Production scheduling with uncertain demand and no stockkeeping

Production scheduling with uncertain demand and no

stockkeeping

Citation for published version (APA):

Dellaert, N. P., & Wessels, J. (1985). Production scheduling with uncertain demand and no stockkeeping. (Memorandum COSOR; Vol. 8522). Technische Hogeschool Eindhoven.

Document status and date: Published: 01/01/1985

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EINDHOVEN UNIVERSITY OF TECHNOLOGY

Department of Mathematics and Computing Science

r

Memorandum COS OR 85-22

Production scheduling with uncertain

demand and no stockkeeping

by

Nico Dellaert and Jaap Wessels

Eindhoven, The Netherlands

November 1985

PRODUCTION SCHEDULING WITH UNCERTAIN DEMAND AND NO STOCKKEEPING

Nico Dellaert, Eindhoven Jaap \'lessels, Eindhoven

Abstract. We consider a production process, in which one part forms the bottle-neck. For this situation, in which there is great uncertainty about future demands and no products are kept in stock, we describe a Inethod for production scheduling and pre-sent some results. The most important feature of the method is that some orders are scheduled on arriving and other orders, with a greater agreed due-data unreliability, are scheduled at a later moment.

Zusammenfassung. Wir betrachten ein Produktionsprozess mit einem Engpass. Fur diese Situation, wo Nachfrage sehr unsicher ist und Produktion nur im Auf trag statt findet, beschreiben wir eine Methode zur Planung der Produktion und wir prasentieren einige Resultate. Das wichtigste Aspekt der Methode ist dass ein Teil der Auftrage gleich beim Eintreffen eingeplant wird und dass Auftrage, wofur die Liefergenauigkeit ge-ringer ist, erst spater eingeplant werden.

1. Introduction

In this paper we will consider the problem of scheduling production for a production process with large set-up times, a very uncertain demand process, no possibility of

stockkeeping, whereas i t is requested to deliver on short notice. This type of situ-ation occurs in several instances and is not covered by the common planning methods. It became problematic in the last few years because of the trend of manufacturers to require very short delivery times from their suppliers. Using an example of such a situation, we will demonstrate an approach for such problems.

In a factory one produces steel pipes to order; for several reasons there are no products kept in stock. When an order arrives, a delivery date has to be agreed upon. In order to realize this delivery date as good as pOSSible, a good

production-schedule is needed.

The production process can be s'plit up into three separate parts: a preliminary treatment, the welding-process and a follow-up treatment. The welding-process is forming the bottle-neck of the production. There are several welding-machines, each with a partially different range of sizes, i t can treat. If we want to make a pro-duct of another size, parts of the welding-machine have to be rebuilt. These

rebuild 2 rebuild

-times depend on the change of size.

In order to keep the total amount of time, needed for rebuilding, small, we divide the products into several groups -of si:<:es, between which the rebuild-times are small. These groups play an important role in the production scheduling. Other important aspects of a good production schedule are the necessity of keeping the delivery dates small and rather constant.

According to the wishes of the factory management we divide the orders into 4 cate-gories, varying from very urgent orders to orders with a requested delivery-date after a few months. For every category of orders the management has given constraints on the average delivery time and the allowed uncertainty in realizing this time. In principle one would like to collect a large set of orders before scheduling them. However, this approach would lead to. long delivery times. Therefore, we designed a method in which orders with high priority are scheduled immediately, whereas the orders with low priority are put into a waiting room. The problem then remains to decide which orders are scheduled immediately and for which orders scheduling is postponed. It will appear in our example that orders of Category 1 and most of the orders of Category 2 can be scheduled upon arrival.

This paper is organized as follows. In Section 2 we describe the structure of the production process, the available welding-capacity and the products that are made. In Section 3 the current production-scheduling method is described, which uses a fixed-cycle schedule. The demands upon the planning method are presented in Section 4. The new production-schedule, with its most important elements, is described in Section 5. Some numerical results are given in Section 6. Conclusions are drawn in Section 7.

2. The production process

In one part of the factory steel coils of different quality and size are stocked. These coils are slitted into rings. After the slitting the rings are transported to the welding-machines, where they are rolled, welded, calibrated and sawed. After-wards several follow-up treatlnents can be done, such as sawing to little pieces, coating, heating and collecting.

For all treatments, except on the welding-n~chines, there is sufficient capacity, so most of the time orders have no substantial waiting-time due to these treatments. The waiting-time caused by the welding-machines can be several days or even several weeks. For this reason we only consider the scheduling on the welding-machines.

In the factory we studied, there were 6 welding-machines, each with a partially different range of sizes, depending on the available sets of rolls on the machine. With every set a group of products, with certain shapes, can be produced. If we want to make a product of another group we have to take another set, if we want to make a product with another shape belonging to the same group, we only have to change a

3

-part of the set. It is understandable that we want to produce products of the same group on a machine as long as possible in order to avoid rebuilding-times.

