scheduling of packaging lines in the process industry: an empirical investigation

International Journal of Production Economics, 30-31 (1993) 579-589 Elsevier

579

Scheduling of packaging lines in the process industry: An empirical investigation

Peter van Dam”, Gerard Gaalmat? and Gerard Sierksmab

a Department of Business Administration and Management Science, Faculty of Economics, University of Groningen. Groningen, The Netherlands. b Department of Econometrics, Faculty of Economics, University qf’ Groningen, Groningen, The Netherlands.

Abstract

In the process Industry, homogeneous products have to be packed For an unpacked product (mtlk. pamt), a variety of packaging materials (glass. tm) and packagmg sizes (4 lure, 1 kilo) are available. Generally, the packagmg lines are used for vartous products (milk, buttermilk) in one type of packaging maternal (glass) and various packaging stzes (i litre, 1 htre). These

posslbihties make the scheduling of the packaging hnes rather complex.

In recent years, under market pressure. the number of products in the process Industry has been Increased, the order sizes have

been reduced, and the delivery times have been shortened. Thts has caused augmented schedulmg tasks and, usually. the

scheduhng systems supporting these tasks have not followed these changes sufficiently.

We have investtgated and compared the ortgms of the Increasing complexity of the scheduling problems of several companies

m the process industry producmg datry products, pharmaceuttcal products, tobacco, paint, chocolate products, and foods. and

we have analyzed the ways m which these compames deal wtth this mcreasmg complextty m drfferent situations. Schedulers have

to deal with a wide range of mformatton such as due dates, availabihty of maternal, sequence-dependent set-up ttmes, and

availability of packaging lines and employees. In most cases the scheduhng IS stall done by hand, which 1s very ttme-consuming.

We show the need for a more adequate support system whtch will provtde necessary information, and speed up the development

and evaluatton of production schedules. We also dtscuss future trends wtth regard to the packaging process. and their hkely effect

on the scheduhng process.

1. Introduction

During recent decades, production control systems such as MRP and JIT have received a lot of attention. However, these systems were mainly developed for the fabrication and as- sembly industries and, as noted in Ref. [l], they are not always applicable to the process industries. Therefore, during the eighties, production control concepts were developed spe- cifically for the process industry (e.g., Ref. [?I). Also, there was a growing interest in software

Correspondence to: J.P. van Dam, Department of Busi- ness Administration and Management Science, Faculty of Economics. University of Groningen, P.O. Box 800, 9700 AV, Groningen, The Netherlands.

that could support production control systems. In Ref. [3], however, it is concluded after research in the Netherlands and Belgium that the available software does not handle the specific demands of the scheduling’ very well.

In the research literature, much attention has been paid to scheduling in process industries (e.g., Refs. [4-71). The methods deal mainly with the scheduling of the process phase rather than that of the packaging of the products. The packaging process in the process industry has characteristics which are different from the production process. These

’ We use the term “scheduling” also at places where “planning and scheduling” or only “planning” is meant.

0925-5273j93/$06.00 cQ 1993 Elsevier Science Publishers B.V. All rights reserved.

differences are particularly important at the operational level. Therefore, if possible, the scheduling of the packaging lines should be treated differently from the scheduling of the process phase. (See also Ref. [S]).

There are only a few articles which deal with the scheduling of packaging lines [8-121. and in all these cases the assumptions which are made are rather restrictive. To obtain a clear image of the scheduling problems of the packaging lines in the process industry, we have examined the scheduling situation in eleven process industries. It is evident that making a schedule is extremely complicated. In this paper, we report the problems connected with the scheduling, and give some in- dications as to where and how the scheduling and the scheduling process can be improved. We also discuss future trends such as the reduction of set-up times, co-makership, and packing on order.

2. Packaging in the process industry

In the process industry, homogeneous com- modities such as chemicals. foods, rubber, tobacco, paint, and energy are produced. The process industry manufactures stand- ardized products in large quantities. Because cost prices per product decrease when production rates increase there is a tendency towards scaling up and automation. The high investment in machine capacity leads to continuous production in flow-shop oriented environments with large production series [ 11.

