests the notion advanced by both Ritzman and King (1993) and Veral (1995) that reduction in batch size produces improvement in delivery performance. 4.1. Performance criteria In chemical processing ® rms changeover time is a critical concern. Process ¯ owtime is typically measured in terms of process hour/units, where the process hours include both changeover and run time. However, because run time/unit is assumed to remain constant in these experiments, we report total changeover time in process hours. The quality of the two-level MPS will also be measured against a lower bound on changeover time. The lower bound on changeover time can be calculated to estimate the minimum changeover time. (See Appendix for calculation of the lower bound.) Customer pressure for improved delivery reliability makes this an important objective in many process industry companies. Here, delivery reliability is de® ned as the degree to which manufacturing can meet the level 1 MPS due dates. In these experiments, two aspects of delivery reliability are measured: order tardiness and order earliness. Order tardiness is measured in terms of the number of scheduling periods each MPS batch is delivered late relative to the level 1 MPS. This measure is converted into total shortages by multiplying order tardiness (measured in terms of scheduling periods) by the average sales forecast per scheduling period. This enables order tardiness to also be expressed in terms of the number of periods of inventory shortages. Because the early completion of MPS batches will increase the inventory for make-to-stock products, batches that are completed early are reported in terms of the number of periods of excess inventory. This calculation is similar to that for total shortages, and re¯ ects performance frequently reported in process industry ® rms, e.g. the number of days of ® nished goods inventory.

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4.2. Experimental design To test the research questions presented earlier, a simulation model was developed using Microsoft Fortran language and run on a Dell OptiPlex GX1 desktop system. The SPSS statistical package was used to analyse the data. A two-way analysis of variance (M £ P) design with 40 replications per cell was used to examine the three research questions listed above. The experimental factor (M) is `MPS scheduling method’ , and (P) is `percent reduction in MPS batch size’ . This design represents a complete crossing of the factors M and P (for factor levels see table 4). The experimental factor (M), MPS scheduling method, was set at 2 levels. The ® rst setting represents the results of using the exploded level 1 MPS in scheduling plant operations. The second setting represents the results of using the two-level MPS which considers sequence-dependent changeovers. This factor provides a means of testing the improvement produced by the two-level MPS scheduling method. The experimental factor (P), percent reduction in MPS batch size, was set at values of 0.0, 0.25, 0.50 and 0.75. The 0.0 factor setting represents the result of using actual operating data obtained in ® eld research. In the remaining factor settings the MPS batch size was reduced by 25% , 50% and 75% , respectively, from the initial formula batch size. These values provide a wide range of problem conditions, including batch size settings, problem sizes (ranging from 50 to 180 orders), and percent changeover time to processing time (ranging from 37% to 70% ). The replications in these experiments were 40 randomly generated product sets similar to the example shown in ® gure 1 and tables 1± 3. Each product set includes 10 products, each having the following data: average period sales forecast for the next 15 periods (in units), the economic MPS batch size (in units), the MPS initial inventory, the formula processing time (in hours/unit) which is constant for all formulas, and the blending process changeover time matrix shown in table 1. Because the average period forecast is ® xed over the planning horizon and the processing time has a linear relationship with sales volume, the diŒerence in performance between the subjects resulted from diŒerences in the randomly generated average period forecast and batch size values. The startup period was determined using Welch’ s (1983) graphical approach. Data were collected after the model reached steady state. The following procedure was used to randomly generate the product structure data for each of the 10 formula products. The parameter values listed in this paragraph are representative of the actual operating data. This procedure was used to provide a wide range of problems to test the proposed scheduling method. First, an average period demand was randomly generated from a product period demand distribution which is uniformly distributed with a mean of 170 085, a lower limit of 3846 and an upper limit of 336 323. Second, the economic time between MPS orders (TBO) value was randomly generated from a uniform distribution having a Factors MPS method Batch size

Treatments

Number of treatments

Initial MPS, 2/Level MPS (SWAP) 1.0, 0.75, 0.50, 0.25

2

Table 4.

Experimental factors.

4

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J. A. Hill et al.

mean of 10 with a lower limit of 4 and an upper limit of 16. Third, the formula product batch size was computed to be the average period demand multiplied by the time between orders (TBO) value. Capacity in hours for the 15-period time horizon was ® xed at 2100 h. Next, a level 2 MPS record was established for each product formula which contained forecast, projected inventory, and MPS rows. These records were processed to develop a 15-period MPS for each formula reported in table 2. In order to provide comparable experimental conditions, the initial inventory conditions, and the product changeover time matrix remained constant for all 40 replications. As a result, the diŒerences in performance between the replications resulted from diŒerences in the randomly generated average period forecast and TBO values between product structures. 5.

