International journal of computer integrated manufacturing , tập 23, số 4, 2010

International Journal of Computer Integrated Manufacturing Vol 23, No 4, April 2010, 297–307 Planning in concert: A logistics platform for production networks Jo´zsef Va´nczaa,b*, Pe´ter Egria and Da´vid Karnoka,b a Computer and Automation Research Institute, Hungarian Academy of Sciences, Hungary; bDepartment of Manufacturing Science and Technology, Budapest University of Technology and Economics, Hungary (Received 15 March 2009; final version received 18 January 2010) In this paper the authors consider supply planning in a production network as a distributed effort for matching future demand and supply by relying on asymmetric and partly uncertain information Even though decisions are made autonomously and locally, partners should act in a concerted way For approaching the two main conflicting goals of a high service level and low overall costs throughout the network, there is a need for a specific coordination media for managing the intentions and interactions of the partners Starting from the design principles, the authors describe a logistics platform that provides a complex service for communicating and evaluating all relevant information that may influence the operation of supply channels A particular interest is in coordinating a focal supply network that produces customised mass products The implementation technologies of the system are outlined together with the first lessons of the deployed application Keywords: production networks; planning; coordination; cooperation Introduction The global behaviour of production networks emerge from the interaction of local intentions and actions of the partners Supply planning is considered in a production network as a distributed effort for matching future demand and supply under continuously changing conditions Even though decisions are made locally in an autonomous manner, partners in a production network should act in a concerted way Given their business goals, market and the production environment that all evolve in time, partners have to reason over their future courses of actions by considering to some extent also the others’ situations and intentions The problem is a distributed planning problem: network members would like to exercise control over some future events by relying on all kind of information they have at hand Some of this information can be considered certain, such as that relating to products, production technologies, resource capabilities, or sales histories An essential part of the accessible information is, however, incomplete and uncertain, such as those items capturing forecasted demand, or expected resource and material availability Industry strategists and academics – while sketching alternative trajectories for technological and organisational developments – agree alike that resolving incompleteness and uncertainty by proper information exchange is a matter of survival for any *Corresponding author Email: vancza@sztaki.hu ISSN 0951-192X print/ISSN 1362-3052 online Ó 2010 Taylor & Francis DOI: 10.1080/09511921003630092 http://www.informaworld.com production network that is to operate under volatile market conditions However, uncertainty and the lack of information is only one side of the coin; different, though equally hard problems ensue from the plethora of information When preparing the ground for informed planning decisions, an enormous amount of behaviour related – i.e., dynamic – data must be handled, synchronised, cleared, filtered, aggregated and archived The decision complexity of planning processes can but grow with the extension of input data, which is in sharp conflict with the requirement of giving timely, almost instant responses to queries during interactive planning sessions Production informatics has well-proven approaches to handle uncertainty and structural complexity Aggregation merges detailed information on products, orders, demand forecasts, production processes, resource capacities, and time Various planning problems – such as production scheduling, production planning or master planning – are formulated by merging more and more details on longer and longer horizons (Pochet and Wolsey 2006) Solutions are generated in a hierarchical planning process where higher-level solutions provide constraints to lowerlevel problems Hence, according to their horizon and detail, plans can have strategic, tactical or operational dimensions At the same level, decomposition 298 J Va´ncza et al separates planning problems into easier-to-solve subproblems This is the case when, e.g., on the tactical level production planning is separated from supply or distribution planning The evolution of planning functions in production management resulted in a generic hierarchical planning matrix (Fleischmann and Meyr 2003, Stadtler 2005) Figure shows typical planning functions on the strategic (long-term), tactical (medium-term) and operational (short-term) level organised along the main flow of information and materials These functions are more or less common at each node of a production network, though, of course, manifest themselves in different forms and complexity Within an enterprise the coordination of segregated planning modules is a grave problem in itself (Fleischmann and Meyr 2003, McKay and Wiers 2003) However, this issue is even more critical in a production network where proper information exchange is the primary precondition of the collaboration between the partners (Maropoulos et al 2006) While the theoretical aspects of coordination and cooperation in production networks have been investigated extensively for a long time, these studies have paid due attention neither to the differentiation of planning functions, nor to the underlying causes Here, one can but remark that the surprisingly low number of deployed manufacturing applications of agent technologies – even on the ‘ideal’ field of supply network management (Monostori et al 2006) – is also a symptom of this lack of focus The authors are motivated in bridging the gap between the theory and practice of coordinated planning in production networks The particular background to this work is a national industry–academia R&D project that is aimed at improving the performance of a network that produces customised mass products (Va´ncza and Egri 2006, Monostori et al 2009) The network is woven around a focal manufacturer by suppliers of components and packaging materials The manufacturer produces in an average several million units per week from a mix of thousands of low-tech electronics products Some of the products are sold by retailers under their own labels what makes the market situation extremely uncertain and complex As Immelt (2006) remarks, ‘[If] you want to see something risky, try selling a lightbulb to a big-box retailer.’ Against all these uncertainties, exploiting economies of scale of mass production technology is a must In this paper, a so-called logistics platform is presented that was developed and deployed to facilitate cooperation of partners in this production network Departing from the design rationale the system is described, together with its main concepts and implementation technologies Finally, application experiences and generalisations of the underlying model are summarised Problem statement 2.1 Scope and objectives Production networks are considered as legally separated enterprises that are linked by material, information and financial flows They produce value in the form of products or services for the ultimate customer The market increasingly demands products that are customised, yet available with shorter delivery times Hence, the greatest pressures are time compression, customisation and cost reduction While any network as a whole is driven by the overall objectives to meet customer demand at the possible minimal production and logistic costs, the efficiency of operations and the economical use of material, energy and resources hinges on the local decisions of the autonomous partners These decisions are made necessarily by relying on asymmetric and uncertain information In general, the network is coordinated, if the service level of the overall network can be guaranteed at a predefined, reasonably high value, and total production and logistics costs along the supply channels are reduced to the minimum