A hierarchical approach to warehouse design

International Journal of Production Research ISSN: 0020-7543 (Print) 1366-588X (Online) Journal homepage: http://www.tandfonline.com/loi/tprs20 A hierarchical approach to warehouse design Timothy Sprock, Anike Murrenhoff & Leon F. McGinnis To cite this article: Timothy Sprock, Anike Murrenhoff & Leon F. McGinnis (2016): A hierarchical approach to warehouse design, International Journal of Production Research, DOI: 10.1080/00207543.2016.1241447 To link to this article: http://dx.doi.org/10.1080/00207543.2016.1241447 Published online: 19 Oct 2016. Submit your article to this journal Article views: 21 View related articles View Crossmark data Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalInformation?journalCode=tprs20 Download by: [La Trobe University] Date: 27 October 2016, At: 04:22 International Journal of Production Research, 2016 http://dx.doi.org/10.1080/00207543.2016.1241447 A hierarchical approach to warehouse design Timothy Sprock∗ , Anike Murrenhoff and Leon F. McGinnis School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, USA (Received 2 December 2015; accepted 16 September 2016) The design of large complex systems, such as warehouses, requires multiple experts and analyses as well as methods to organise and integrate their knowledge. While there are many models for optimising individual aspects of warehouses, there is not, today, a comprehensive design methodology that incorporates and supports all of the design decisions and provides a method to effectively integrate the solutions to these subproblems into a complete warehouse system specification. In this research, we propose a hierarchical design decision support methodology based on decomposing the design problem into a set of subproblems and using a formal model of the system to integrate the solutions to these subproblems. The methodology enables a thorough search of the design space and the identification of many candidate designs for consideration by the design decision maker. The hierarchical design methodology is demonstrated with an example of designing a forward pick area. Keywords: warehouse design; multi-disciplinary optimisation; formal domain modelling; SysML; model-based system engineering 1. Introduction Modern distribution warehouses, such as those serving grocery chains like Kroger or Ahold, or e-tailers like Amazon, are large complex discrete event logistics systems (DELS) whose design requires decisions spanning multiple disciplines and having significant consequences for investment and operating costs. The emergence of new technologies, like Symbotics and Kiva, is a testament to the urgency of making these systems faster, cheaper, more reliable and more robust. The scale, scope and risk of such warehouse design problems calls for an integrated engineering design methodology and supporting computational tools. This level of integration does not yet exist, although nearly 60 years of active research into many aspects of warehousing by a global community of scholars and practitioners has produced a wealth of theory and models of particular aspects of warehouses that is available for potential integration. What is missing is a way to exploit the extant literature on warehouse analysis, a comprehensive design framework that is: (1) based on a complete set of design questions and corresponding analysis subproblems that must be solved during the design process; and (2) provides a modelling platform to integrate all of these individual aspects – both analytically and computationally – into a repeatable design process. Contemporary efforts to develop a design framework are hampered by the lack of a formal common language for describing the warehouse being designed and the inability to integrate existing analytical models. Today, engineering design of other large-scale complex systems, like microprocessors or jumbo jets, is rooted in two methodologies: (1) hierarchical decomposition, which structures the design space so that tractable subproblems are identified, and (2) multi-disciplinary design optimisation (MDO), which formally specifies the interfaces between subproblems so that the design space can be searched and candidates evaluated effectively. Adapting these methods to warehouse design would require a formal system model, integrating all relevant aspects of the warehouse specification, an approach for decomposing the design problem into tractable subproblems, precise specification of the interfaces between subproblems and a rigorous and repeatable way to search the design space. The research reported here proposes such an adaptation and illustrates its key elements through a simple use case. The main contribution is to show that there is, in fact, a way forward that can lead to the desired goal of integrated engineering methods and tools for designing large-scale complex distribution warehouses. The paper is organised as follows: Section 2 provides background on the methodologies being applied in this paper, including hierarchical design (Section 2.1), formal domain modelling (Section 2.2) and warehouse design methodologies (Section 2.3). Section 3 describes the hierarchical warehouse design methodology developed in this research including a formal warehouse reference model and the proposed ∗ Corresponding author. Email: tsprock3@gatech.edu © 2016 Informa UK Limited, trading as Taylor & Francis Group 2 T. Sprock et al. design hierarchy. This methodology is illustrated in Section 4 by presenting a computational use case focused on designing a single warehouse subsystem, the forward pick area, where all key elements of the methodology are exercised. 