In the research literature (e.g., Refs. [l, 31) the process industry is found to include the following characteristics: ~ a flow-shop oriented environment, ~ high capital intensity and low labour inten-

sity. ~ production mainly determined by the ma-

chine capacity, ~ low work-in-progress inventories, ~ long (sequence-dependent) set-up times be-

tween products.

Usually two phases can be distinguished: the process phase, during which the products are manufactured, and the packaging phase. during which the unpacked products are packed. The above-mentioned characteristics of the process industry are mainly applicable to the process phase. The importance of the packaging phase varies greatly according to the situation. Industrial goods are packed in large quantities in only a few packages, but consumer goods are packed in many packages, differing in material, size and label. The packaging phase is much more important for consumer goods than for industrial goods. In this paper, we will concentrate on industries producing mainly consumer goods, such as the food industry. the tobacco industry, and the pharmaceutical industry. The general characteristics of the packaging phase in the observed industries are:

small order sizes, a large variety of end products because the fact that products can be packaged in a variety of different ways gives rise to an explosion in the number of products during the packaging phase (see Fig. 2), packaging lines. to enable products to be packed in various sizes, large (sequence-dependent) set-up times between orders, high labour intensity. unskilled labour. The different characteristics of the process

and packaging phase are summarized in Table 1. The qualifications of the packaging phase (large, small. high) are relative to the process phase. Because of these different characteristics. it seems reasonable to use different

Table I Differences between the process phase and the packaging phase

Process phase Packaging phase

Small variety of products Large variety of products Large order sizes Small order sizes Low labour mtensitj High labour intensity

P. van Dam et al./Scheduliny of packaying lines in the process industq 581

scheduling for each phase, especially at the operational level. However, as we shall see, this is not always possible.

In our research we have carried out eleven case studies in process industries producing dairy products, pharmaceutical products, tobacco, paint, chocolate products, and foods. These cases give a good overview of the prac- tices in process industries producing consumer goods. We were mainly interested in the scheduling of the packaging lines. In this paper, the emphasis is on situations where the packaging phase is scheduled separately from the process phase.

3. The scheduling of the packaging lines

Figure 1 shows a typical situation in the process industry, namely, the production of tablets in bottles and blister packs in the pharmaceutical industry. The figure shows three stock positions: a stock of raw materials, a stock of end products, and a stock of unpacked products decoupling the process phase and the packaging phase. During the process phase the tablets are manufactured on two lines. The tablets are packed in two types of

Stock of

raw materials

Stock of

unpacked products

packaging materials: bottles and blister packs. There is one packaging line for bottles consisting of two packaging stages, and there are three packaging lines for blister packs consisting of three packaging stages. The scheduling of packaging lines will be examined by reference to this figure.

3.1. Stock positions

The scheduling is influenced by the stocks decoupling successive stages of the production process and thereby allowing the stages to work independently. In this way, stock leads to greater flexibility in production scheduling [13]. Figure 1 shows three possible stock positions which we observed in our case studies. However, each situation is different. Some industries have a stock at only one or two of these positions.

The stock of raw materials differs strongly from one industry to another. In the tobacco and coffee industry, for strategic reasons, a stock of more than a year is common, whereas in the diary industry the stock of raw milk is not more than a few days because of the de- terioration of milk.

Stock of

end products

Bllsterrmcks


Fig. 1. Production process in the pharmaceutxal industry.

582 P. wn Dum rr ul./Scheduhg qf‘puckuging linrs in the process industq

For the stock of end products the market situation is of particular importance. Cus- tomers, such as supermarkets or other wholesalers, often purchase frequently, but irregularly. The total demand during a year is, therefore, easily predictable, but there is substantial variation in periodic demand. In several food industries, products intended for the home market and the market in neighbouring countries, which ask for short delivery times, are delivered from stock because of the fluctuating demand. They, therefore, need a large stock of end products. In many cases, the industries keep a stock of end products, ranging from a few weeks to a few months, for their home market. This stock cannot be used for export because foreign customers also ask for their own packages. Delivery times for the export market are longer and allow packaging on order.

