Keywords Warehouse Management, Optimization, Decision Support, Hierarchical Coloured Petri Network.

Transcription

1 Volume 3, Issue 9, September 2013 ISSN: X International Journal of Advanced Research in Computer Science and Software Engineering Research Paper Available online at: Modeling of the Physical Flow of Goods within the Warehouse by the Hierarchical Coloured Petri Nets Hajira Bakkali, Abdellah Azmani, Abdelhadi Fennan Faculty of Science and Technology Tangier (FSTT) Laboratory of Computer, Systems and Telecommunications (LCST) University of Abdelmalek Essaadi Morocco Abstract in this article, we propose the modelling process of import and export -of the goods in warehouse by the hierarchical Coloured Petri nets. It is a question of describing the physical flow of the goods inside the warehouse, initiated by the reception of orders, or at the arrival of goods in order to describe the state of the warehouse and detect any operational conflicts of sharing human and material resources. Keywords Warehouse Management, Optimization, Decision Support, Hierarchical Coloured Petri Network. I. INTRODUCTION The operation of storage, in a warehouse appears to be at the same time beneficial (solution to fluctuations in customers demand but also the seasonality effect and the reduce of the delivery time) and restrictive (financial capital and additional cost of warehousing which can reach 25% of logistics cost [1]).Consequently, optimization of operations in the warehouse and their organization [20] contributes to the improvement of logistics chain s productivity and reduces its costs. [3] In this context we are trying to develop, using techniques and methods from artificial intelligence, a tool designed for decision support in order to develop the optimization of the operational functions of a warehouse, considering the different physical flows in which they transit. In this context, the following paper presents a model of Hierarchy Coloured Petri Network (HCPN) for managing the physical flow of goods. II. METHOD PROPOSED To model the physical flow of goods inside the warehouse, we propose the following enchainment: - Definition of business processes: In this article we focus on the parallel operation of two processes, the receipt of goods and the receipt of order. - Definition of states variables and events: this step concerns the definition of places (states goods, available personnel, material handling equipment, etc...) and transitions (loading control, unloading, etc ) of our model. - Construction of HCPN models: for the creation of HCPN graphs we used the CPN Tools software [8] [17]. - The initial marking and simulation graph: this step concerns the insertion of coloured tokens in places and to pass transitions models simulation. - Validation and verification of model: these operations are made by calculation of marking graph and drawing the Strongly Connected Component Graph (SCC-graph). III. DESCRIPTION OF OPERATION IN THE WAREHOUSE Physical flows of goods transition between the functional areas of a warehouse [12] [13] can be represented by the following diagram: Fig.1 Transitions of the flows of goods between warehouse areas. 2013, IJARCSSE All Rights Reserved Page 863

2 The functioning in the warehouse is based on four main operations: [2] receiving, storage, order picking and shipping: - Reception: three flows exiting the receiving area can be distinguished o Transfer of the goods to the storage area (supply). o Direct transfer of the goods to the shipping area (cross-docking: The main objective is to redirect the flow to another destination.). o Transfer of the goods to the order preparation area (rush order or stock shortage). For different flows, we make the following operations: o Unloading the goods: using different handling equipment according to the handled logistics units. o Physical Control (qualitative and quantitative): check of goods correspondence between the delivery slip and the order emitted. Storage: the affectation of the goods in the suitable location following the characteristics of products [14] [19] (nature, volume, rotation, influence of the environment, etc.). This operation allows the preservation of the goods for a later use (use in the process of production or constitution of orders). Preparation of order: in the normal process, we collect from the zone of storage, in case of emergency or stock shortage; we can pass the goods directly from the reception area. After the collecting, we make the following operations: o Sorting: sort and assemble products by orders number. o Orders Consolidating: regrouping and packaging of all preparations in detail regarding the same order, the same client and then the same final destination (geographical area, city, country...). Cross docking: this step includes the wait departure, loading in transport and delivery to the customer. IV. PROCESS INPUT AND OUTPUT OF THE GOODS After description of the warehouse functioning, we have defined in the following diagram (Fig. 2) the input and output process flows of goods [18]. Process of goods reception: the first stage in this process is to verify if the goods are destined for the direct expedition (cross-docking) or for the storage. In the first case we transfers directly the goods to the expedition area for unloading, control and loading of the content, in another means of transportation without making the goods undergo packaging operations. In the second case, we check if there is a rush order or stock shortage, to make a direct transfer (without the goods enter physically in stock) of all goods or just a part (decomposition of goods) to the area of order preparation. If not, we check the availability of storage space to unload only the quantity corresponding to the empty locations, and return the remainder to another warehouse. After the operation of unloading, the goods pass by the following operations: quantitative and qualitative control, packaging and labeling, movement towards the zone of storage. Process of order reception: after receiving an order, the corresponding quantity of goods is removed from the storage area, transferred to the orders preparation area, for sorting and packing, finally, the order is moved to the shipping area for loading and is delivered to clients. V. THE COLOURED PETRI NETS Petri nets are a graphical and mathematical modeling tool based on the use of discrete variables [4] [5] presented by Carl Adam Petri in his thesis in 1962 [15], they represent a generalized form of finite automata. There are several types of extensions of Petri nets: generalized, timed, continuous, and coloured. In our case, we opted for the use of coloured Petri nets [6] [7][16] for the representation of different natures of products and the differentiation between human and material resources categories. The formal definition: A Petri net is a directed bipartite graph with two kinds of nodes: places and transitions. We define a coloured Petri nets with a 6-tuple <P, T, C, W-, W+, M0> P: is the set of places. T: is the set of transitions as P T = Ø and P T Ø. C: defined for each place and each transition its field of color. The domains of color are usually Cartesian products W- (= Pre) and (W+ = Post): indexed P x T are impact matrices back and before the network. W-(p, t) and W+ (p, t): are linear functions of defined colors Bag (C (t)) in Bag (C (p)). (Bag (C) denotes the set of multi-sets of C). M0: is the initial marking of the network, which is a vector indexed by P and M0 (p) is an element of Bag (C (p)). VI. ARCHITECTURE OF PETRI NETS UNDER CPN TOOLS There are numerous simulation tools for Petri nets, in our case; we chose to use the software CPN tools. It was developed by researchers at Aarhus University. It allows the simulation of high levels Petri net [8] [9] (coloured, hierarchical and timed). The definitions of colors, variables and functions in CPN Tools are specified in functional language Standard SML [10] [11]. The model proposed for management flow consists of four sub networks. Each sub network is represented in the main page (entry and exit of goods process) by a special transition called transition substitution (Fig.3.) Sub network for the process of storing goods (Fig.6). 2013, IJARCSSE All Rights Reserved Page 864