2. Formal warehouse design methodologies 2.1 Hierarchical design methodologies System design is naturally hierarchical – decisions about overall system architecture identify subsystems and their interfaces, subsystems may be further decomposed, and finally, specific detailed decisions are made regarding concrete realisations of system components and their interconnections. The hierarchical approach allows questions of ‘what’ (e.g. to use forward picking) to be answered differently than questions of ‘how’ (e.g. the particular storage technology). While there may be analysis models and methods that are appropriate for supporting individual subsystem design decisions, it is rarely the case that the same models and analyses apply across multiple interacting subsystems. For example, the analysis to determine the configuration of a storage system that minimises floor space is very different from the analysis that estimates the average labour hours per pick, which clearly depends upon the pick method as well as the storage system configuration. Thus, the decomposition can align with and take advantage of domain specialties (Gray, Karmarkar, and Seidmann 1992; Subrahmanyam, Pekny, and Reklaitis 1994). MDO grew out of structural engineering as a methodology based on hierarchical decomposition, hierarchical optimisation methods, approximation techniques and tools to facilitate efficient organisation of models and data (Sobieszczanski-Sobieski and Haftka 1997). While this methodology is used extensively in other engineering disciplines where model-based design is more routine, its applicability and effectiveness in the warehouse domain has not, until now, been demonstrated. Applying these methods requires effectively structuring the design space, i.e. partitioning the design tasks and providing a detailed functional specification and interface to the resulting subcomponents. For each component in the decomposed design problem, domain specialists can select appropriate approximations and tailor search heuristics to the specific application as necessary; e.g. layout and routing control design decisions each have a dedicated and specialised literature to support efficient decisionmaking. While the decomposition process supports domain-specific knowledge and strategies, it often requires the use of surrogate objectives, or approximate models of one subsystem to reflect its influence on design decisions in other subsystems. A given surrogate model can be refined as its related subsystem design is elaborated. 2.2 Formal domain modelling methodology Formal system models provide an agreed-upon and explicit definition of the actual system and subsystems of interest, thus supporting interoperability and consistency between the subproblems within a warehouse design hierarchy. A formal model of a domain requires an explicit language, i.e. a domain-specific language (DSL), for describing components of a system within that domain and rules for assembling those language components into meaningful and accurate models of the system. Object-oriented modelling (OOM) is a natural way to model a complex system because it builds upon the domain expert’s ability to view a system as collections of related objects, including attributes of those objects, subcomponents of those objects, groupings of similar objects and associations between objects (Coad and Yourdon 1991). OMG’s SysML ™ (OMG 2012), an extension of the UML, provides an OOM environment that is used in many system engineering design methods, such as Model-Based Systems Engineering (MBSE) (Estefan 2007) or Object-Oriented Systems Engineering Method (Friedenthal, Moore, and Steiner 2014). SysML is not the only applicable modelling language, but it is used widely in other engineering disciplines and it provides the modelling capabilities needed to support warehouse design. Prior research has established that an appropriate DSL can support automatically generating analysis models from a formal system model. The process requires first creating a DSL, then describing an instance of the system of interest using the DSL, and finally using model-to-model transformation methods to transform a description of a system model specified using the DSL into a target analysis language. The approach has been demonstrated in a variety of logistics settings for discrete event simulation (see, e.g. Huang, Ramamurthy, and McGinnis 2007; Schönherr and Rose 2009; Thiers and McGinnis 2011; Batarseh and McGinnis 2012; Sprock and McGinnis 2014; Batarseh, Huang, and McGinnis 2015). Formal domain modelling approaches, such as constructing object-oriented reference architectures, have been demonstrated to provide a flexible and reusable framework for capturing system models in the manufacturing and supply chain domains (see e.g. Wysk and Smith 1995; Smith and Becker 1997; Narayanan et al. 1998; Van Brussel et al. 