ÏÐÎÁËÅÌÛ ÓÏÐÀÂËÅÍÈß 6/2005

Ìåòîäû îïòèìèçàöèè â óïðàâëåíèè

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ÓÄÊ 65.012

OPTIMIZATION OF CAPACITY IN AN INTANGIBLE PRODUCTION

O. Zaikin(1), A. Dolgui(2), E. Kushtina(1), P. Korytkowski(1)

1Szczecin University of Technology, Poland;

2Ecole Nationale Supérieure des Mines de Saint Etienne, France

The paper addresses the problem of capacity planning for a production system of intangible products that can be interpreted as an open queuing network. The capacity is controlled through a number of parallel uniform servers and buffer capacity at each processing node. More specifically, an optimization model is presented that complies with resource utilization, production cycle, and cooperation levels under budget constraints. The proposed heuristic algorithm combines analytical modeling with discrete-event simulation. The approach is illustrated by a printing industry example.

ÎÏÒÈÌÈÇÀÖÈß ÏÐÎÈÇÂÎÄÈÒÅËÜÍÎÑÒÈ ÎÁÐÀÁÀÒÛÂÀÞÙÈÕ ÌÎÙÍÎÑÒÅÉ Â ÍÅÌÀÒÅÐÈÀËÜÍÎÌ ÏÐÎÈÇÂÎÄÑÒÂÅ

O. Çàèêèí(1), A. Äîëãèé(2), Å. Êóøòèíà(1), Ï. Êîðèòêîâñêèé(1)

(1)Òåõíè÷åñêèé óíèâåðñèòåò, ã. Ùåöèí, Ïîëüøà

(2)Âûñøàÿ ãîðíàÿ øêîëà â Ñåíò-Åòüåí, Ôðàíöèÿ

Ðàññìîòðåíà çàäà÷à ïëàíèðîâàíèÿ çàãðóçêè ïðîèçâîäñòâåííîé ñèñòåìû, “ñûðüåì” êîòîðîé ñëóæàò ïðîäóêòû èíòåëëåêòóàëüíîé äåÿòåëüíîñòè, ïîñòóïàþùèå â öèôðîâîé ôîðìå. Ïîêàçàíî, ÷òî òàêàÿ ñèñòåìà ìîæåò áûòü ïðåäñòàâëåíà â âèäå îòêðûòîé ñåòè ìàññîâîãî îáñëóæèâàíèÿ. Ïðîèçâîäèòåëüíîñòü ñèñòåìû êîíòðîëèðóåòñÿ ñ ïîìîùüþ ðÿäà îäíîòèïíûõ ïàðàëëåëüíûõ ñåðâåðîâ è áóôåðíîé åìêîñòè êàæäîãî óçëà îáðàáîòêè. Ïðåäñòàâëåíà îïòèìèçàöèîííàÿ ìîäåëü, îïèñûâàþùàÿ èñïîëüçîâàíèå ðåñóðñîâ, ïðîèçâîäñòâåííûé öèêë è óðîâíè êîîïåðàöèè ïðè áþäæåòíûõ îãðàíè÷åíèÿõ. Ïðåäëîæåí ýâðèñòè÷åñêèé àëãîðèòì, ñî÷åòàþùèé â ñåáå ïîñòðîåíèå àíàëèòè÷åñêîé ìîäåëè è èìèòàöèîííîå ìîäåëèðîâàíèå äèñêðåòíûõ ñîáûòèé. Ïîëó÷åííûå ðåçóëüòàòû ïðîèëëþñòðèðîâàíû ïðèìåðîì èç ïîëèãðàôè÷åñêîãî ïðîèçâîäñòâà.

INTRODUCTION

In this paper we address the problem of determining capacity levels in an intangible production. Insufficient capacity can cause elongation of production cycle that leads to late deliveries and high levels of work-in-process. Excess capacity is a waste of expensive resources due to low utilization of equipment. The problem is complicated further by the stochastic behavior of the production system like unpredictable time of orders arrival. To take into account the random behavior manufacturing systems are often modeled and analyzed using queuing network theory [1 – 3].

To provide a decision making tool that takes into account capacity costs and the tradeoff between cycle times, performance and cooperation, we formulate a capacity optimization model that involves minimizing capacity costs while satisfying a set of systems constrains.

Development in means of communication and digital data exchange leads to establishment of new kind of goods – intangible products [4]. Increasing computerization of manufacturing processes caused appearance in various areas for example: banking, printing and publishing, entertainment, advertisement and many others new type of manufacturing – intangible production. For this kind of production particularly arise problem of resource capacity optimization because high competitive market, close relationships with customers, high cost of equipment, etc.

An intangible product is a good that possesses a digital form, which is a direct result of an intellectual work of a man. An intangible product could be materialized through its recording or printing. The fact of materialization does not change its content, but the form of distribution.