3 Sub network for the return of goods because of lacking of storage space (Fig.5). Sub network for the process of order preparation (Fig.7). Sub network for the process of Cross docking (Fig.4). Fig.3. HCPN Main page "management of input and output flows of the goods in a warehouse" TABLE1. DESCRIPTION THE TRANSITIONS AND PLACES OF HCPN MAIN PAGE P0 Goods arriving P 1 Goods for storage Places Transitions transitions of substitution P2 Goods for order picking P 2 Goods for order preparation P3 Goods accepted for storage P6 stored Goods P7 Goods shipped C0 Goods ordered C4 Orders delivered Em E3 Locations in the warehouse Material Handling Equipment RHs staff available B1 control place for direct shipping T0 Test for direct shipping T1 Test for transfer to the order preparation area T6 Storage Cross docking, preparation of orders, storage, Return Goods 2013, IJARCSSE All Rights Reserved Page 865

4 Fig.4 Module for the Cross docking. TABLE.2 DESCRIPTION OF THE TRANSITIONS AND PLACES OF CROSS-DOCKING T 0 Unloading of merchandise shipped with control P 1 Goods for Cross docking T7 Return truck RHCD staff available E2CD Control apparatus Fig.5.Module for the Return goods 2013, IJARCSSE All Rights Reserved Page 866

5 Fig.2 Reception process of orders and / or goods in a warehouse TABLE.3 DESCRIPTION OF THE PLACES AND TRANSITIONS OF RETURN GOODS RHR T7 T2 staff available Return trucks Checking the availability of storage space P 3 Returned goods Reception of order Taking of the storage areas Transfer to the preparation area Sorting and packaging loading Delivery Order [No] Returning the truck to another warehouse decomposition goods vailability / quantity? Available space? Transfer_Pick_Order unloading Quality control Preparation Affectation of the location Storage of the goods [No] [No] Transfer quantity unloading_transfer Arrival of goods Coss_Docking Transfer to shipping area Unloading shipment Physical check Loading shipping Shipping goods [No] [No] Fig.2 Reception process of orders and / or goods in a warehouse 2013, IJARCSSE All Rights Reserved Page 867

6 Fig.6. Module for the storage of goods Fig.7. Module for the preparation of order 2013, IJARCSSE All Rights Reserved Page 868

7 TABLE 4 DESCRIPTION OF THE PLACES AND TRANSITIONS OF GOODS STORAGE T3 P4 T4 P5 T5 E1 E2 RHST unloading Goods unloaded for control Control Non defective goods Preparation (Packaging and labeling) Control equipment Packaging materials and labeling staff available TABLE 5 DESCRIPTION OF THE PLACES AND TRANSITIONS OF PREPARATION ORDER TC0 TC1 TC2 TC3 C1 C2 C3 EmPC E3PC RHPC E2PC E1PC Removal of the storage area Unloading and control Preparation of orders Delivery to the final customer Merchandise Removed from storage area Merchandise Removed from reception area prepared orders Location condition Material Handling Equipment Staff available Control hardware Packaging materials and labeling VII. SIMULATION AND ANALYSIS OF RESULTS The simulation results in the CPN Tools with different initial marking allowed us to validate our model: The simulation shows the normal functioning of two parallel processes (preparation of orders and receiving goods), as well as the current status of locations after the input and output flow (increase of the number of empty locations and decreased of the number of locations filled). The simulation shows the normal process of direct Cross-docking. 2013, IJARCSSE All Rights Reserved Page 869