As we have already mentioned, there may be a stock in the process phase, decoupling two stages within it. This stock can occur in many places in the process phase. Because our interest is really in the packaging phase, however, we will only discuss the stocks that influence the scheduling of that phase. An example of such a stock can be found in the paint industry where there is a stock of basis paint and pig- ment near the end of the process phase. In this

case, when an order arrives, the paint is col- oured and packed without an intermediate stock of unpacked products. This situation can also be found in industries which prepare ready-made food.

In a number of observed cases, for example in the pharmaceutical and tobacco industries, the process phase and the packaging phase are decoupled by a stock of unpacked products. Often this stock arises out of the different characteristics of the process phase and the packaging phase (see Table 1). Furthermore, as is schematically depicted in Fig. 2, the number of different products is usually small between the process phase and the packaging phase. In this figure the number of raw materials exceeds the number of unpacked products, this can also be the other way around. (Fig. 2 shows the stages of the production process horizontally and the number of products during each stage vertically.) The explosion in the number of products during the packaging phase may give an advantage to a stock of unpacked products over other stock positions. In several process industries, such as the diary industry. a large stock of unpacked products is impossible because the products deteriorate quickly.

The packaging phase can only be scheduled separately from the process phase when the


Number of

products

Fig. 7 Product structure (schematically).

P. van Dam et al/Scheduling of packagrng lines in the process mdustr) 583

stock between both phases is large enough. In one observed case both phases were decoupled by small bunkers, each connected to a packaging line. In this case the scheduling of both phases was strongly connected, with the result that separate scheduling was very difficult.

Often the packaging process consists of a few steps. For an observed case in the pharmaceutical industry, for instance, Fig. 1 shows the following steps in the packaging process of tablets in blister packs: (1) the tablets are packed in blister packs, (2) the blister packs are packed in boxes (the

consumer packages), (3) the boxes are packed in large boxes (the

shipment units). In this case there is a stock between steps

1 and 2. Generally, such a stock position is rare.

3.2. Scheduling tasks

The scheduling of the packaging lines is a complicated task, because many restrictions and possibilities play a part. For a large number of (customer and stock) orders with due dates, the scheduler has to determine when the order is packed. During the scheduling process, the scheduler has to take into account the availability of material, packaging lines, and employees. We will discuss the most important aspects of these.

An unpacked product can be packed in a large number of packages. For some low- priced products, such as milk-powder, the cost of the packaging material is a substantial part of the selling price. To avoid a large stock of packaging material the specific packaging material is purchased (often by the scheduler) as soon as the order is scheduled. As a consequence the planning horizon has to cover the delivery times for the packaging material, which can vary from a few weeks to a few months.

In general, the packaging of an order can be carried out on several packaging lines. In Fig. 1, for example, three packaging lines are suitable for the packaging of tablets in blister packs. These packaging lines may differ in

production speed, number of necessary employees, set-up times, and tools needed. The allocation of orders to packaging lines should be as efficient as possible with regard to the sequence-dependent set-up times. Long set-up times (sometimes more than one day) may occur between different unpacked products and between different sized products. Simul- taneously with the allocation, the orders are sequenced per packaging line (in such a way that the due dates can be met).

We distinguish three types of set-up times: (1) format changes (when the size of the

packaging material changes), (2) product changes (when the product that

has to be packed changes), (3) end product changes (when the unpacked

product and the size of the packaging material does not change, but the labell- ing of the packaging material does).

A format change will require a retuning of the packaging line, whereas a product change may involve the cleaning of the packaging line. An end product change includes the changing of the order-specific packaging materials. The set-up times often determines the production sequence. For instance, a product change does not always involve the cleaning of the packaging line. In the tobacco industry, cleaning can be ignored during a sequence from light tobacco to heavy tobacco. The format changes and the product changes give rise to the most important set-ups. Which one of these is the most important depends upon the situation. Product groups are formed which are determined by the longest set-up times. These product groups consists of products sharing the same set-up.