On the 6 welding-machines products of about 150 different shapes, length not consi-dered, can be made. These products can be grouped into 30 groups. Most of the groups can be produced on two different machines, some groups on only one machine and a few groups on three machines.

3. The present scheduling

In the present situation, it is decided every year how often and on which machine(s) orders from a certain group are produced. Some groups are made every 3 weeks, other groups, with smaller demand, every 6 or 12 weeks. The groups are made in a fixed or-der and during a fixed time, except in case of emergencies.

The main advantage of this way of scheduling is its simplicity from the point of view of the production department, the customers as well as the sales department. The main disadvantage is its inflexibility. This inflexibility becomes particularly clear if demands deviate from their forecasts and if urgent order~ come in. As a consequence one uses ad-hoc policies for urgent orders and delivery dates become instable and large.

4. Demands upon the scheduling

We divide the orders into 4 categories in order of priority: 1. very urgent orders;

2. urgent orders from industrial users; 3. urgent orders from stocktraders; 4. non-urgent orders.

The company stated the following requirements for the average delivery times and the accuracy in realizing the delivery date:

category delivery time (in weeks) accuracy (in days)

1 1-1,5 ± 1

2 3-4 ± 3

3 6-7 ±8

4 as requested (> 7) ±8

Table 1. Requirements for the production planning.

In the present situation these requirements can only be satisfied for the last two categories.

4

-5. Proposed scheduling method

The base of the proposed scheduling method is formed by capacity reservations for groups of sizes. A new capacity reservation is made if one wants to schedule an or-der but there is not sufficient capacity available in a reservation for its group. The amount of reserved capacity dependB on the forecasted amount of production time, needed for orders belonging to the considered group, that will arive before the ex-pected production moment of the group and that would best be scheduled in that servation. So, for every machine we have a sequence with scheduled orders and re-served capacity (Fig. 1).

Machine 1

scheduled orders from group i

reserved capacity for orders from group i

Fig. 1. Example of a machine-sequence.

Furthermore for every group of sizes we have a stand-by sequence. Orders which are not immediately scheduled are put into the stand-by sequence for their group. In this company this leads to the following situation in which we have 6 machine-se-quences and 30 stand-by semachine-se-quences (Fig. 2):

Machine Machine Group 1

.

•

~

•

~~

~

~

~/~

;,0b

Fig. 2. Example of a possible situation.

3

Now we have to decide on the precise use of these sequences:

- when do we open a new reservation and on which machine do we open it?

I I

5

when are orders of a stand-by sequence scheduled, i.e. transported to a machine sequence?

Suppose an order arrives. If the order is of Category 1 or the order is of Category 2 and has a current size, i t is placed in a machine-sequence, either in a reserved part or after the last reserved part on a machine, in which case new capacity is re-served. The delivery-date is based upon the place in the sequence. If the order is of Category 3 or the order is of Category 2 and has not a current size, i t is put into a stand-by sequence and its delivery date is based upon the total amount of production time and reservations in the Inachine-sequences and the currency of the order. If the order is of Category 4 i t is also put in a stand-by sequence, but now the delivery-date is the same as the delivery-date required by the customer.

Orders of a stand-by sequence are scheduled if: - they are nearly too late;

- if in the neighbourhood of their last possible production moment an order of (nearly) the same size is planned.

6. Numerical results

We did several simulations with real orders. In Table 2 and Table 3 the results of a representative simulation with real orders during a period of 4 months are given.

Category %

<

<

<

4

<

1 89 98 100 100

2 14 62 80 98

3

a

Table 2. Delivery-dates in a simulation study.

Category %

<

<

<

<

Table 3. Accuracy of delivery-dates in a simulation study.

In this case the occupation of the lllachine was 76% for net production and 15% for rebuilding. Compared with the real situation during the period which generated the orderdate, there was a considerable improvement in delivery time for orders of

Cate 6 Cate

-gory 1 and 2. Moreover, the accuracy of delivery-dates was much better, while the

total amount of rebuilding-time remained the same.

7.

Conclusions

The planning problem considered in this paper has a couple of aspects which are easy

to handle separately, but hard in combination. These aspects are: production

order-by-order, uncertain demand, considerable change-over times and requested fast

deli-very. The method of scheduling presented in this paper appears to be quite helpful

in a realistic situation. Nevertheless, one should be aware of the fact that one

cannot reach every goal by a good scheduling method only. Usually, it will also be

important to pay attention to the control of the instreaming workload.

The method of scheduling which has been sketched in the preceding sections has

se-veral parameters which can be set and adjusted and also sese-veral free structural

choices. This freedom makes

method applicable in several situations. We will

treat the meaning of these parameters and structural choices in a forthcoming paper.

In that paper we will also show how these choices can be used to adapt the method to

a particular situation.