8 The simulation can detect the blocking of system in transition T5 due to lack of packaging materials in the place E1. The graph marking and states spaces permit the qualitative analysis of model in order to ensure the correct system construction. The verification report generated by CPN Tools shows that: o The marking graph: contains 6212 nodes and arcs. o Full states spaces graph: contains 6212 nodes and arcs, figure 5 shows part of the graph. Fig.5. Part of the full states spaces of the model proposed. We note that the number of nodes in the marking graph is equal to that present in the graph of states spaces, which means that our model does not contain a cycle, so our network is irreversible. o Home Markings: none o Dead marking: starting from these nodes, there is no active transition. In our model there are ten dead nodes: [6212, 6211, 6210, 6209, 6208, 6207, 6206, 6205, 6204, and 6203]. o Dead transitions: with any marking, the transitions T 0 and T 7 are not crossed (the case of cross-docking). o Living transitions: in our model there is no living transition, it means that there is no active transition by any marking. o Fairness Properties: no infinite recurrence sequences; there is no sequence with transitions that are repeated several times. VIII. CONCLUSION AND PERSPECTIVES In this paper we proposed a hierarchical coloured Petri nets for flow management transiting within the warehouse. The simulation of our model with CPN Tools can detect blockages due to lack of shared resources and status locations in realtime control. This result is a step of our work that we will extend to the development of a generic model timed considering all flows (physical and informational) that pass within a warehouse. This work is brought to consolidate through our work about the integration of fuzzy logic in the evaluation of the parameters of the Petri net. References [1] Pimor Yves, Fender Michel : Logistique, Production, Distribution, Soutien, 5e édition, Dunod, [2] Roux Michel : Tout ce qu il faut savoir pour concevoir une unité de stockage, 4e édition, Groupe Eyrolles, [3] Roux M., Liu Tong : Optimisez votre plate-forme logistique, Les Editions d Organisation, [4] Murata: Petri nets: Properties, analysis and applications. Proceedings of the IEEE, Vol. 77, N 4, pp , [5] Vernadat : Contribution à la modélisation et à la vérification des systèmes communicants. Habilitation à diriger les Recherches. Université Paul Sabatier, Toulouse, , IJARCSSE All Rights Reserved Page 870

9 [6] Jensen: Coloured Petri Nets. Basic Concepts, Analysis Methods and Practical Use.Volume 3, Practical Use. Monographs in Theoretical Computer Science, Springer-Verlag, [7] Van.W der Aalst and Stahl.C: Modeling Business Processes. A Petri Net-Oriented Approach. MIT Press, [8] CPN Tools.: [9] Kurt Jensen, Lars Michael Kristensen, LisaWells: Coloured Petri Nets and CPN Tools for modelling and validation of concurrent systems, Springer-Verlag 2009 [10] Robin Milner, Mads Tofte, Robert Harper, and David MacQueen: The Definition of Standard ML: Revised The MIT Press, [11] Ullman.J. D: Elements of ML Programming (ML 97 edition). Prentice-Hall, [12] Koster.R, Le-Duc. T and Roodbergen. K. J.: Design and control of warehouse order picking: a literature review. European Journal of Operational Research, 182: , 2007 [13] J. P. van den Berg: A literature survey on planning and control of warehousing systems. IIE Transactions, 31: , 1999 [14] Heragu.S.S, Du.L, Mantel.R.J and Shuur.P.C.: Mathematical model for warehouse design and product allocation. International Journal of Production Research, 43(2): , 2005 [15] Carl Adam Petri : Communication with Automata, thesis presented in 1962 at the University of Darmstadt [16] Francesco Basile n, Pasquale Chiacchio,Domenico Del Grosso : A control oriented model for manual-pick warehouses. Control Engineering Practice, 20: , 2012 [17] Kurt Jensen Lars Michael Kristensen LisaWells: Coloured Petri Nets and CPN Tools for modelling and validation of concurrent systems, Int J Softw Tools Technol Transfer 9: [18] Hajira Bakkali, Abdellah Azmani, Abdelhadi Fennan: Identification of the parameters considered in the warehouse management and modeling its physical flow of goods, in proceeding of the 6th International Symposium LOGISTIQUA, May [19] Hajira Bakkali, Abdellah Azmani, Abdelhadi Fennan : Dynamic allocation of goods to storage areas, in proceeding of International Conference on Software Engineering, Databases and Expert Systems (SEDEXS'12), July2012. [20] Hajira Bakkali, Abdellah Azmani, Abdelhadi Fennan :. Modular Organization of warehouse, in proceeding of international conference on business intelligence and technology, May , IJARCSSE All Rights Reserved Page 871