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A design for a management information system with consideration for stochastic variability
Int. J. Production Economics 60—61 (1999) 171—176
A design for a management information system with consideration for stochastic variability Kenichi Nakashima* Faculty of Engineering, Department of Industrial Management, Osaka Institute of Technology, 5-16-1, Omiya, Asahi-ku, Osaka, 535 Japan
Abstract A management information system (MIS) is one of the important systems to control materials and information harmoniously. The previous design approaches dealt with it qualitatively. Therefore, it was impossible to smooth the office works in the management system. In this paper, we design the MIS using a stochastic Petri net (SPN). First, we describe a typical MIS and explain the concept of SPN. Next, we construct the MIS as the SPN model and obtain the total expected sojourn time of documents in each section. Finally, we propose the design for the MIS with consideration for the smoothing of the office works. 1999 Elsevier Science B.V. All rights reserved. Keywords: Information technology; Management information system; Smoothing of office works
1. Introduction A management information system (MIS) is one of the important systems to control materials and information harmoniously. The MIS is now expressed by the following keywords: (1) network, (2) open system, (3) down sizing, (4) multi-vendor and, that is to say by the other words, as “4F and 1R”, (1) Fast, (2) Flexible, (3) Flat, (4) Fusion, (5) Real. Today, most people say that the data should be processed at the place where the data occurs, and should be returned and fed back quickly with real time. In addition, network and database are required in order to utilize the huge volume of data
* Tel.: 81 69544788; fax: 81 69546197; e-mail: nakasima@dim. oit.ac.jp.
effectively. Such an information system should not be constituted by the style of a conventional batch system, but by the form of an integrated or total system. Now, we shall imagine a small-scale retail store, e.g., a fruit store, a vegetable store, a drag store, and a fresh fish store, etc. In such stores, originally the master would be a system like the random and real-time access information processing. On the other hand the master deals with sales commodities, schedules of purchasing plan and checks the amount of stock, and so on. Then, he could get all the required information only by his own activities, and therefore would be able to make accurate decisions. The master becomes equivalent to the integrated management system or the total management system itself. As we know from the case above, when we do not use a computer in
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K. Nakashima/Int. J. Production Economics 60—61 (1999) 171—176
conventional business, it is quite natural to deal with and control the management and/or the production information by the form of an integrated or total system. In this way, as long as the size of the business is small, the manager can control management organization or function intuitively and easily. However, after the computers and electronic data processing system (EDPS) became the standard tools in business, according to the progress of factory automation and office automation, the management organization became separated and specialized. Furthermore, the data processing interval becomes long, and the unprocessed management information increases in accordance with the increase of the computer’s processing capacity. Consequently, the remarkable delay of the feedback information which is required for managers or foremen would also occur. Recently, a data and function oriented approach (DFOA) has been proposed as a concept of a design for the MIS [1,2]. This approach enables the designers to easily design and understand the huge MIS without expert knowledge for the management. The style of the analysis and design has been proceeded from the static point of view. That is, it was not a quantitative, but a qualitative method. Hence, it was impossible to smooth the office work load in the system. In this paper, we investigate the MIS using a stochastic Petri net (SPN). The SPN is recognized as a modeling tool for analyzing the performance of discrete-event systems with stochastic variability. It enables one to find the existence of imbalances in such a system, and to improve on those points. In Section 2, we consider a typical MIS which consists of four sections in a model company. Furthermore, the MIS is expressed by an office flowchart. In Section 3, we explain the concept of the Petri nets. The SPN is introduced as a kind of Petri net where each transition is associated with an exponentially distributed random variable which expresses the delay from the enabling to the firing of the transition. In Section 4, we model the typical MIS as the SPN. In Section 5, the expected sojourn time of documents in each place is obtained by simulation. Moreover, we reconstruct the framework of the sections of the MIS, and propose the design for the MIS with consideration for the smoothing of the office works.