Often there is overcapacity on the packaging lines. In such cases the capacity of the packaging department is determined by the limited number of employees. During the scheduling process the availability of the employees (capability, overtime, idleness, temporary employment, illness, holiday, etc.) has to be taken into account. In some of the observed cases there was overcapacity on some packaging lines, but undercapacity on others. Also, the scheduling of the employees is complicated

because the number of necessary employees at a packaging line often fluctuates. The number of employees needed depends on the packaging line and the type of product. Some packaging lines and orders need more employees than others.

In the scheduling of packaging lines and employees, the balancing of the capacities of both is very important because of the variations in the periodic demand, especially in cases of undercapacity. To accommodate these variations, the scheduler has a number of options. Orders can be packed some time before their due date and stored for a while, or. after consulting the marketing department and the customers, they can be packed later on. Alter- natively, the capacity can be expanded by producing in overtime, using more shifts, putting work out to contract, or hiring extra employees. A lot of the work is low skill, which makes recruitment of temporary employees at short notice relatively easy. Balancing is also important when there is overcapacity in the number of employees. Here too the planner has several options. For example, he can find other work for the employees, such as cleaning, institute some collective free days, or make some employees redundant.

3.3. Scheduling hierarch_t>

So far we have mentioned some scheduling tasks. such as the allocation of orders to packaging lines and the purchasing of packaging material. The tasks have to be carried out before the production time. How long before differs for each task. Packaging materials have to be purchased between a few weeks and a few months before production, but the definitive scheduling of the employees cannot be carried out until a short time before production because of the possibility of the unexpected absence of personnel, through illness for example. The different options for increasing capacity complicate the scheduling still further. Tem- porary employees can sometimes be recruited on the day of production. Overtime working can also be arranged quickly. The impact of either of these options, however, is rather low.

Introducing an additional shift yields a much more substantial expansion of the capacity because it can last for a relatively long period (several weeks if necessary), but it requires much more preparation time.

In the companies which we observed we distinguish two scheduling levels (see Fig. 3). The first level, which we will call the Detailed Planning Level (DPL), has a planning horizon of between a few week and a few months (mostly dependent on the delivery time of the packaging material), with planning periods of one week or one month. The second level, which we will call the Scheduling Level (SL), has a planning horizon of between one day and a few weeks and a planning period of one hour, one day or one week. Different sections of the organization deal with these two levels. Usually, the production scheduling department or the logistics department is responsible for the DPL, and the packaging department is responsible for the SL.

The main tasks at the DPL are the genera- tion of production orders for the end products and the balancing in time of the capacity of packaging lines and employees. The production orders are customer orders and/or stock replenishment orders, based on the expected demand. (The building up of stock is determined by an aggregate production plan, which we will not discuss in this paper.) For the

Orders

J----l Detail Planning

Fig. 3. Scheduling hierarchy.

P. LVN Dam et al./Scheduling qf packaging lines in the process industq 585

balancing of the capacity the period (for instance the week or the month) during which the orders are packed is determined. Because of the long sequence-dependent set-up times this has to include the allocation of product groups to packaging lines and, simultaneously, the sequencing of the product groups. Also the capacities of packaging lines and the capacity of the employees are, if necessary, expanded. On the basis of this scheduling, the packaging material is purchased.

Most important at the SL is the scheduling and monitoring of the production progress, for which the packaging department is responsible. Therefore, at this level, the definitive allocation of orders to packaging lines is made, the production sequence is chosen, the production times are calculated, and the employees are allocated to packaging lines. Another task at this level is rescheduling to take account of significant lost time caused by disturbances.