1998; Biswas and Narahari 2004; Kim and Rogers 2005; McLean et al. 2005; Lemaignan et al. 2006). International Journal of Production Research 3 2.3 Prior research on warehouse design methodologies There is an extensive literature addressing the many subproblems related to designing and optimising a warehouse, see, e.g. Heragu et al. (2005), De Koster, Le-Duc, and Roodbergen (2007), Gu, Goetschalckx, and McGinnis (2010); and Hassan (2010), for recent treatments of the design problem. However, the literature addressing integrated design for the entire system is more limited. Closely related to the approach proposed in this paper, Gray, Karmarkar, and Seidmann (1992) propose a multi-level hierarchical approach that uses simple calculations to evaluate the trade-offs and prune the design space to a few superior alternatives. Rouwenhorst et al. (2000) organise the design decisions into strategic, tactical and operational decisions related to the processes, resources and organisation (control) of the warehouse although a computational implementation is not discussed. Baker and Canessa (2009) propose a high-level methodology for the design process itself, similar to systems engineering approaches for designing complex systems. Dallari, Marchet, and Melacini (2009) construct a taxonomy of order picking technologies and incorporate it with an empirical approach, similar to Apple, Meller, and White (2010), for selecting and configuring order picking technologies appropriate to the context, e.g. meeting required throughput rates. Chen et al. (2010) develop a methodology based on data envelopment analysis to analyse several interrelated problems in order picking systems. Typically, research on warehouse design relies on an implicit model of the warehouse being designed and there is limited integration with computational tools that provide analytical support throughout the design process. McGinnis (2010) addresses this opportunity and proposes a foundation for applying model-based systems engineering methods to warehouse design processes. To bridge the gap between process-oriented research on warehouse design and the mathematically oriented approaches, McGinnis (2012) proposes an object-oriented and axiomatic warehouse design methodology. McGinnis, Schmidt, and Spee (2014) discuss recent developments in applying model-based systems engineering methodologies. 3. Hierarchical warehouse design The proposed approach to adapting hierarchical decomposition and MDO employs formal domain modelling to construct a reference architecture and conforming instances of system models in a way that organises the design tasks and allows supporting analysis models to be generated from candidate system models. In this approach, relevant analysis models from the extant warehouse design literature can be integrated within the reference architecture to provide candidate decompositions of the design space as well as appropriate analysis methods and surrogate models to support hierarchical design. The hierarchical warehouse design methodology proposed here builds upon the design process proposed in McGinnis (2012), which most closely aligns with mainstream systems engineering design methodologies (Estefan 2007). This design process starts by defining the context, the INFlows of SKUs, and OUTFlows of orders. These flows are the basis for the functional requirements analysis stage, which constructs a logical architecture for the transformation of INFlows into OUTFlows. This logical architecture, captured as a functional requirements network (FRN), is then used in the functional and embodiment design stages that elaborate and specify the details of the system’s products, processes, resources and facility as well as its control. The rest of this section provides the details on the hierarchical design methodology that is the contribution of this work. First, Section 3.1, presents an abstract meta-hierarchy that decomposes the design decisions into structural, behavioural and control design decisions. Then Section 3.2 discusses the reference architecture that is central to constructing candidate system models throughout the design process. Finally, Section 3.3 discusses how the meta-hierarchy and the reference architecture are integrated with the existing design process outlined in McGinnis (2012). 3.1 Meta-hierarchy: structure, behaviour and control An effective hierarchical design method requires intelligently structuring the design space which can be achieved by effectively partitioning and sequencing the design tasks and decisions. The meta-hierarchy proposed here is derived from a theory of DELS specification, see chapters 3 and 4 of Thiers (2014) and chapters 2 and 3 of Sprock (2015). DELS, is a class of dynamic systems that creates value by transforming discrete flows through operations performed by a network of interconnected subsystems (Mönch et al. 2011). The DELS domain includes systems such as supply chains, factories, transportation networks, warehouses and health care delivery systems, among many others. The theory of DELS specification provides a layered domain-specific language (DSL) for DELS for modelling, analysing and designing the structure, behaviour and control of the system of interest (Figure 1). The Structure Layer models the logical or organisational networks, flow networks and process networks that are the foundation for many system and analysis models in the logistics domain. The structural layer is an abstraction of the behaviour of the system which is useful for constructing FRNs (McGinnis 2012), structuring the subsystem decomposition, and specifying process networks. 