2. Description of the MIS The ideal style of the integrated or total management system should be constructed so as to gather the required information easily and quickly by the form required in each field. That is to say, data do not exist to be recorded and accumulated in files but also to feedback or feedforward in order to circulate all over the management organization and utilized for all purpose, like the blood in the body. Blood plays an important role to change energy, to refresh and to restrict our body, day by day. Management organization is also changeable to a company with management circumstances as well as in the case of human organization. When the circumstance of management changes, the company should acquire the data in order to know its changes. Furthermore, the data should be utilized to restructure the management organization in the same way as the blood in human organization. For the purpose of clearing those problems, there are various approaches to investigate the office works. The office flowchart is one of the effective approaches in the previous studies. It is known as a qualitative approach to the data flow analysis. The office works and the corresponding notations of a typical flowchart are shown in Table 1. We now consider a typical MIS in a model company. The system consists of four sections, i.e., the sales, the process management, the material purchasing and the production section. Each section has the work shown in Table 1. For example, Fig. 1 illustrates the sales section and the process management section of the MIS denoted by the office flowchart.
Table 1 Notations of office works Meaning Posting Check Collection Custory
Notation
K. Nakashima/Int. J. Production Economics 60—61 (1999) 171—176
173
negative integer. If a marking assigns to place p a nonnegative integer k, we say that p is marked with k tokens. Pictorially, we place k black dots (tokens) in place p. A marking is denoted by M [3]. A stochastic Petri net (SPN) is a Petri net where each transition is associated with an exponentially distributed random variable that expresses the delay from the enabling to the firing of the transition. In a case where several transitions are simultaneously enabled, the transition that has the shortest delay will fire first. A formal definition of the SPN is given by a 6-tuple:
Fig. 1. Flow chart of the MIS.
SPN"(P, ¹, I, O, M , K), where P"(p , p , 2, p ) is a finite set of places, 1 ¹"(t , t , 2, t ) a finite set of transitions. * ILP;¹ a finite set of input arcs from a place to a transition. OL¹;P a finite set of output arcs from a transition to a place, M "(m , m , 2, m1) an initial marking, K"(j, j,2, j*) a vector of firing rates of the transitions. Notice that S and ¸ denote the total number of places and that of transitions, respectively [3].
3. Stochastic Petri net model 4. The MIS modeled by the SPN A Petri net is a graphical and mathematical modeling tool applicable to real systems such as the production system [3,4]. It is a promising tool for describing and studying information systems that are characterized as being concurrent, asynchronous, distributed, parallel, nondeterministic, and/or stochastic. As a graphical tool, the Petri net can be used as a visual-communication aid similar to flow charts, block diagrams, and networks. In addition, tokens are used in these nets to simulate the dynamic and concurrent activities of systems. As a mathematical tool, it is possible to set up state equations, algebraic equations, and other mathematical models governing the behavior of systems. The Petri net is a particular kind of directed graph, together with an initial state called the initial marking, M . It consists of two kinds of nodes, called places and transitions, where arcs are either from a place to a transition or from a transition to a place. In this graph, places are drawn as circles and transitions are drawn as bars or boxes. A marking (state) assigns to each place a non-
We now consider the office works in the model company described in Section 2. Let us represent the number of documents and the location of them by the number of tokens and the places, respectively. Moreover, flow of documents and that of the feedback are denoted by a directed actual arc and directed dotted arcs, respectively (Fig. 2). Both the interarrival time of the demand and each operational time of the system are exponentially distributed. Fig. 3, for instance, shows the SPN model of the sales and process management sections of the
Fig. 2. Examples of the MIS denoted by SPN.
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K. Nakashima/Int. J. Production Economics 60—61 (1999) 171—176
Fig. 3. The MIS modeled by the SPN.
system corresponding to Fig. 1. In this MIS model, the total number of places, S is equal to 150, and that of transitions, ¸ is equal to 60.