At both levels a schedule is made. These schedules are not identical. At the DPL a schedule is made to balance the capacity, whereas at the SL the definitive schedule for the packaging department is made. It is difficult to predict the production progress at the DPL because of disturbances. In many observed cases, only about 50% of the available production time (besides scheduled idle time) is actually given to the packing of products on packaging lines. About 30% is needed for set- up, and for about 20% of the production time the packaging lines are not working because of disturbances. Therefore, at the DPL norms for the production capacity are used. The resulting schedule is changed at the SL into the definitive schedule, because at the SL it is more easy to take disturbances and availability of materials and employees into account. But, because of the long sequence-dependent set-up times, in most cases the schedule at the SL will be, to a large extent, similar to the schedule at the DPL.

In most cases the schedulers have many tasks and the making of a production schedule is only one of those. Often the most important task of schedulers on both levels is trouble shooting.

4. Problems with respect to the scheduling

During our investigations, two problems, especially with regard to the DPL, emerged. In the first place, in cases of high demand for capacity, not all the alternatives (stock, overtime, etc.) were taken into account extensively. In the second place the scheduling process turned out to be very time-consuming. We will discuss both problems more thoroughly.

4.1. No good consideration of alternatives

Often, the periodic variation in demand is substantial, resulting in a strongly fluctuating demand for production capacity. It appears that the schedulers usually have a few alternatives to meet this fluctuating demand, among others the building up of stock, back ordering, overtime, additional shifts, the hiring and fir- ing of employees, and putting work out to contract. We observed that in practice the schedulers use a hierarchy of alternatives. They first try to dampen the demand for capacity by producing some orders on stock (some time before their due date). If capacity problems remain, the other alternatives are brought into play. In building up stocks the schedulers mainly consider the set-up times. They try to reduce the total set-up time and do not take holding costs into account. The effectiveness of this hierarchy of alternatives for reaching “the best” production schedule is not known. The main objective at the DPL is to balance the production capacity by building up stock. However, we suspect that in most cases better production schedules can be developed.

4.2. Time-consunzing scheduling procedure

The scheduling procedure is very time-consuming. A lot of time is required for gathering the necessary information and organizing it in a suitable way. The development of the schedule itself is also very time-consuming. We have often observed that the scheduling takes one day per week, or two or three days per month. During the scheduling process the scheduler is also occupied with daily tasks. Therefore, it

586 P. LWI Dam et a/./Scheduling of‘ packaging lines in rhe process industr)

takes much more time before the schedule is ready.

4.3. Origins

The above-mentioned problems also occur in many other scheduling situations. A scheduler of timetables, for instance, or a scheduler in a job-shop environment, will have to deal with them. The differences lie in some of the origins of the problems and in the way the scheduling can be improved, though even here there are a lot of similarities. In the process industry most problems arise as follows.

Especially at the DPL, the scheduler needs a lot of information (see Fig. 4) such as the orders with their due dates, the stock positions, the available capacity of packaging lines and employees, the characteristics of the packaging lines and employees, and the cost data (includ- ing holding costs, costs of overtime, etc.). Not all the necessary information is usually known to the scheduler. In the investigated cases, for example, the cost data are seldom known (depicted in Fig. 4 by the missing arrow from the cost data to the scheduling process). Some information, such as that pertaining to set-up times, may be out of date. The availability of employees and packaging lines (disturbances!),

Schedule

Fig. 4. Information needed for the scheduling.

cannot be precisely determined during the scheduling process, but have to be estimated (depicted by the interrupted arrows). At the DPL these estimations are often inaccurate, resulting in production schedules which have to be regularly adjusted at the SL. This causes unrest at the packaging department and requires a great deal of communication between the departments involved.