Figure Matrix of strategic, tactical and operational planning functions Whenever order lead times acceptable by the market are typically shorter than the actual production lead times, these main criteria are in conflict: owing to uncertain market conditions, inventories (of components, packaging materials, products) are inevitable to provide service at the required level On the other hand, low costs can be achieved only with larger lot International Journal of Computer Integrated Manufacturing sizes, which involve, again, higher product and component inventories as well as increased work-inprocess Though, if in the future demand unexpectedly ceases for a product then accumulated inventories become obsolete The key to coordinated planning is just to master such essential conflict situations time and again, in a robust and reliable way The authors’ goal is to develop such methods that are applicable also under practical conditions When doing so, one has to face issues related to the lack, uncertainty, inconsistency as well as the abundance of information that might affect the efficient operation of a production network 2.2 Related work Research of coordinated supply planning goes back to inventory management where the main questions are when to order and how much to order However, coordinating even a two-echelon supply chain via orders is not really possible, because optimal production quantities (and periods) depend also on factors – such as set-up and production costs, resource capacities – that are known to the supplier only Further on, a supplier that serves several customers at a time may exploit economies of scale by aggregating distinct demands By placing orders, the customer intrudes into the planning process of the supplier Typically, centralised channel coordination models have been developed where one of the partners had all the information available to make optimal decisions The centralised approach is though hardly realisable in practice owing to the legally separated supply chain partners Instead, upstream planning is the most widespread form of collaboration at the moment (Albrecht 2010) Since in reality no partner can control the chain, let alone a complete network, there is an increased interest in decentralised control, both in deterministic and stochastic settings (Cachon 2003) Actual investigations take mostly the approaches of theories of games and economy with asymmetric information In a real network there is always an information gap between the partners: the supplier is familiar with the production and setup cost for the components, while the end product manufacturer (in the customer’s role) can estimate better the finished goods demand This demand is distorted by the internal planning processes: normally, master plans are generated which are further refined into production plans and schedules In the meantime, lot sizing decisions are made and parallel component demands are aggregated As a result, the actual component demand forecast can hardly be related to the original finished good forecast (see Figure 2) Although in the age of electronic Figure 299 Transition of demand forecasts information exchange this gap could be bridged easily, partners not have incentives for sharing private business information On the practical side, there are various information sharing solutions that support order processing in production networks One example is the centralised SupplyOn platform for automotive and manufacturing industries, developed by several European automotive part suppliers (SupplyOn 2007) It facilitates information sharing between numerous planning tasks in the fields of engineering, sourcing, logistics and quality management It uses Electronic Data Interchange (EDI) as a basic format, but also supports WebEDI, which technically requires only Internet access A similar approach called myOpenFactory (Schuh et al 2008) proposes a centralised information sharing agency It is based on a standardised, industry–neutral data and process model, and provides commercial service with the implemented system The data format is designed to be open and flexible, therefore it is specified by XML schemas Just like in the previous case, this solution is also confined to order processing and monitoring 2.3 Roadmap to cooperation Nowadays, various paths to coordinated – and eventually, even to cooperative – planning in production networks are under extensive investigations Together with related researches (Li and Wang 2007), for such studies the authors suggest the following general roadmap: (1) Development of processes and establishment of media for sharing information about the actual and expected situations, as well as of the future intentions (i.e., plans) of autonomous network partners (2) At each level of aggregation, development of powerful local planners and schedulers which are able to solve the richer, extended models (3) Design and set up of incentive mechanisms that facilitate truthful information exchange, the sharing of risks and benefits, and cooperative behaviour, after all 300 J Va´ncza et al In earlier research (Va´ncza and Egri 2006, Va´ncza and Egri 2008, Monostori et al 2009), the authors addressed all the above issues; some results are summed up in Section The sequel to this works focused on the first issue, i.e., information exchange perspectives both of the customer and the supplier Special regard is needed for anticipating future situations where demand and supply mismatch The LP should keep the privacy of individual customer-supplier relationships Finally, the system should be prepared for an anytime, asynchronous and concurrent usage by a large number of planners representing all partners in a supply network Specification of the logistics platform (LP) 3.1 Design rationale In order to make both the conflicting objectives of coordinated planning manageable, it is suggested detaching them: while the service level should be tackled on the short-term (where information concerning demand is almost certain), cost-efficient production should be the main concern of medium-term planning The two levels should be coupled by proper inventory management Consequently, there is a need to share and fit demand and supply plans on several levels of aggregation, both in the medium and in the shortterm This matching should be performed time and again, on a rolling horizon, with some tolerance to eventual inconsistencies between aggregated and detailed plans However, as regards of making planning decisions, the system should be passive and leave all planning decisions to the actual (or future) local planning modules The LP anticipates and calls the attention of planners to conflicting situations (exceptions), but does not make decisions on behalf of them Hence, it provides only an interface both within and between enterprises, for making better informed and timely decisions 3.2 These functional requirements lead to the following main services of the system: User authorisation and the management of access rights and user profiles System administration services for filling in and maintaining the system’s master data General navigation that provides easy access to all information on both levels Automatic updating the system with dynamic data on a regular basis, according to a given protocol Checking the consistency of data, matching supply and demand plans both on the medium and the short-term, anticipating shortage situations and checking the fulfilment of inventory handling regulations, generating alerts and warnings While checking is automatic, alerts and warnings are to be processed by the users Measuring, reporting and archiving past performance of channels, users and partners Generating aggregate reports for specific purposes (such as capacity planning, transportation planning) Requirements towards the LP The functional requirements toward the logistics platform are as follows: The LP should link the planning functions of a manufacturer and its suppliers both at the levels of tactical and operational planning (i.e., production planning and scheduling, transportation planning) This sharing makes the situation symmetric, i.e., both partners along a channel have access to the same information, at the same time, in the same way The LP should be flexible in supporting a wide range of supply methods, from traditional purchase orders via