4 T. Sprock et al. Figure 1. The meta-hierarchy conforms to a layered abstraction of DELS that captures the structure, behaviour and control of the system specification. The Behaviour Layer reflects a recurring product, process, resource and facility (PPRF) pattern that is used to describe many system models in the DELS domain. For example, the design of the warehouse facility includes many decisions such as department layout, sizing and dimensioning [facility]; as well as ‘how many storage departments, employing what technologies [resources], and how [what process] orders [products] will be assembled’ (Gu, Goetschalckx, and McGinnis 2010). The PPRF pattern embedded in the DSL contains all the necessary language constructs to extend the domain models, e.g. to accommodate new resources or unique processing steps. Finally, the Control Layer provides a comprehensive functional specification of the activities that are required to control the behaviour and operation of the system. This functional specification provides a mapping from the decision variable in an analysis formulation of a control question to a control behaviour of some corresponding actuator that can execute the decision in the physical system. In the warehousing context, these control functions have the following interpretation: (1) Admission control may evaluate available resource capacity, both inventory on hand and fulfilment capacity, to decide whether or not to accept an order for current fulfilment; (2) Sequencing customer orders includes decisions such as coordination (of orders outbound on the same truck), batching (wave planning and release), delaying (back-ordering orders) and splitting (splitting a complete order to be picked from different zones); (3) Resource assignment control includes assigning labour and material handling equipment to load and unload the carrier trucks, put-away products into storage and retrieve items for order fulfilment. However, there are also auxiliary resources such as docks, sorter lanes and storage locations that need to be assigned to trucks, orders and SKUs to be stored, respectively; (4) Routing, or process planning, includes building routes for pickers and optimal routing for automated material handling systems (AMHS), as well as routing orders through the facility to the different processes required or when additional processing is required as in the case of exceptions or quality inspection; (5) Changing the capability or capacity of resources includes, e.g. replenishment of stocked inventory, maintenance on automated systems to maintain capacity, or anticipatory moves and pre-positioning of inventory or AMHS pickers/vehicles. 3.2 Warehouse reference architecture A useful warehouse reference architecture should provide the necessary semantics to describe a warehouse system model, support a high-level subsystem decomposition and provide a template for assembling all of the subsystem components (Figure 2). Reference architectures extract and model the commonalities across a family of system models and provide a pattern, language and model libraries for constructing new system models (Cloutier and Verma 2007). The warehouse reference architecture proposed here is constructed using the DSL identified in Section 3.1 and exhibits the same structure, behaviour and control layers that are found in the meta-hierarchy. Organising the system model, the design meta-hierarchy, and the system decomposition methods around a consistent DSL enables the construction of a reusable and extensible design process, libraries of composable system modelling components and interoperable analysis tools. As a pattern, the base reference architecture can be extended to accommodate new elements, including unique subsystems, processes or resources; e.g. defining new classes of material handling equipment or subsystems to support value-added logistics services. The result is that there may be several layers of sub-domain specific reference models, e.g. from the International Journal of Production Research 5 Figure 2. The reference architecture for the warehouse system provides a high-level subsystem decomposition and a model to integrate all of the related design subproblems into a complete system specification. This model is a partial model of the complete system, and each subsystem needs to be elaborated with additional details, see, e.g. the detailed storage department model in Figure 5. generic warehouse reference model there may be models specific to cross docks, cold-chain, e-fulfilment, high volume pharmaceutical, etc. 3.3 Integrating the reference architecture with the design process The reference architecture is based on the same DSL that structures the meta-hierarchy, supports the broader design process in McGinnis (2012) and is essential to integrating the methods and tools necessary to support an engineering design methodology for warehouses. At the top of