We will illustrate this by specific reference to the packaging line capacity which is, of course, essential for the scheduling. The available time for the production can be divided into the actual production time, the scheduled idle time, the set-up time, and the lost time caused by disturbances. The first two can be determined with certainty, but the last two have to be estimated. The set-up times are fairly con- stant and can be estimated quite closely. The lost time caused by disturbances, however, is not predictable. It is usually discounted in the actual production time with a fixed factor (e.g., 1.4 times the actual production time; this means that if an order needs 7 h production time, then 10 h are reserved for that order). At the DPL, only the set-up times between product groups are considered and the total time needed for set-ups within a product group is discounted in a manner similar to lost time caused by disturbances. This discounting is correct so long as the set-ups are equally divided among the packaging lines. Often, however, they are unequally divided. There is a great deal of difference in production time between a product group consisting of two large orders and one consisting of ten small ones. In the case of ten orders, more time is needed for set-ups and the greater number of set-ups increases the chance of disturbances. For a closer estimation of the capacity needed at the DPL a great deal of extra information is needed. The scheduling process will thus become even more time-consuming.

The availability of employees is difficult to estimate at the DPL. Absence of employees because of illness cannot usually be known until shortly before. The scheduling of the employees is therefore carried out at the SL. At the DPL, the overall need for employees is determined.

P. van Dam et al./Scheduliny of packaging lines in the process industrJ1 587

The scheduler has to deal with a substantial amount of information, of which a lot, such as the order file and the stock file, is stored in a computer system and printed out before the scheduling. The scheduler then organizes the information in a suitable way, for example by partitioning the orders with regard to the product groups, due dates, etc. Then a schedule is made. Most of these activities are carried out by hand, the most important tools being the pencil, paper, and eraser. It therefore takes a lot of time to make one schedule, and even more to evaluate alternative schedules or make “what-if” analyses.

In Section 3 we have described the complexity of the scheduling problem. To handle this problem the scheduler uses several rules of thumb. These simplify the scheduling process, but do not necessarily result in ‘the best’ schedule.

5. The scheduling needs

We have noted that most schedulers use pencil, paper, and eraser. Occasionally some schedulers use self-developed tools (such as a spread-sheet program). In one case the scheduler uses scheduling software. This was developed for a job-shop environment and cannot handle sequence-dependent set-up times. This scheduler uses only the Gantt- chart option of the package. He organizes the orders and stores them in the computer by hand. Then he allocates the orders (with a mouse) to a packaging line and sequences them. This scheduler is quite enthusiastic about his software because it saves him a lot of time; it enables him to make “what-if” analyses, and rescheduling is much simpler. It also supports communication between the scheduling and packaging department. However, the planning process is still time-consuming, the software does not have a procedure to generate a (starting) solution, and review criteria, for instance with regard to the costs of a schedule, are not used.

Most schedulers are not satisfied with their situation. They want to take cost data and exact capacity information into account, but

lack of time prevents their making better production schedules.

The managements of many companies also want to change the current situation. They want to be less dependent on the knowledge and experience of the scheduler, and they want to achieve cost reductions by making more efficient use of the capacities of packaging lines and emp!oyees.

Summarizing, we found a great need for tools to support the scheduling - tools which can handle the information in an appropriate way, which are quick and which provide the opportunity to generate, review, and compare alternative schedules - tools which make better schedules in less time.

We did not find support systems suitable for the packaging line environment. We, therefore, plan to specify a software system which is suitable for these situations and in which the emphasis is on the scheduling procedures.

6. Future trends

With regard to packaging in the process industry, we expect in the coming years a few trends (see Fig. 5) which will influence the scheduling.

In recent years environmental considerations have become increasingly important and there is a growing interest in packaging materials that are recyclable. Because packaging lines are usually suitable for only one type of packaging material, the use of new packaging materials needs new packaging lines.

The trend towards more products, small order sizes and short delivery times has led not only to more pressure on the scheduling, but also to a reconsideration of the relationship with the supplier of packaging materials. Konijnendijk and Wijngaard [14] show the advantages of co-makership relationships between suppliers of packaging materials and process industries: a good cooperation with the supplier may result in a more adequate delivery, in time as well as in quantity, yielding quicker reactions to changing demands.

588

Fig. 5. Future trends

Market pressure results in a reconsideration of the logistic strategy. More and more industries are moving from delivery from stock to packing an order. The advantage of this trend is a reduction of the stock, but it will also reduce the demanded lead times, and the order sizes, of the packaging department.