vendor-managed inventories to coordinated supply It should monitor near-time component supply and give feedback information to both aggregation levels It should support the evaluation and analysis of the performance of supply channels, taking the The main requirement concerning the applied information and communication technologies is that the services of the LP can be accessible via the Internet Of course, the system should keep the privacy of each customer-supplier relationship and comply even with the most rigorous security requirements of the partners Finally, as far as possible, it should use the existing information resources and avoid storing and handling data in a redundant way System design Following the main design principles, the logistics platform is hierarchical and consists of two levels (see Figure 3) On the scheduling level, the supplier meets the exact, short-term component demand of the customer This demand is generated from the International Journal of Computer Integrated Manufacturing 301 Coordinated channels for managing supply without orders, giving more responsibility to the suppliers Figure Information flow through the LP actual daily production schedule of the customer in form of call-offs and can be satisfied only by direct, just-in-time delivery from an inventory This short-term demand of the customer is responded by the supplier’s actual delivery schedule Decisions are made on a daily basis, on a horizon of to weeks With this short look-ahead, demand uncertainty is hedged by safety stocks On the planning level, the supplier has to make preparations for satisfying the short-term demand of the customer Hence, the supplier receives medium-term demand forecasts of components from the customer, together with some information about the reliability of forecasts Managing inventories, deciding about the periods and optimal lot sizes of production is the supplier’s responsibility The demand forecast of the customer should be acknowledged by the supplier, either by simply accepting/rejecting it or by responding with an appropriate production plan On this level, decisions can be made in a longer (even weekly) cycle The LP is organised around the concept of the supply channel Each channel is defined by a customer, a supplier and a particular component that is delivered through the channel There could be multiple channels between the same partners, and the same component may arrive through parallel channels Each channel is assigned to at least one planner on both sides Planners can handle only channels which are under their authority There are two basic channel types: Purchase Order channels for capturing the traditional process, where supply is controlled by the orders of the customer For each channel, there is a complex inventory composed of the in-transit, consignment, as well as of the on-hand inventories at the supplier and the customer The LP keeps track of the inventory items on a daily basis However, as Figure shows, inventory is a passive element whose level is influenced by the local decisions of the supplier (who builds up the inventory) and the customer (who consumes the inventory) The LP collects, presents, analyses and aggregates all relevant information concerning the future, present and past of the channels Hence, each channel has various dynamic future-related information, such as forecasted demand, open orders, scheduled demand (generated by the customer), production plan and delivery schedule (generated by the supplier) Departing from the actual inventories, projected inventories are calculated both in the medium and short term, and inventory statuses are evaluated from both partners’ point of view The channels can be controlled by the customer according to particular inventory handling rules Minimum coverage rules guarantee that the production schedule of the customer can be executed even in face of uncertainties Hence, safety stock requirements are expressed in this way Maximal coverage rules warn the supplier from overfilling the customer’s inventory In general, amount of the on-hand inventory at the customer should always be between the minimal and the maximal required quantities Rules can be given either in terms of past average daily usage (backward coverage), fixed amounts, or future forecasted demand (forward coverage) For Purchase Order channels, the LP checks also whether orders really cover the scheduled demand The actual warnings and alerts are of distinct priorities; e.g., short term shortage situations must certainly be avoided, while overfilling the inventory in some distant period is far from being critical The LP supports the planners in sorting and filtering these exceptions according to type and priority; hence they can focus on the most critical cases first In order to initiate informed decisions, the LP presents statistical data about past usage of the components, their substituting materials and other details The past performance of channels is evaluated from both perspectives Since performance evaluation is essential for coordinated and cooperative planning, these measures are also discussed in some detail (see Section 6) Results can be aggregated and presented for any past period 302 J Va´ncza et al Summing up, the LP provides an interface between various planning functions of the customer and the supplier Decisions have to be made locally, but the various checks – whether production schedule of the customer is really served by a delivery schedule Figure Implementation technologies of the LP Figure Detailed scheduling level data of a channel of the supplier, or safety stocks are really sufficient – are executed within the LP Implementation and system integration The developed and deployed version of the LP follows the focal structure of the supply network where it is applied The LP is a Java Enterprise Edition (EE) web application built on the customer’s proprietary web application framework This framework manages the database connection pool, the request dispatching and corporate Single Sign On (SSO) authentication (see Figure 4) The application can be accessed from the customer’s intranet as well as from the external suppliers through the Virtual Private Network (VPN) of the customer Each user has an associated list of channels which he/she can see and modify This allows the privacy to be retained between different suppliers On a channel, every assigned user can read the same data, but users at the sides of the customer and supplier have different modification rights For example, the supplier’s user can modify the delivery schedule for the component while the customer’s user cannot On the other way around, the inventory checking rules of a channel can be set solely at the customer’s side (see Figure 5) International Journal of Computer Integrated Manufacturing The web application collects data from legacy systems either via direct Java Database Connectivity (JDBC) data access to the customer’s scheduling and planning systems, or XML-based (eXtensible Markup Language) data exchange with the suppliers’ and customer’s enterprise resource planning (ERP) systems The XML-based data exchange with the suppliers can be automatic by using Secure-SOAP (Simple Object Access Protocol) services built into the web application or direct XML file upload in which case the loggedin user’s account is used for the data validation context The data and information acquisition process works in three different ways: periodically scheduled, event-based and ad hoc Currently, a job is running every morning right after the customer’s scheduling system has generated its new production schedule (and, subsequently, its scheduled component demand) This job collects also the actual inventory data as well as the material planning and forecast data (from the customer’s planning system) During the day, the customer’s operators can change the initial schedule by hand and this change is propagated automatically to the LP In the general case, the web application’s administrator can trigger any time a complete resynchronisation of the LP with the related systems The web application’s report and input screens are designed for maximum data and access security by utilising: user roles, page level access check and object access checks; client- (JavaScript) and server-side form validation and data integrity checks; and anti-SQL injection