Experimental results The experimental results show the eŒect on manufacturing performance of: the initial MPS with the two-level MPS design and adjustments in MPS batch size. 5.1. Two-way ANOVA results Table 5 gives an overall view of the results, showing the average performance at each experimental setting. Table 6 summarizes the two-way ANOVA results showing the main eŒect and two-way interaction for each dependent variable. The results in table 6 indicate the main eŒect of scheduling methods and batch size is signi® cant at p ˆ 0.05 for all dependent variables, and there is a signi® cant interaction between the MPS method chosen and batch size for all dependent variables. Table 5 shows that at each factor setting the two-level MPS method has lower changeover time and shortages than the initial MPS and ® nished goods inventory increases slightly. Also, solution quality improves signi® cantly when we move from the initial MPS to the two-level MPS. Further analysis was performed at each level of MPS method to further understand the interaction between batch size and MPS method. 5.2. One-way ANOVA results for initial MPS A one-way ANOVA was run against the initial MPS with batch size as the independent variable for each performance measurement. A Tukey pairwise comparison test was run to determine the signi® cance between all levels of MPS batch size. Tables 7± 10 are results of the Tukey test for each dependent variable. Table 7 Batch size reduction factor (% )

Shortages (units)

Inventory (units)

Changeover time (h)

% over lower bound

Initial MPS

0.0 25 50 75

81 106 153 279

4 6 7 7

724 978 1470 2755

30.3 33.2 37.8 46.7

Two-level MPS

0.0 25 50 75

38 34 35 17

8 12 17 43

613 806 1171 1970

10.4 10.2 9.9 4.9

Scheduling method

Table 5.

Average performance at each setting.

MPS in sequence-dependent process industries Dependent variable: shortages Source Scheduler Batch size Scheduler £ batch size Dependent variable: inventory Source Scheduler Batch size Scheduler £ batch size Dependent variable: changeover time Source Scheduler Batch size Scheduler £ batch size Dependent variable: % over lower bound Source Scheduler Batch size Scheduler £ batch size

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F-value

P-value

1170.3 120.1 181.6

0.00* 0.00* 0.00*

222.5 83.6 65.4

0.00* 0.00* 0.00*

259.4 1251.0 51.8

0.00* 0.00* 0.00*

1575.7 11.7 46.5

0.00* 0.00* 0.00*

* Signi® cant at 0.05 level.

Table 6.

Two-way ANOVA results.

Independent variable Batch size

F-value

P-value

165.5

0.00*

Dependent variable: shortages.

Table 7(A).

1 2 3 4

One way ANOVA on initial MPS.

1

2

3

4

1.0 0.06 0.00* 0.00*

1.0 0.00* 0.00*

1.0 0.00*

1.0

* Signi® cant at 0.05 level.

Table 7(B).

Independent variable Batch size

Tukey multiple comparison.

F-value

P-value

2.6

0.06

Dependent variable: inventory.

Table 8(A).

One-way ANOVA results on initial MPS.

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J. A. Hill et al. 1

2

3

4

1.0 0.54 0.08 0.09

1.0 0.71 0.73

1.0 1.0

1.0

Table 8(B). Tukey multiple comparisons.

Independent variable Batch size

F-value

P-value

628.5

0.00*

Dependent variable: changeover time.

Table 9(A).

1 2 3 4

One-way ANOVA results on initial MPS.

1

2

3

4

1.0 0.00* 0.00* 0.00*

1.0 0.00* 0.00*

1.0 0.00*

1.0

* Signi® cant at 0.05 level.

Table 9(B). Tukey multiple comparison.

Independent variable Batch size

F-value

P-value

29.8

0.00*

Dependent variable: % over lower bound.

Table 10(A).

1 2 3 4

One-way ANOVA results on initial MPS.

1

2

3

4

1.0 0.41 0.00* 0.00*

1.0 0.07 0.00*

1.0 0.00*

1.0

* Signi® cant at 0.05 level.

Table 10(B).

Tukey multiple comparisons.

shows there is a signi® cant diŒerence in total shortages between every level of batch size except between level 1 and level 2. Table 8 demonstrates there is no signi® cant diŒerence in ® nished goods inventory between any level of batch size. Table 9 shows there is a signi® cant diŒerence in changeover time between every level of batch size. Likewise, Table 10 indicates there are signi® cant diŒerences in solution quality between level 1 with levels 3 and 4, and level 2 and level 3 with level 4.

MPS in sequence-dependent process industries

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5.3. One-way ANOVA results for two-level MPS A one-way ANOVA was run against the two-level MPS with batch size as the independent variable for all performance measurements. A Tukey pairwise comparison test was run to determine the signi® cance between all levels of MPS batch size. Tables 11± 14 are results of the Tukey test for each dependent variable. Table 11 indicates there is no signi® cant diŒerence in total shortages between levels 1, 2 and 3

Independent variable Batch size

F-value

P-value

18.8

0.00*

Dependent variable: shortages.