5. Numerical results Let us consider the MIS with the changeable firing rates of the transitions in the model company. Fig. 4 shows the total expected sojourn time of the documents in each section in the case where each
service rate in the system is one, and the arrival rate of demand is half. Fig. 4 shows that the office works are not smooth in the MIS. Hence, we can reconstruct the system by controlling the firing rates, which means the automation, labor management and so on. Fig. 5 illustrates the total expected sojourn time in each section after controlling the firing rates. We can see smoothing of the office works. As a result, the flow of documents can be synchronized in the MIS.
K. Nakashima/Int. J. Production Economics 60—61 (1999) 171—176
Fig. 4. Total expected sojourn time before smoothing.
Fig. 5. Total expected sojourn time after smoothing.
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K. Nakashima/Int. J. Production Economics 60—61 (1999) 171—176
6. Conclusions In this paper, we investigate the MIS using the SPN model with consideration for the stochastic variability such as the operational time and the interarrival time of the demand. Numerical results show the total expected sojourn time of the documents in each section of the MIS, so that this approach makes it possible to find the existence of unbalanced office work load. Furthermore, we can reconstruct the system by controlling the operational times in each section of the MIS. As a result, it is possible to design the MIS with the smoothing of the office works.
Acknowledgements The author would like to express his gratitude to Professor S. Kuriyama of Setsunan University,
Professor T. Nose of Osaka Institute of Technology and Mr. Nakabayashi of Ishikawa Corp. for supervising this thesis. Their continuous encouragement and invaluable comments have helped to accomplish this paper.
References [1] T. Nose, S. Kuriyama, K. Akou, A design for management information system by work-design technique, Proceedings of 16th International Conference on Computer and Industrial Engineering, 1994, pp. 662—665. [2] T. Nose, S. Kuriyama, A design of management information system, Proceedings of 20th International Conference on Computer and Industrial Engineering, 1996, pp. 1063—1066. [3] T. Murata, Petri nets: Properties, analysis and applications, Proceedings of the IEEE 77 (4), 1989, pp. 541—580. [4] M.C. Zhou (Ed.), Petri Nets in Flexible and Agile Automation, Kluwer Academic Publishers, Dordrecht, 1995.
A design for a management information system with consideration for stochastic variability Kenichi Nakashima* Faculty of Engineering, Department of Industrial Management, Osaka Institute of Technology, 5-16-1, Omiya, Asahi-ku, Osaka, 535 Japan
Abstract A management information system (MIS) is one of the important systems to control materials and information harmoniously. The previous design approaches dealt with it qualitatively. Therefore, it was impossible to smooth the office works in the management system. In this paper, we design the MIS using a stochastic Petri net (SPN). First, we describe a typical MIS and explain the concept of SPN. Next, we construct the MIS as the SPN model and obtain the total expected sojourn time of documents in each section. Finally, we propose the design for the MIS with consideration for the smoothing of the office works. 1999 Elsevier Science B.V. All rights reserved. Keywords: Information technology; Management information system; Smoothing of office works
1. Introduction A management information system (MIS) is one of the important systems to control materials and information harmoniously. The MIS is now expressed by the following keywords: (1) network, (2) open system, (3) down sizing, (4) multi-vendor and, that is to say by the other words, as “4F and 1R”, (1) Fast, (2) Flexible, (3) Flat, (4) Fusion, (5) Real. Today, most people say that the data should be processed at the place where the data occurs, and should be returned and fed back quickly with real time. In addition, network and database are required in order to utilize the huge volume of data
* Tel.: 81 69544788; fax: 81 69546197; e-mail: nakasima@dim. oit.ac.jp.