and Cross Site Scripting (XSS) techniques by using only JDBC’s PreparedStatement and HTML-encoding of all user entered text before presentation Beyond guaranteeing security, another primary design goal was to make the access of the vast amount of data behind the LP fast and filterable The speed requirement was achieved by using in-memory object caching technology for critical data such as actual inventory levels Filtering is a key feature in the application, because each user can have hundreds of assigned channels, but space and time restrictions allow them to operate only on a small subset at a time Therefore each user can define his/her own set of filters which he/ she can use later on in any situation The filters which 303 are logical constructs of 5property – value set4 pairs belong to the personal profile of the users Note that filters are used also for collecting basic and generating aggregate values for a set of channels, such as for evaluating the overall performance of a supplier who is responsible for a number of channels Performance evaluation The traditional, order-based supply has standard performance evaluation techniques that measure the fulfilment of orders on the one hand, and the inventory or overall logistics costs on the other hand (Hon 2005) In cooperative supply however, the responsibilities are more complex because the decisions of any partner may propagate throughout the network Certain kinds of the uncertainties that emerge from an unpredictable market environment or from the system’s properties are hard to avoid (for a categorisation, see (Mula et al 2006)) However, in a production network the other members’ operation is also a source of uncertainty which is often charged by factors that are, in fact, unnecessary For example, when the supply planners of the customer are measured by the material shortage, then they tend to inflate the demand and forward too optimistic plans towards suppliers On the contrary, if the planners are rewarded for over-performing their plans, then they deliberately underestimate the demand and share too pessimistic plans with the suppliers The suppliers can be aware of the biases and may not accept the demand information without critique They rather tinker the forecasts based on their own past experiences, but this cannot completely restore the quality of the forecast This way the network as a whole operates far away from its main objectives: while the service level is corrupted (and is to be restored time and again by urgent orders at the price of increased system nervousness and additional costs), large, even obsolete inventories may also accumulate All in all, the selfish distortion of information necessarily decreases the performance of the network Hence, in the LP the performance of all partners is measured with a kind of deviation between their promised and actual activities 6.1 Measuring plan imprecision The customer’s main criterion is the deviation of the medium-term plans it shares with the supplier from its actual component usage Hence, plan imprecision is measured by the difference between the plan and its execution On a rolling horizon, plans are generated period by period with some look-ahead Since these plans are overlapping, measuring plan deviation is not evident 304 J Va´ncza et al One option is to use the standard measurement of forecast errors that are generally some variants of the following form: errori;n ¼ n X À Á aj fiÀj;i À ui j¼1 This formula measures the difference between the forecasted quantities and the realised demand in a particular week i, where the fi–j,i forecast for week i was generated on week i-j, ui is the realised demand of week i, aj is a discount factor and n is the length of the stability horizon, the basis of the measurement In a commonly used version of this formula the absolute value of fi–j,i – ui is taken An important property of this kind of error measurement is that it charges a double penalty if some demand is shifted from a week to another within the stability horizon However, in cases when demand is fulfilled from the inventory, such shifts are almost negligible whenever the total demand is not changed Therefore also a different type of measurement is proposed that regards the precision of a single forecast generated on a particular week The form of the plan deviation measurement is the following: deviationj;n ¼ n X 1À i¼1 n fj;jþi À ujþi Á In this case, discounting is not desirable, because it would differentiate between the forward and backward direction of the demand shift Figure presents a snapshot of a particular channel history Weeks are indexed backwards from the actual Figure week For instance, the column of manufacturing week -5 contains the forecasted demand for this week, generated on weeks -8, -7 and -6, respectively, while the row of week -5 shows the realised demand (1,108,530) Having calculated the errors for week -5, the maximal negative deviation (MND) was -19.5%, the maximal positive deviation (MPD) was 28.6%, the discounted forecast error (DFE) was 5.4%, while the discounted absolute forecast error (DAFE) was 23.2% Accordingly, the demand was overestimated, and the relatively large distance between the deviations shows that the stability of plans are low (which is the cause of the nervousness syndrome) The row of week -5 contains also the forecast for the next three weeks, made on week -5 Since the realised demands of the next three weeks are already known, one can compute the value of the plan deviation (PD) which is 74.8%, i.e., this forecast underestimated the demand When comparing the absolute errors with the absolute plan deviations one can see that errors are usually larger, because they contain double penalty for demand shifting, while plan deviation disregards them The choice between these two types of evaluation should be based on the production and purchase characteristics: if the demand shifts cannot cause shortage or necessary re-scheduling, then plan deviation is appropriate, otherwise the forecast error should be used 6.2 Measuring service level The supplier is responsible for avoiding the shortage on the customer’s side by feeding the factory with components, having respect to the short-term scheduled demand Primary criterion is that scheduled tasks Measuring weekly forecast error and plan deviation on a planning and stability horizon of weeks International Journal of Computer Integrated Manufacturing should not remain without their required components The authors have implemented the measurement of the supplier’s service level using the principle of forward coverage: the customer’s on-hand inventory together with the supplier’s scheduled delivery must always cover demand of the next few days Any situation where this coverage does not hold calls for immediate actions: either from the supplier (urgent delivery) or from the customer (re-scheduling), or from both This service level is measured with the CLIPA and CQPA (Component Line Item/Quantity Production Attainment) values: CLIPA ðnÞ tasks without components of the next n days ¼1À total number of tasks on the next n days CQPA is similar, but regards the number of items instead of tasks Providing input for the LP 7.1 Planning at the customer Static, master data about the channels are fed into the LP from the transactional ERP system of the consumer As for the dynamic data, the customer periodically runs a master planner that determines the output of end products for a longer horizon Dependent component demand forecasts are generated from this master plan by standard material requirements planning (MRP) methods (Hopp and Spearman 1996) Demand for the same components are summed up and feed into the LP as medium-term demand forecasts Purchase order channels are also filled in with orders generated by the supply planners of the customer In parallel to developing the LP, an automatic production scheduler was developed and deployed at the production facilities of the customer (Dro´tos et al 2009, Monostori et al 2009) This scheduler assigns in time each task to appropriate production resources so that it guarantees the satisfaction of hard technological, temporal and resource capacity constraints, while approaches optimisation objectives such as maximal resource utilisation and minimal backlog The scheduler concerns also the availability of material: in a