An intangible production is an advanced manufacturing, where input materials, semi products and final products are in digital form. Manufacturing and distribution of work articles is realized with broad use of telecommunication and computer networks. It enables to establish a production process with technological operations that are distributed geographically and dynamic assignment of works between workstations. One of the main peculiarities of the intangible production is the fact that there are no mechanical operations, excluding final stages of technological process, when for example the product is printed or burned on CDs. Intangible production is usually a multi product one. Within one manufacturing system wide nomenclature of final products are produced basing on the same communication infrastructure and workstations. Intangible production is a customer oriented one. It gives unique possibility to customize all final products according to customer requirements if the company is capable of introducing it.

Described properties of intangible production enable to characterize a manufacturing process as a network of sets of work stations called later processing nodes. The network consists of processing nodes and telecommunication channels that connect them and enables to exchange semi-finished articles. Traffic inside the production network due to its multi product character is a mixture of traffic that is generated by a production process of each kind of final products. Network of intangible production may be represented as a digraph. The vertices of the digraph are the processing nodes and the arcs are workflows. Listed features of the production network give a possibility to circumscribe it as a network:

with stochastic workflows of semi finished articles,

unified work stations that could service several types of products.

Under term of a processing node we understand a set of uniform work stations performing the same technical operation with an input buffer that stores semi articles before sending them to one of the working posts. Output capacity of processing node is a sum of productivities of each workstations being its part. Productivity of a workstation is a number of semi finished articles that could be processed during a period of time. Processing node can be interpreted as a queuing system with parallel servers.

In an intangible production a buffers that are placed at each processing nodes should be rather considered in terms of time than space or volume. In this case articles and semi-finished products are in digital form; it means they don’t have dimensions and weight. Nowadays data carriers are cheap, so it’s not a problem to store semi-finished products. The challenge is to produce faster and faster. In order to do so we are considering a buffer as a source of a time loss that is wasted on waiting for servicing and we ought to avoid them. Waiting times in manufacturing are very common and probably they are inevitable. One of the methods to deal with this problem is to devolve some works to another cooperating with as company that is capable of performing that particular technological operation. It’s obvious that we could not pass a lot of works other company. The tradeoff in this case is between the cycle time and the resource utilization level. The increase of cooperation will lower the cycle time; the decrease will hoist the utilization. The level of cooperation can be modeled by limitation of buffer capacity. The buffer overflow indicates the need for cooperation.

That leads us to laying down objectives of capacity planning in an intangible production:

– minimize capacity costs;

– minimize cycle time;

– minimize of jobs rejection.

The objectives depend on the number of servers and buffers capacity in an opposite way: while the number of servers increases the cycle time is falling and the idle time of servers rises. In turn while the buffer capacity increases the cycle time is rising and the costs of cooperation are reduced.

Let’s introduce two constrains:

the network’s construction costs cannot exceed the given budget;

capacity of each processing node must be sufficient to serve an average workflow that is directed to it.

Before discussing the capacity planning problem further, we need to define some queuing network terminology. A manufacturing system can be considered as a queuing network that consists of processing nodes where works are routed from one node to another to obtain necessary processing. As comes off production processes queuing network is an open one with deterministic routing.

The formulated task if considered as Marcovian processes of arrival and servicing can be easily solved using the Burke’s Theorem [5] and decomposition of the network into separate processing nodes. However, the problem becomes more complicated when the arrival and servicing processes are given in a general form. In this case the Burke’s theory is not working any longer and the optimization task requires combined usage of analytical modeling and simulation [6, 7].

REFERENCES

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8. Zaikin, O., Dolgui A., Korytkowski P. Optimisation of Resource Allocation in Distributed Production Networks / in: B. Dunin-Klepicz, E. Nawarecki, eds., Lecture Notes in Artificial Intelligence 2296. – Berlin. Springer-Verlag, Berlin, 2002. – Ð. 322–332.

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12. Hillier F.S. and Lieberman G.J. Introduction to Operations Research. – N.-Y.: McGraw-Hill, 2001.

13. Zaikin O. Resource Distribution in Automatic Production Control for Nonmaterial Products: A Mathematical Model // Automation and Remote Control. – 2002. – Vol. 63. – N 8. – Ð. 1351–1356.

14. Zaikin O., Korytkowski P., Kushtina E., Malachowski B. Modelling of the supply chain for a distributed publishing enterprise / in: A. Dolgui, J. Soldek, O. Zaikin, eds., Supply chain optimisation product/process design, facility location and flow control. – Boston: Springer, 2005. – Ð. 161–170.

15. Kelton W.D., Sadowski R.P., Sadowski D.A. Simulation with Arena. – Boston: McGraw-Hill, – 1998.

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E-mail: ozaikine@wi.ps.pl, dolgui@emse.fr