effectively. Such an information system should not be constituted by the style of a conventional batch system, but by the form of an integrated or total system. Now, we shall imagine a small-scale retail store, e.g., a fruit store, a vegetable store, a drag store, and a fresh fish store, etc. In such stores, originally the master would be a system like the random and real-time access information processing. On the other hand the master deals with sales commodities, schedules of purchasing plan and checks the amount of stock, and so on. Then, he could get all the required information only by his own activities, and therefore would be able to make accurate decisions. The master becomes equivalent to the integrated management system or the total management system itself. As we know from the case above, when we do not use a computer in
0925-5273/99/$ - see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 5 2 7 3 ( 9 8 ) 0 0 2 0 3 - 5
172
K. Nakashima/Int. J. Production Economics 60—61 (1999) 171—176
conventional business, it is quite natural to deal with and control the management and/or the production information by the form of an integrated or total system. In this way, as long as the size of the business is small, the manager can control management organization or function intuitively and easily. However, after the computers and electronic data processing system (EDPS) became the standard tools in business, according to the progress of factory automation and office automation, the management organization became separated and specialized. Furthermore, the data processing interval becomes long, and the unprocessed management information increases in accordance with the increase of the computer’s processing capacity. Consequently, the remarkable delay of the feedback information which is required for managers or foremen would also occur. Recently, a data and function oriented approach (DFOA) has been proposed as a concept of a design for the MIS [1,2]. This approach enables the designers to easily design and understand the huge MIS without expert knowledge for the management. The style of the analysis and design has been proceeded from the static point of view. That is, it was not a quantitative, but a qualitative method. Hence, it was impossible to smooth the office work load in the system. In this paper, we investigate the MIS using a stochastic Petri net (SPN). The SPN is recognized as a modeling tool for analyzing the performance of discrete-event systems with stochastic variability. It enables one to find the existence of imbalances in such a system, and to improve on those points. In Section 2, we consider a typical MIS which consists of four sections in a model company. Furthermore, the MIS is expressed by an office flowchart. In Section 3, we explain the concept of the Petri nets. The SPN is introduced as a kind of Petri net where each transition is associated with an exponentially distributed random variable which expresses the delay from the enabling to the firing of the transition. In Section 4, we model the typical MIS as the SPN. In Section 5, the expected sojourn time of documents in each place is obtained by simulation. Moreover, we reconstruct the framework of the sections of the MIS, and propose the design for the MIS with consideration for the smoothing of the office works.
2. Description of the MIS The ideal style of the integrated or total management system should be constructed so as to gather the required information easily and quickly by the form required in each field. That is to say, data do not exist to be recorded and accumulated in files but also to feedback or feedforward in order to circulate all over the management organization and utilized for all purpose, like the blood in the body. Blood plays an important role to change energy, to refresh and to restrict our body, day by day. Management organization is also changeable to a company with management circumstances as well as in the case of human organization. When the circumstance of management changes, the company should acquire the data in order to know its changes. Furthermore, the data should be utilized to restructure the management organization in the same way as the blood in human organization. For the purpose of clearing those problems, there are various approaches to investigate the office works. The office flowchart is one of the effective approaches in the previous studies. It is known as a qualitative approach to the data flow analysis. The office works and the corresponding notations of a typical flowchart are shown in Table 1. We now consider a typical MIS in a model company. The system consists of four sections, i.e., the sales, the process management, the material purchasing and the production section. Each section has the work shown in Table 1. For example, Fig. 1 illustrates the sales section and the process management section of the MIS denoted by the office flowchart.
Table 1 Notations of office works Meaning Posting Check Collection Custory
Notation
K. Nakashima/Int. J. Production Economics 60—61 (1999) 171—176
173
negative integer. If a marking assigns to place p a nonnegative integer k, we say that p is marked with k tokens. Pictorially, we place k black dots (tokens) in place p. A marking is denoted by M [3]. A stochastic Petri net (SPN) is a Petri net where each transition is associated with an exponentially distributed random variable that expresses the delay from the enabling to the firing of the transition. In a case where several transitions are simultaneously enabled, the transition that has the shortest delay will fire first. A formal definition of the SPN is given by a 6-tuple:
Fig. 1. Flow chart of the MIS.
SPN"(P, ¹, I, O, M , K), where P"(p , p , 2, p ) is a finite set of places, 1 ¹"(t , t , 2, t ) a finite set of transitions. * ILP;¹ a finite set of input arcs from a place to a transition. OL¹;P a finite set of output arcs from a transition to a place, M "(m , m , 2, m1) an initial marking, K"(j, j,2, j*) a vector of firing rates of the transitions. Notice that S and ¸ denote the total number of places and that of transitions, respectively [3].