pre-determined time window it takes material availability as hard constraint and postpones tasks that have no guaranteed supply Component supply is sufficient if the total of inventories together with the scheduled delivery matches the actual demand on each day of this time window Short-term scheduled demand for components is derived from this detailed production schedule As for an example, consider Figure 5: in the next few days no daily shortage is 305 projected, hence the production schedule is feasible, even thought with a longer, 10 days look-ahead material shortage can already be expected given the actual inventories, scheduled delivery and demand 7.2 Planning at the supplier For supporting the cost-oriented decisions of the supplier on the planning level, the authors have developed a portfolio of novel coordinated supply planning methods that take into account all the logistics costs and calculate also with the uncertainty of demand that may stop whenever market demand for the end-product(s) built of the component ceases for any reason In this situation called run-out the component inventory becomes obsolete The methods decide the time periods and quantities of component production The total cost to be minimised includes the setup, inventory holding and expected obsolete inventory costs Hence, decisions that coordinate a specific channel can be made on the basis of information coming partly from the customer (demand and its uncertainty) and partly from the supplier (setup, production and inventory holding costs) Various methods have been developed for different situations: typically, when plans should be made for the whole horizon (Egri and Va´ncza 2007), or when it is enough to plan for the close future (Va´ncza and Egri 2006) The coordinated supply planning methods have been extensively tested on industrial datasets and surpassed the performance of the actual methods (Egri 2008), although, it is the individual supplier’s decision whether they apply them or stick to their existing practice This is the case also with generating delivery schedules: while some suppliers rely on the built-in methods of the system that produce delivery schedule as a response to scheduled demand automatically, some apply more advanced distribution and transportation planning methods and optimise not only for minimal material shortage but for minimal transportation costs, too Experiences and extensions The logistics platform has been deployed at the focal manufacturer of a production network producing customised mass products and is now used on a daily basis both by the planners of this manufacturer (in the customer’s role) and of its strategic suppliers As for now, channels for almost 10000 components (including packaging materials) have been set up Since the current business processes are based on orders, only Purchase Order type channels could be defined The first main experience is that thanks to this application, the overall supply planning process 376 J.-L Hou et al locations All these operations have to utilise the inventory status of storage locations acquired from the previous step in order to rank the storage locations according to their used storage space In addition, the utilisation ratio of the total storage space can be used to derive the necessary information for storage location division The above three tasks are described in the following storage space (TSV) The mathematical expressions of the above operations are as follows: TS ¼ njt X snlt X nkt X SSi;j;k ; TSV ¼ i¼snft j¼1 k¼1 The main purpose of this step is to rank the storage locations in the re-allocated storage area based on their used storage space (SRi,j,k) This can provide the manager with the inventory status of the storage locations and the ranks of storage locations can be served as the basis for the subsequent storage location division The storage locations are ranked by ranking the storage space (SRi,j,k) of storage locations in the reallocated area in ascendance (i.e ranking the space utilisation ratio (SRti,j,k) in descendance) and each storage location is assigned a corresponding rank (RS(SRi,j,k)) A list consisting of the sequenced storage locations based on unused storage spaces can be represented as follows: RSRð1Þ < RSRð2Þ < Á Á Á Á Á Á < RSRðxÞ < Á Á Á Á Á Á < RSRðTSNÀ1Þ < RSRðTSNÞ Step (B2-2): Determine the division ratio In this step, an appropriate division ratio of storage locations can be determined The division ratio will be used in the subsequent task of storage location division The division ratio is determined based on the space utilisation of storage locations in the reallocated storage area (i.e the utilisation ratio of total storage space of the current phase (TSRt)) Using the division ratio, the sorted storage locations are divided into two segments with ratios of TSRt and 1-TSRt and the two storage location segments consist of SFN and SBN storage locations respectively (Figure 4) The utilisation ratio of total storage space is regarded as the division ratio and can be obtained on the basis of total storage space of storage locations (TS) and total used Figure Illustration of storage location division ratio SVi;j;k i¼snft j¼1 k¼1 Psnlt Pnjt Pnkt i¼snf j¼1 k¼1 SVi;j;k i¼snft j¼1 k¼1 SSi;j;k TSRt ¼ Psnlt t Pnjt Pnkt Step (B2-1): Rank the storage locations njt X snlt X nkt X  100% ¼ TSV  100% TS SFN ¼ bTSRT  TSNc; SBF ¼ TSN À SFN Step (B2-3): Divide storage locations By using the above division ratios (TSRt and 1-TSRt), storage location segments and their corresponding items can be identified The storage locations can be divided into the first segment (i.e the set (SF) of storage locations in the first part with the ratio TSRt) and the second segment (i.e the set (SB) of storage locations in the remaining part with the ratio (1TSRt)) On the other hand, the item set includes the items stored in the two segments (B(SF) and B(SB) respectively) and all the items stored in each segment (B , B ¼ B(SF) þ B(SB)) The relationships of storage location sets and item sets derived after storage location division are shown in Figure All storage locations are classified into two segments so that the storage locations with high utilisation (i.e those in the first segment) are supplemented with items from locations with low utilisation (i.e those in the second segment) That is, the unused storage spaces in the first segment are supplemented with the items stored in the second segment (B(SB)) As a result, after re-allocation, the total space utilisation ratio of the first segment is close to the total space utilisation ratio of the re-allocated storage area (i.e TSRt) 3.2.3 Step (B3): phase I of storage location re-allocation The purpose of this step is to re-allocate space utilisation of storage locations of the first segment 377 International Journal of Computer Integrated Manufacturing Figure Relationship of storage location sets and item sets close to total space utilisation ratio (TSRt) by means of storage location re-allocation so that items stored in the second segment can be reduced (i.e the space utilisation of the second segment is reduced) In this phase, storage location re-allocation involves re-allocation of items in the second segment The operation is based on the sequence of ranked storage locations and division segments of storage locations acquired from the previous two steps Storage locations in the first segment are the target spaces for item storage re-allocation and items in the second segment are selected to fill the target spaces The items with space requirements closest to the unused space of the target storage locations in the first segment are reallocated to the target storage locations In addition, for the first segment, the storage location with the least unused space (i.e RSR(1)) is first selected as the target storage location for re-allocation For the second segment, stored items can also be ranked based on their required space (BS(x,l); x ¼ SFN þ 1, SFN þ 2, , SFN þ SBN) by descending As the rank of sorted items are given (i.e R[BS(x,l)]; x ¼ SFN þ 1, SFN þ 2, .,SFN þ SBN), an item list can be formed according to the required spaces of all items in the second segment RBSð1Þ > RBSð2Þ > Á Á Á Á Á Á > RBSðrÞ > Á Á Á > RBSðnðxÞ Þ The element RBS(r) denotes the storage space required by the rth item Each item in this list is assigned a corresponding