Figure 2, the INFlow of SKUs from Suppliers and OUTFlow of orders (its product) to Customers define the context of the warehouse system and its environment as well the interface to this environment for material flow and order flow. During the functional requirements analysis design phase, these flows are analysed and classified into SKU families (resources) and order families (products), respectively. This is the starting point for roughly defining the expected behaviour of the system (Figure 1). This functional requirement as well as the behaviour description are input into the functional design phase that designs the logical structure of the system, including a FRN constructed as a flow network abstraction of the transformation of inflows into outflows and a corresponding subsystem decomposition, see, e.g. Figure 4 of SeBok (2016a). While the logical design can be elaborated and recursively decomposed, the embodiment design is focused on transforming the FRN into a facility layout, resource selection, process refinement and control behaviour specification. Whereas in many analysis models of specific subsystems the assumptions about the properties and behaviour of the other subsystems are captured implicitly, the reference architecture and the DSL provide the necessary tools to explicitly express both the details of the system design as well as the behavioural capabilities of system components. This explicit representation supports a range of analysis models, from simple approximations to high-fidelity simulations. Surrogate models are important for documenting the assumptions used to make particular design decisions and can be continuously refined throughout the design process. For example, when evaluating the impact of structural configurations, an analysis model may assume uncapacitated, or capacity-sufficient, resources executing tours formulated using an optimal TSP algorithm. While this may not be the final behavioural and control specification of the system, it provides a surrogate for that behaviour that allows an analysis model, e.g. a simulation, to be constructed to support the decision-making process for selecting other system attributes. Effectively implementing this methodology requires a process to select a surrogate model for each system attribute from a model library of plug-and-play components and evaluating the impact that the selection of any particular default behaviour will have on the rest of the design process. The design process is often iterative or incremental, where each iteration improves the information available about the complete system design and updates the set of assumptions about a particular subsystem, interdependencies with other subsystems, and constraints and requirements imposed upon other subsystems (SeBok 2016b). The system model provides an explicit expression of these constraints and interdependencies and an architecture to integrate all of the subsystems for evaluation after each successive iteration. Propogating these constraints and interdependencies and resolving conflicts that 6 T. Sprock et al. arise depends on the relative importance of different subsystems, where the importance may be dependent on the type of warehouse being designed. For example, designing a plant-finished goods warehouse might require emphasis on storage systems, while designing an e-tailer fulfilment centre might require emphasis on item retrieval and order assembly. The reference architecture can be used to harvest recurring design patterns, including dominant designs, relative priorities or conflict resolution rules, for different classes of warehouses. Ultimately, the goal of integrating the reference architecture with the design process is to enable a designer to explore the design space cost effectively. In this exploration, candidate partial designs will be identified at each level of the hierarchy for further elaboration. As the designer explores the design space and considers multiple often conflicting system performance measures, re-visiting previous decisions may be appropriate. For example, while elaborating structure alternatives by considering alternative resources, the designer may very well want to go back to the structure level of the design hierarchy and consider some new structure alternatives. The reference architecture and design process also can be used to highlight areas where additional research, models, methods and tools are needed and provide a framework to formulate the research question and integrate the results. The same approach can be used to extend the reference architecture and contribute to the model library by completely characterising the behaviour and performance of new subsystems or technology solutions. 