Because of the long set-up times, industries pay, and should pay, more attention to their reduction by such methods as: _ standardizing the packaging material in

order to reduce the number of different sizes,

_ changing the organization, for example by employing multi-skilled workers, or increasing the number of employees assisting a set-up.

- developing new packaging lines with smaller set-up times, and adapting existing packaging lines. Companies want to be more and more flex-

ible with regard to their employees. Employees are taught to be more versatile so that they can serve on more packaging lines. Innovations on packaging lines make it possible to work with fewer employees.

The problems described in this paper will not disappear in the near future. The need for support systems will increase. Although the set-up times will be reduced. they will remain of importance because order sizes and delivery

‘a Employees

times will also be reduced as a consequence of the trend towards packing on order. Also, the scheduling frequency will increase and the planning horizon will be reduced. The effects of the growing attention to environmental considerations and the new relationships with suppliers are uncertain, but they are unlikely to simplify the scheduling problem.

7. Conclusion

The scheduling of packaging lines in the process industry gives rise to a number of problems. It is very time consuming, alternatives are not considered, the relevant costs are missing and the data concerning capacity and set-up times is not precise. The schedulers make no use of advanced tools. In a forthcom- ing study we will design a support system which takes into account the specific characteristics of packaging lines. In this the emphasis will be on the development of scheduling procedures.

References

[I] Taylor. SC.. Seward. S.M. and Bolander. S.F.. 198 I Why the process industries are different. Pro- ductlon and Inventory Management, Fourth Quarter: 9-24.

P. mm Dam et ul.,i’Scheduliny of puckaying lines in the process rndustr~ 589

[2] Taylor, S.G., Seward, SM., Bolander. S.F. and Heard, R.C., 1981. Process industry production and inventory planning framework. a summary. Production and Inventory Management, First Quarter: 15-32.

[3] Marks, H.C.M., 1991. Software for production control. Tijdschrift voor Inkoop & Logistiek. 6( 1. 2): 31-35 (in Dutch).

[4] Schultz, H K.. 1977. Product scheduling in the plas- tic industry. Production and Inventory Manage- ment, Third Quarter: 93399.

[5] Taylor, S.G. and Bolander, S.F.. 1986. Scheduling product families. Production and Inventory Man- agement, Third Quarter: 47755.

[6] Ku. H.M., Rajagopalan, D. and Karimi. I.A., 1987. Scheduling in Batch Processes. Chemical Engineer- ing Progress, August: 35545.

[7] Birewar. D.B. and Grossmann. IE, 1990. Simul- taneous production planning and scheduling in multiproduct batch plants. Ind. Eng. Chem. Res.. 29(4): 570-580.

[S] Smith-Daniels, V.L.. 1988. A heuristic procedure for scheduling packaging lines in process industries. IIE Trans., 20(3): 2955305.

[9] Bruvold, N.T. and Evans, J.R., 1985. Flexible mixed- integer programming formulations for production scheduling problems. IIE Trans., 17( 1): 2-7.

[lo] Smith-Daniels, V.L. and Smith-Daniels. D.E., 1986. A mixed integer programming model for lot sizing and sequencing packaging lines in the process industries. IIE Trans., 18(3): 2788285.

[ll] Vickery, S.K. and Markland. R.E.. 1986. Multi- stage lot-sizing in a serial production system. Int. J. Prod. Res., 24(3): 517-534.

[12] Smith-Daniels. V.L. and Ritzman, L.P., 1988. A model for lot sizing and sequencing in process industries. Int. J. Prod. Res.. 26(4): 647-674.

[13] Hill, T.J., 1991. Production/Operations Manage- ment. Prentice Hall, London, pp. 2566257.

[14] Konijnendijk. P. and Wijngaard, J., 1991. Co- makership in the delivery of packaging materials. Int. J. Oper. Prod. Manage., ll(3): 21-31.

scheduling of packaging lines in the process industry: an empirical investigation

Documents