re-allocation coefficient RBA(r) The unused space of the target storage location RSR(1) to be re-allocated can be compared with the space require by each sorted item in the second segment Once the space required by the items stored in the second segment can fit in the unused storage space of the target storage location, the items can be re-allocated into the target storage location and the corresponding re-allocation coefficient of the items will be changed to show its re-allocation status The above item re-allocation procedure can be repeated until the spaces required by the remaining items in the second segment are larger than the unused space of the target location Repeat re-allocation of subsequent storage locations is made according to the above re-allocation method The essential for re-allocation of items stored in the second segment is that storage space required for the selected items in the second segment should be close to the unused space of the target storage locations to be re-allocated The above re-allocation method can be expressed as follows: IF (RSR(x)jx THEN RBA(r) ¼ x RSR0ðxÞ ¼ RSRðxÞ À SFN) ! RBS(r) and P BðSBÞÀB0 ðSBÞ ðRBSðrÞ Â RBAðrÞ Þ RBAðrÞ ELSE IF (RSR(x)jx SFN) RBS(r) THEN RBA(r) ¼ and RSR0ðxÞ ¼ RSRðxÞ Storage location re-allocation in the current phase includes two stages The first stage is to identify the target storage locations to be re-allocated in the first segment, and the second stage is to select the items to be re-allocated in the second segment The method for identifying the storage locations to be re-allocated and the items to be re-allocated has been described above Therefore, the workflow for re-allocation of the mth sorted storage location in the first segment in the current phase (namely, the storage location SPu,v,w with 378 J.-L Hou et al unused storage space RSR(m)) is described as follows First, the storage location set (SF) corresponding to the first segment in the storage area to be re-allocated is considered as the storage locations to be re-allocated and the item set stored in the location set is B(SF) The locations with smaller unused spaces are selected as the target locations first Without loss of generality, as the target location SPu,v,w with a unused storage space SR(m) is concerned, the item set stored in the target location is BK(SPu,v,w) (where BKðSPu;v;w Þ ¼ HowYall l fBPu;v;w;l g ¼ fBPu;v;w;1 [ BPu;v;w;2 [ Á Á Ág) ever, the items in the second segment to be re-allocated should be ranked by descending order, based on their required storage space (BR(x,l)) Items are assigned with corresponding ranks (R[BS(x,l)]), and an ordered list (i.e RBSð1Þ > RBSð2Þ > Á Á Á Á Á Á > RBSðrÞ > Á Á Á > RBSðnðxÞ Þ ) can be established Each sorted item RBP(r) is assigned a re-allocation coefficient RBA(r) Without loss of generality, the item RBP(r) can be the lth item stored in location SPi,j,k (i.e RBP(r) ¼ BPi,j,k,l; RBA(r) ¼ BAi,j,k,l) Based on the unused space of the target location RSR(m), appropriate items should be selected according to the above re-allocation procedure During the re-allocation, the selected items to be re-allocated are gathered in the variant set (i.e BC) The re-allocation coefficients corresponding to the items in this set are non-zero (i.e BC ¼ {RBP(r) ¼ BPi,j,k,l if RBA(r) 6¼ 0}) On the other hand, the re-allocation coefficients corresponding to the unselected items in the second segment are zero (namely, RBA(r) ¼ BAi,j,k,l ¼ 0) Reallocation of the item set in the current phase is shown in Figure Concerning the mth ordered storage location in the first segment, its corresponding variant item set is Figure The item sets before and after phase I re-allocation BC(m) (i.e BC(m) ¼ {RBP(r); if RBA(r) ¼ m}) and reallocation coefficients of the items in this set are identical (i.e RBA(r) ¼ m) The relationship of the variant sets can be represented as follows: BCðxÞ ¼ fRBPðrÞ ; if RBAðrÞ ¼ xg BC ¼ fRBPðrÞ ; if RBAðrÞ 6¼ 0g ¼ Y fBCðxÞ g; x ¼ 1; 2; ; SFN all x ¼ fBCð1Þ [ BCð2Þ [ Á Á Á [ BCðSFNÞ g In the storage location re-allocation of this phase, taking the mth ordered location in the first segment as an example, once the variant item set selected from the second segment (i.e BC(m)) is re-allocated into the target location in the first segment, the storage locations of the items in the set are changed into the re-allocated locations (SPu,v,w) from the original ones (SPi,j,k) That is, the storage locations of the items in the variant set are changed (BPi,j,k,l ! BPi0 ,j0 ,k0 ,l0 where i0 ¼ u, j0 ¼ v, k0 ¼ w ) and item sets corresponding to the first and second segments are changed into B0 (SF) (i.e B0 (SF) ¼ B(SF) þ BC(m) ) and B0 (SB) (i.e B0 (SB) ¼ B(SF)–BC(m)) respectively The storage location sets in the first and second segments (SF and SB) and all items stored (B .) remain unchanged However, the inventory status of storage locations in the first and second segments would be changed after reallocation The number of items in the first segment will be increased (i.e BK0 (SPu,v,w) ¼ {BPu,v,w,l} þ BC(m) ¼ {BPi0 ,j0 ,k0 ,l0 }) and the number of items in the second segment will be reduced (i.e BK0 (SPu,v,w) ¼ International Journal of Computer Integrated Manufacturing {BPu,v,w,l}–BC(m)) Inventory status of storage locations, including the used storage space (SV0 i,j,k), space utilisation (SRt0 i,j,k) and unused space (SR0 i,j,k) of reallocated storage locations, is also changed owing to the storage space used by the re-allocated items The mathematical expressions related to the change information resulting from storage location re-allocation are as follows: B0 ðSFÞ ¼ BðSFÞ þ BC; B0 ðSBÞ ¼ BðSFÞ À BC BSi0 ;j0 ;k0 ;l0 ¼ P BSi;j;k;l if i0 ¼ i; j0 ¼ j; k0 ¼ k; l0 ¼ l > > < ðBSi;j;k;l  BAi;j;k;l Þ BSi0 ;j0 ;k0 ;l0 ¼ BðSBÞÀB ðSBÞ ; BAi;j;k;l > > : 0 if BAi;j;k;l 6¼ 0; i 6¼ i; j 6¼ j; k 6¼ k; nli0 ;j0 ;k0 SV0i;j;k ¼ X BSi0 ;j0 ;k0 ;l0 ; SRt0i;j;k ¼ l0 ¼1 SV0i;j;k  100% SSi;j;k nli0 ;j0 ;k0 SR0i;j;k ¼ SSi;j;k À SV0i;j;k ¼ SSi;j;k À X BSi0 ;j0 ;k0 ;l0 l0 ¼1 At this stage, after re-allocation is carried out for the storage location with the smallest unused space RSR(1), the following locations in the sorted location list (i.e RSR(2), RSR(3), ) of the first segment are then selected for location re-allocation On the other hand, selection of storage locations in the second segment has been described above The un-reallocated items in the second segment are selected according to the sorted sequence until all storage locations in the first segment have been re-allocated Finally, the change information resulting from re-allocation of storage locations in the first segment can be tabulated in the re-allocation suggestion table of phase I in order to facilitate subsequent re-allocation suggestions Besides, this information should be used to re-order the ordered storage locations in the first and second segments based on the remaining space (RSR0 i,j,k) and managers will be able to realise the status of storage locations after re-allocation in this phase After storage locations are re-allocated in phase I, they are re-ordered according to their remaining storage spaces: RSR0ð1Þ < RSR0ð2Þ < Á Á Á Á Á Á < RSR0ðSFNÞ < RSR0ðSFNþ1Þ < Á Á Á Á Á Á < RSR0ðSFNþSBNÀ1Þ < RSR0ðSFNþSBNÞ 379 location of new items due to the non-empty storage locations (i.e the storage locations with stored items) That is, the excessive non-empty storage locations may make it difficult for the warehouse managers to determine the storage locations of new items Thus, main purpose of phase II is to increase the number of storage locations with utilisation ratio of zero (i.e to decrease the number of storage locations with non-zero utilisation ratio) As a result, the flexibility for the warehouse managers to determine the storage location of new items can be enhanced and the difficulty that the warehouse managers determine the storage locations of new items can be significantly reduced In this phase, storage locations in the second segment are re-allocated for the purpose of centralising and re-distributing items un-re-allocated in the second segment in phase I to the other locations in the second segment That is, the items in storage locations of the second segment have to be centralised and thus the number of storage locations with zero utilisation can be maximised (namely, the number of storage locations that are fully empty is maximised) Before