Table 11(A).

1 2 3

One-way ANOVA results on two-level MPS.

1

2

3

1.0 0.60 0.99

1.0 0.68

1.0

4

* Signi® cant at 0.05 level.

Table 11(B).

Tukey multiple comparisons.

Independent variable Batch size

Fvalue

P-value

97.2

0.00*

Dependent variable: inventory.

Table 12(A).

1 2 3 4

One-way ANOVA results on two-level MPS.

1

2

3

4

1.0 0.32 0.00* 0.00*

1.0 0.17 0.00*

1.0 0.00*

1.0

* Signi® cant at 0.05 level.

Table 12(B).

Independent variable Batch size

Tukey multiple comparisons.

F-value

P-value

710.2

0.00*

Dependent variable: changeover time.

Table 13(A).

One-way ANOVA results on two-level MPS.

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J. A. Hill et al. 1

2

3

4

1.0 0.00* 0.00* 0.00*

1.0 0.00* 0.00*

1.0 0.00*

1.0

* Signi® cant at 0.05 level.

Table 13(B).

Tukey multiple comparisons.

Independent variable Batch size

F-value

P-value

24.6

0.00*

Dependent variable: % over lower bound.

Table 14(A).

1 2 3 4

One-way ANOVA results on two-level MPS.

1

2

3

4

1.0 0.98 0.92 0.00*

1.0 0.99 0.00*

1.0 0.00*

1.0

* Signi® cant at 0.05 level.

Table 14(B). Tukey multiple comparisons.

of batch size though there is a signi® cant diŒerence between levels 1, 2 and 3 with level 4. The results in table 12 show there is no signi® cant diŒerence in total inventory between level 1 and level 2, though there is a signi® cant diŒerence between level 1 and 3 and level 1 and 4 for MPS batch size. For total changeover time the results in table 13 indicate there is a signi® cant diŒerence between all levels of batch size. The results in table 14 indicate there is no signi® cant diŒerence in solution quality between levels 1, 2 and 3 of MPS batch size, though there is a signi® cant diŒerence between levels 1, 2 and 3 with level 4. These results are demonstrated graphically in ® gures 3± 6.

Figure 3.

Total shortage results.

MPS in sequence-dependent process industries

Figure 4.

Total inventory results.

Figure 5.

Changeover time results.

Figure 6.

Solution quality results.

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6. Discussion 6.1. MPS design The experimental results presented in table 5 show the eŒect of considering sequence-dependent changeovers in the two-level MPS design. They demonstrate that this method provides a simultaneous improvement in both changeover time reduction and total shortage reduction (delivery performance) at every level of MPS batch size. In these experiments, the increase in plant capacity made possible through the use of the pair-wise swap heuristic provides important gains in reducing

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the total shortages observed in the initial MPS. Further, the reduction in total shortages is much greater in the case of very small batch sizes as shown in table 5. It is important to note that the magnitude of such improvements is clearly dependent upon the proportion of changeover time for any given process. 6.2. MPS batch size These experiments indicate that the improvement in total shortages depends on two factors: the MPS batch size and the use of the two-level MPS with the SWAP sequencing heuristic. The eŒect of the MPS batch size on total shortages is shown in table 5. Table 5 along with table 7 presents results from the initial master production schedule before the SWAP scheduling heuristic is applied. These conclusions are the opposite of those of Ritzman and King (1993), and Veral (1995). These authors showed improvement in shortages with a reduction in batch size. However, our results suggest that as batch size is reduced there is a signi® cant increase in total shortages. A reduction in batch size causes an increase in changeover time in the initial MPS thus causing the completion of orders to be delayed. This result is a direct indication of operating in a capacitated environment with sequence-dependent changeovers. In these environments the initial MPS in some cases is not a feasible schedule and needs to be designed to take sequencing restrictions into consideration. Table 5 also presents results after the SWAP heuristic has been applied. These results with those in table 11 indicate that there is no signi® cant diŒerence in total shortages between the ® rst three levels of batch size, though there is a signi® cant reduction in total shortages when the batch size has been reduced by 75% . This is because the two-level method has signi® cantly reduced the total amount of changeover time enabling orders to be completed earlier. Along with this reduction in shortages comes an increase in ® nished goods inventory. What this means for a practicing manager is small batches should only be used as a lever to reduce shortages in master production scheduling with sequence-dependent changeovers when a two-level MPS approach has been adopted. Without a two-level MPS approach, reducing batch size will cause an increase in changeover time in the MPS leading to an increase in shortages. Instead, a scheduling heuristic such as SWAP can be applied using the two-level MPS approach to reduce total shortages and improve changeover time simultaneously. 6.3. Two-level MPS performance with heuristic versus initial MPS performance These experiments indicate that solution quality, measured as % over changeover time lower bound (table 5) is aŒected by changes in batch size for the initial MPS but not for the two-level MPS method. Again this indicates the initial MPS is not designed to handle processes with sequence-dependent changeovers. For the initial MPS there is a signi® cant degradation in performance as batch sizes get smaller, though the two-level MPS is equally eŒective in reducing changeover times for all batch sizes studied. In fact, performance of the two-level MPS improves signi® cantly when batch sizes are reduced by 75% . 7.