3. Stochastic Petri net model 4. The MIS modeled by the SPN A Petri net is a graphical and mathematical modeling tool applicable to real systems such as the production system [3,4]. It is a promising tool for describing and studying information systems that are characterized as being concurrent, asynchronous, distributed, parallel, nondeterministic, and/or stochastic. As a graphical tool, the Petri net can be used as a visual-communication aid similar to flow charts, block diagrams, and networks. In addition, tokens are used in these nets to simulate the dynamic and concurrent activities of systems. As a mathematical tool, it is possible to set up state equations, algebraic equations, and other mathematical models governing the behavior of systems. The Petri net is a particular kind of directed graph, together with an initial state called the initial marking, M . It consists of two kinds of nodes, called places and transitions, where arcs are either from a place to a transition or from a transition to a place. In this graph, places are drawn as circles and transitions are drawn as bars or boxes. A marking (state) assigns to each place a non-
We now consider the office works in the model company described in Section 2. Let us represent the number of documents and the location of them by the number of tokens and the places, respectively. Moreover, flow of documents and that of the feedback are denoted by a directed actual arc and directed dotted arcs, respectively (Fig. 2). Both the interarrival time of the demand and each operational time of the system are exponentially distributed. Fig. 3, for instance, shows the SPN model of the sales and process management sections of the
Fig. 2. Examples of the MIS denoted by SPN.
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K. Nakashima/Int. J. Production Economics 60—61 (1999) 171—176
Fig. 3. The MIS modeled by the SPN.
system corresponding to Fig. 1. In this MIS model, the total number of places, S is equal to 150, and that of transitions, ¸ is equal to 60.
5. Numerical results Let us consider the MIS with the changeable firing rates of the transitions in the model company. Fig. 4 shows the total expected sojourn time of the documents in each section in the case where each
service rate in the system is one, and the arrival rate of demand is half. Fig. 4 shows that the office works are not smooth in the MIS. Hence, we can reconstruct the system by controlling the firing rates, which means the automation, labor management and so on. Fig. 5 illustrates the total expected sojourn time in each section after controlling the firing rates. We can see smoothing of the office works. As a result, the flow of documents can be synchronized in the MIS.
K. Nakashima/Int. J. Production Economics 60—61 (1999) 171—176
Fig. 4. Total expected sojourn time before smoothing.
Fig. 5. Total expected sojourn time after smoothing.
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6. Conclusions In this paper, we investigate the MIS using the SPN model with consideration for the stochastic variability such as the operational time and the interarrival time of the demand. Numerical results show the total expected sojourn time of the documents in each section of the MIS, so that this approach makes it possible to find the existence of unbalanced office work load. Furthermore, we can reconstruct the system by controlling the operational times in each section of the MIS. As a result, it is possible to design the MIS with the smoothing of the office works.
Acknowledgements The author would like to express his gratitude to Professor S. Kuriyama of Setsunan University,
Professor T. Nose of Osaka Institute of Technology and Mr. Nakabayashi of Ishikawa Corp. for supervising this thesis. Their continuous encouragement and invaluable comments have helped to accomplish this paper.
References [1] T. Nose, S. Kuriyama, K. Akou, A design for management information system by work-design technique, Proceedings of 16th International Conference on Computer and Industrial Engineering, 1994, pp. 662—665. [2] T. Nose, S. Kuriyama, A design of management information system, Proceedings of 20th International Conference on Computer and Industrial Engineering, 1996, pp. 1063—1066. [3] T. Murata, Petri nets: Properties, analysis and applications, Proceedings of the IEEE 77 (4), 1989, pp. 541—580. [4] M.C. Zhou (Ed.), Petri Nets in Flexible and Agile Automation, Kluwer Academic Publishers, Dordrecht, 1995.