re-allocation in this phase, all un-reallocated items in the second segment after phase I are gathered in a item group (B0 (SB)) and will be selected for subsequent redistribution Moreover, the storage locations in the second segment shall be ordered according to their unused storage spaces (by descending order) It will also be taken as the basis for selection of the locations for subsequent re-allocation The storage locations with larger storage spaces in the second segment should be selected first (i.e the re-allocation begins with the storage location with the largest unused space in the second segment) The storage locations in the second segment can be ordered according to their unused storage spaces as follows: SS0ð1Þ < SS0ð2Þ < Á Á Á Á Á Á < SS0ðxÞ < Á Á Á Á Á Á < SS0ðSBNÀ1Þ < SS0ðSBNÞ Re-distribution of items is similar to the selection of items in the second segment indicated in phase I First, the un-reallocated items stored in the second segment can be ranked according to their required storage space (BS0 (x,l)); that is, items are assigned ranks (namely R[BS0 (x,l)]; x ¼ 1,2, .,SBN) after ordering An ordered list can be derived as follows: RBS0ð1Þ > RBS0ð2Þ > Á Á Á Á Á Á > RBS0ðrÞ > Á Á Á > RBS0ðnðxÞ Þ 3.2.4 Step (B4): phase II of storage location re-allocation As new items are to be stored in the warehouse, the warehouse managers cannot easily determine the storage The element RBS0 (r) denotes the storage space required by the rth item in the ordered sequence which might originally be stored in the storage location SP0 i,j,k 380 J.-L Hou et al (SP0 i,j,k ¼ SPSi,j,k) Items in the ordered list are also assigned corresponding re-allocation coefficients: RBA0 (r) Spaces of the storage locations to be reallocated (SS0 i,j,k ¼ SSi,j,k) are compared with the unreallocated items stored in the second segment Once the spaces required by the items stored can be met by the unused space of the storage locations to be reallocated, the items can be assigned to the locations and re-allocation coefficients of the corresponding items can be changed to denote their status The above procedure for item selection and re-allocation can be repeated until the unused space of the storage locations to be re-allocated is less than the storage space required by the un-reallocated items Moreover, the above procedure can be repeated subsequently for the storage locations to be re-allocated The principle for selection of the un-reallocated items in the second segment is that storage spaces required by the selected items are close to the unused space of the storage location to be re-allocated The above re-allocation concepts can be expressed as follows: IF (SS0 (x)jx SBN) ! RBS0 (r) THEN RBA0 (r) ¼ x and P RSR00 ðxÞ ¼ SS0ðxÞ À ðRBS0ðrÞ Â RBA0ðrÞ Þ RBA0ðrÞ B0 ðSBÞÀB00 ðSBÞ taken as an example (i.e the storage location SPe,f,g in the second segment that has been ordered based on storage space via phase I) The set of the remaining items from the storage locations re-allocated in phase I is: B0 (SPe,f,g) The set of all un-reallocated items in the second segment are gathered and re-distributed to the storage locations in the second segment Accordingly, as the storage locations in the second segment are emptied ready to be distributed with items, the item set stored in the target storage locations is temporarily an empty one (B0 (SPe,f,g) ¼ f) Each item in the un-reallocated item set (i.e B0 (SB)) of the second segment can be re-distributed on the basis of the spaces of storage locations to be reallocated (SS0 i,j,k ¼ SSi,j,k) and the required storage space (BS0 i,j,k,l) and re-allocation coefficients (BA0 i,j,k,l) of the item The selected items to be re-allocated are collected in the re-distributed item set (i.e BD) and all the re-allocation coefficients corresponding to these items to be re-allocated are non-zero (i.e BD ¼ {BP0 i,j,k,ljBP0 i,j,k,l B0 (SB) if BA0 i,j,k,l 6¼ 0}) On the other hand, the re-allocation coefficients corresponding to those items that are not re-distributed are assigned zeros (i.e BA0 i,j,k,l ¼ 0) The items to be re-allocated to the nth storage location in the second segment are: BD(n) (namely BD(n) ¼ {BP0 i,j,k,ljBP0 i,j,k,l B0 (SB); if RBA0 i,j,k,l ¼ n}) The set of items to be re-distributed is represented as follows: ELSE IF (SS0 (x)jx SBN)5RBS0 (r) THEN RBA0 (r) ¼ and RSR00 (x) ¼ RSR0 (x) BDðyÞ ¼ fBP0i;j;k;l jBP0i;j;k;l B0 ðSBÞ; if RBA0i;j;k;l ¼ yg BD ¼ fBP0i;j;k;l BP0i;j;k;l B0 ðSBÞ; if RBA0i;j;k;l 6¼ 0g ¼ Y fBDðyÞ g; y ¼ 1; 2; ; SBN all y Storage location re-allocation in the current phase includes two parts The first part involves selection of storage locations to be re-allocated and then the unreallocated items of the second segment in phase I are redistributed The selection method of the storage locations to be re-allocated and the items to be reallocated were described above The complete procedure for the storage location re-allocation in this phase is described as follows First, re-allocation of this phase begins with selection of the storage location set (SB) in the second segment with the largest space (SS0 (1) ¼ SS(1)) Second, the un-reallocated items in the second segment after the reallocation in phase I can be grouped as an item set (B0 (SB)), and these items can be allocated to the corresponding locations to be re-allocated based on the storage spaces of the locations In order to describe the storage location re-allocation procedure in the phase, the nth location in the second segment that has been ordered based on their space can be ¼ fBDð1Þ [ BDð2Þ [ Á Á Á [ BDðnÞ g In the re-allocation of the phase, change of the items in the storage locations to be re-allocated results in the change of storage locations of the items to be re-distributed (namely BPi,j,k,l ! BPi00 ,j00 k00 ,l00 ) On the other hand, the storage location set (SF) in the re-allocated first segment, the storage location set in the second segment (SB) and the corresponding item set (i.e B00 (SF) ¼ B0 (SF); B00 (SB) ¼ B0 (SB)) and all inventory items (B .) remain unchanged In addition, re-distribution of all of the items in the storage locations in the second segment changes the unused space of locations in the second segment (BSi00 ,j00 ,k00 l00 ) and changes the inventory information of locations (e.g., the used space of re-allocated storage locations (SV00 i,j,k), utilisation of re-allocated storage (SRt00 i,j,k) and unused space of re-allocated storage locations (SR00 i,j,k)) The mathematic expressions of the International Journal of Computer Integrated Manufacturing changed information through this phase are as follows: P BSi00 ;j00 ;k00 ;l00 ¼ if  BP0i;j;k;l B0 ðSBÞÀB00 ðSBÞ ðBS0i;j;k;l  BA0i;j;k;l Þ BA0i;j;k;l 00 00 ni00 ;j00 ;k00 SV00 i;j;k ¼ X BSi00 ;j00 ;k00 ;l00 ; SRt00 i;j;k ¼ l00 ¼1 SV00 i;j;k  100% SSi;j;k ni00 ;j00 ;k00 SR00 i;j;k ¼ SSi;j;k À SV00 i;j;k ¼ SSi;j;k À X BSi00 ;j00 ;k00 ;l00 l00 ¼1 In brief, the re-allocation in the phase can be summarised as follows After the storage location with the largest unused storage space (SS0 (1)) in the second segment is re-distributed with items, the following storage location (SS0 (2), SS0 (3), .) shall be re-allocated if undistributed items exist Finally, the changed information resulting from re-allocation of storage locations in the second segment can be tabulated in the re-allocation suggestion table of phase II to facilitate subsequent implementation of reallocation suggestions 3.2.5 Step (B5): Integration of re-allocation suggestions derived in the two phases As the storage location re-allocation of the two phases is completed, the storage location re-allocation suggestions corresponding to the two phases can be integrated The storage locations of all items before and after the re-allocation should be compared to derive the revised storage locations in the re-allocation suggestion table (Table 1) This information can be taken as the basis to move the items to be re-allocated in the implementation stage 3.3 Stage (C): Implementation of storage location re-allocation The procedure is actually to re-allocate storage locations of items Through the above procedure, the Table 1 n tabulated storage location re-allocation suggestions are taken as the basis for implementation of storage location re-allocation on the shop floor ;  0; i ¼ ¼ i; j 6¼ j; k ¼ k BP0i;j;k;l B00 ðSBÞ 00 381 Tabulated re-allocation