Conclusions The modi® ed design of the MPS and the use of a sequence-dependent scheduling heuristic can provide important improvements in changeover time and total shortages in process industries with sequence-dependent changeovers. This paper

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illustrates how a two-level master production schedule can be used with a scheduling heuristic to consider processes with sequence-dependent products. Clearly, other master scheduling design options, which consider a diŒerent approach than the two-level design used here, could be developed to accommodate various types of process structures found in process industries. These are areas for future research. The proposed two-level master scheduling approach represents a practical means of combining the time-phased MPS data readily available in conventional MRPII systems with scheduling heuristics to provide important performance improvements in large problems. The results also demonstrate that when a two-level design is not considered in master scheduling sequence-dependent processes, major reductions in batch size will cause a signi® cant degradation in total shortages. Such reductions in batch size can also lead to an increase in changeover time. While these experiments lead to diŒerent results reported by Ritzman and King (1993), and Veral (1995), as with most research studies the results reported are true for the experimental conditions reported here. These experiments suggest that processes with sequence-dependent changeovers can improve both changeover time and total shortages by using a two-level approach to master production scheduling. Hence, if a two-level approach is not used these experiments support the use of large batch sizes. Finally, the experiments demonstrate the value of using a simple local heuristic to incorporate product sequence restrictions in the two-level MPS approach. They indicate that further work should be performed on master production scheduling which take into account both sequence-dependent changeovers and delivery criteria in process industries. Future research should examine the performance sensitivity of these scheduling methods under diŒerent process conditions. Appendix (a) Pair-wise swap heuristic notation n i m P…i† Q…i† R…i† C…k; l†

S…i†

number of MPS production orders (batches), MPS production order sequence number (i ˆ 1; n), MPS scheduling period length (in h), product formula type, batch quantity, product formula run time (in h/lb), process changeover time from product formula k to product formula l: (1) if sequence alternative i equals 1, then k ˆ the product formula currently setup; (2) if k ˆ l, then C(k, l) =  a very large number, the time savings from switching the ith and the i ‡ 1 product formulas in the sequence.

Schedule length ˆ C…P…0†; P…1†† ‡ ‡

n X

Qi R i

iˆ1

with P…0† ˆ current product setup.

n¡1 X iˆ1

C…P…i†; P…i ‡ 1†† ‡ Mink C…P…n†; k†

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The objective of the heuristic is to minimize the changeover time. At each step in the heuristic an evaluation of the change in the total changeover time is made. Speci® cally, the heuristic proceeds as follows: Step 1. For all i ˆ 1, n ¡ 1, calculate the changeover time savings, S…i†: S…i† ˆ C…P…i ¡ 1†; P…i†† ‡ C…P…i†; P…i ‡ 1†† ‡ C…P…i ‡ 1†; P…i ‡ 2†† ¡ C…P…i ¡ 1†; P…i ‡ 1†† ¡ C…P…i ‡ 1†; P…i†† ¡ C…P…i†; P…i ‡ 2†† if i ˆ n ¡ 1, then C…P…i ‡ 1†; P…i ‡ 2†† ˆ Mink C…P…i ‡ 1†; k† and C…P…i†; P…i ‡ 2†† ˆ Mink C…P…i†; k†: Step 2. Select the maximum positive S…i† and make the two-way swap. Find S…k† ˆ Maxi S…i†. If S…k† µ 0 stop. Otherwise, swap MPS orders k and k ‡ 1. Step 3. Return to step 1. (b) Lower bound A lower bound on the total changeover time can be calculated to estimate the minimum schedule length. This involves summing two values. (1) The minimum changeover time from the current formula setup to any other product formula, Miniˆ1;n C…P…0†; i†. (2) The sum of the minimum changeover time for each product formula in the sequence to any other product formula, n X

Minkˆ1;n C…P…i†; k†:

iˆ1

The lower bound on the changeover time for the example shown in tables 2 and 3 is 256 h. In this case, 6 h is the smallest changeover time possible after ® nishing product 1 (the current product). Because the processing run time is 405.9 h for this example, the lower bound on the total schedule length is 661.9 h. In contrast, the initial schedule length in table 3(A) is 725.9 h, and 685.9 h for the heuristic solution (or 9.7% and 3.6% over the lower bound, respectively).

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