suggestions Variant item Original location Suggested location BPu,v,w,x BPi,j,k,l SPu,v,w SPi,j,k SPu0 ,v0 ,w0 SPi00 ,j00 ,k00 System framework plan and functions According to the storage location re-allocation method proposed in the previous section, this study used Visual Basic 6.0 and Microsoft SQL Server 2000 to develop a storage location management system in order to assist management and re-allocation of storage locations in a warehouse In order to meet the different requirements for storage location management, the suggestions for corresponding operations are presented via tabulated and visualised displays based on the existing storage locations and inventory status of items The user-friendly interface can assist warehouse managers of logistics centres efficiently and accurately to make decisions The system operation framework and system functions are described in the following 4.1 System operation framework The operation framework of the storage management system developed in the study is depicted in Figure Users can use the Storage Location Maintenance Module to acquire information about storage locations and inventories (e.g User in Figure 7) and obtain the information concerning available storage locations that meet the storage requirements In addition, the system can also provide the above information via visual display (e.g User in Figure 7) that can be used as the reference for selection of storage locations for new items Users can also set the storage area for storage location re-allocation, assign the storage location division ratio and re-allocate storage locations via Storage Location Re-allocation Module Using this module, managers can acquire the inventory status of storage locations in the reallocated area, appropriate storage location divisions, and storage location re-allocation suggestions (e.g User in Figure 7) However, in order to identify variables in stored items, most logistics centres divide storage areas based on their characteristics (such as shelf types and supplier characteristics) to facilitate storage location management and reduce complexity of storage location re-allocation The storage management system developed in the study can be divided into four areas based on shelf category (including heavy shelf area, medium shelf area, light shelf area and old shelf area) to plan re-allocation of storage locations 382 Figure J.-L Hou et al Operation framework of the storage location management system first and the second segments should be reallocated subsequently based upon the division ratio of storage locations The tabulated and visualised re-allocation results of the two phases are then integrated and can serve as references for managers in actual storage location re-allocation 4.2 System function descriptions The storage management system developed in this study includes two modules: a storage location maintenance module (Figure 8) and a storage location re-allocation module (Figure 9) Functions of the two modules are described as follows (1) Storage location maintenance module As new items are to be stored in the warehouse, inventory status and the relative locations of items in the warehouse should be considered The storage location maintenance module can be divided into two sub-functions including item-based inventory information inquiry and location-based inventory information inquiry The former can be used to reveal information related to items and the latter can reveal inventory status and related information concerning storage locations (2) Storage location re-allocation module The storage location re-allocation module includes the main functions of re-allocation range setting, storage information inquiry, storage location division and storage location re-allocation All the functions are interrelated First, re-allocation range of storage locations should be assigned, and the related inventory information should be derived to trigger the subsequent operations of storage location division and storage re-allocation Second, a proper division ratio of storage locations in the re-allocation range has to be assigned for subsequent storage location reallocation Finally, storage locations in the System verification and evaluation In order to verify the feasibility and performance of the proposed methodology and system, the warehouse of the largest DC of the printing industry in Taiwan is taken as a demonstration case in this study In the following, the system verification and evaluation are divided into descriptions of the verification method, definitions of evaluation indices and analysis of verification results 5.1 Verification method descriptions Before system verification, the verification data collected in the demonstration case (including basic data about books, storage locations and storage shelves) were imported into the database of the back-end system to serve as the basis for subsequent system verification The data used for verification include the inventory data of 6,410 storage locations with 26,059 SKUs of the demonstration case The verification method is described as follows A group of storage locations to be re-allocated were first generated randomly by the system The inventory information corresponding to the storage locations to be re-allocated was also extracted After that, the storage locations were divided into two segments International Journal of Computer Integrated Manufacturing Figure 383 Storage location maintenance module according to the storage division ratio suggested by the system and the expected space utilisation ratio of the storage locations in the first segment (namely 100%) The planning time for storage re-allocation, the number of empty storage locations before and after storage re-allocation, and space utilisation of the storage locations in the first segment before and after re-allocation were derived The above system testing procedure was performed 30 times and the 30 testing records were used to evaluate improvement of the planning time, increment of empty storage locations and increment of space utilisation of storage locations in the first segment In addition, sensitivity analysis was also carried out to determine the influences of several factors (such as re-allocation ranges, expected space utilisation and reallocated storage areas) on the planning time, increment of empty storage locations and space utilisation of locations 5.2 Definitions of performance indices In order to realise the performance of the proposed storage management system in the storage location management (e.g., addition and re-allocation of storage locations), improvement of the storage management tasks conducted by the proposed system is evaluated In this paper, the relative frequency is used to analyse the results derived by the system Accordingly, definitions of relevant parameters used in the performance indices (e.g., improvement of planning time, conformance of reasoned results and increment of empty storage locations) used in this study are described as follows: (1) Improvement of average planning time Improvement of average planning time (RAIi) indicates how the planning time is reduced as the proposed system is used to accomplish 384 J.-L Hou et al Figure Storage location re-allocation module storage location re-allocation (TSi) and can be represented as follows: Improvement of i RAIi ¼ THÀTS TH average planning time: (2) Conformance of reasoned results Conformance of the reasoned results (RAi) can be used to express how the space utilisation of the storage locations in the first segment conforms to the expected space utilisation assigned by the domain experts It can be expressed as follows: RUSi Conformance of reasoned results: RAi ¼ RUE i (3) Increment of empty storage locations Increment of empty storage locations (REi) denotes the increment of number of empty storage locations after storage location reallocation It can be represented as follows: Increment of i ÀNEOi REi ¼ NESNEO i empty storage locations: 5.3 Analysis of verification results In this study, results of storage location re-allocation for 30 re-allocation ranges generated randomly by the system and the performance improvement are summarised [...]... factory Computers in Industry, 5 0, 5–14 Monostori, L ., Va´ncza, J ., and Kumara, S ., 2006 Agentbased systems for manufacturing 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