4. Computational use case: design of a forward pick area This use case focuses on applying the hierarchical design methodology to the detailed design of a forward pick area, which is sufficiently complex to exercise the design methods discussed above. In the context of this research, the intent of the use case is to demonstrate the principles of hierarchical design, especially the recursive nature of the meta-hierarchy decomposition coupled with a system decomposition based on the system model. It also serves to highlight the beginning of an analysis library with models and tools that can be composed into a single computational model of the system, which is used to evaluate the quality of each candidate design. A common semantic framework described by the DSL and reference architecture enables the development of a library of reusable system modelling components, analysis models and computational tools. The resulting plug-and-play analysis tools support the design process, including the decomposition and hierarchical methods. The DSL and reference architecture also capture the complete functional specification and interface definition of the storage and order picking subsystem that are the output of the earlier structural and functional decomposition design phases. This enables other design methods for specifying the order picking system, see, e.g. Dallari, Marchet, and Melacini (2009) or Chen et al. (2010), to be used in conjunction with our decomposition approach. The computational models developed in this section to support the design process are implemented in MATLAB® ’s object-oriented programming language. For each system design generated during the search process, a corresponding simulation analysis model is constructed algorithmically to help predict the performance of that particular design (Figure 3). 4.1 The storage subsystem model and corresponding detailed design hierarchy The initial design phases specify the broad functional and structural decomposition of the complete warehouse system, and the next phase is focused on the detailed design of each of the subsystems. To address the design of a particular subsystem such as the storage subsystem, the functional specification identifies the capability or behaviour each subsystem must provide but not necessarily how that capability is implemented. Often the product specification is included as an input to the design process, e.g. constructing mixed pallets or case orders versus storing and picking unit load orders. A process selection approach based on Dallari, Marchet, and Melacini (2009) or Apple, Meller, and White (2010) may suggest an order picking process, such as a picker-to-goods system where cartons are picked manually from all levels of the shelves by a set of pickers using order picking trucks. The high-level process and product specifications provide guidance for designing the storage subsystem, which in this use case may be more appropriately considered a subclass of storage systems, i.e. a picker-to-goods forward storage subsystem. The rest of this section elaborates the system model (Figure 5) and discusses how the components of the system map to the decomposition of the design decisions which are then organised into the corresponding detailed design hierarchy (Figure 4). The first layer of the design hierarchy screens the alternatives in the design space for the best performing structure of the forward pick area. In addition to the aisle structure, e.g. ladder structure, flying V, etc. there are three parameters that affect the physical dimensions of the storage department: the number of SKUs that will be stored in the forward area, the number of levels of the storage equipment and the shape factor. The structure of the storage department is captured in the picker and storage networks, which specify the layout of the facility, maintain the access locations of the storage slots within the warehouse (StorageNetwork) and define the valid travel pathways between two locations (PickerNetwork). The International Journal of Production Research 7 Figure 3. Each candidate system model has a corresponding simulation model in Matlab. The structure of this pick area, consisting of six aisles and three levels, captures the individual storage slots (red dots) and the network or access locations for the storage slots (the orange stars and black lines). Figure 4. The detailed design hierarchy refines the structure, behaviour and control layers of the meta-hierarchy from Figure 1 and organises the sub-components of the storage subsystem model in Figure 5. screening criteria for this level are the footprint of the storage department and the mean travel time per stop (a proxy for labour efficiency) determined using a simple heuristic. The output of the structure layer is a set of candidate structural models, which becomes the input to the behaviour layer. The behavioural attributes result from selecting the particular equipment to be used in the forward area. The selected storage equipment defines the storage locations, or slots, available to the system which are captured as addresses in the storage network. In a concrete system model, the storage equipment may consist of simple pallet racks or more sophisticated racking solutions that work in conjunction with automated picking solutions. Similarly, the material handling system consists of picking equipment, such as humans, forklifts or more advanced automated solutions. Much like designing components for any engineered system, selecting the best resource types for the mission may require selecting a specific equipment type from a catalogue of options or specifying the desired attributes for a custom equipment design. Since control is addressed last, the default behaviours, or proxy models for each control strategy in Figure 5, assume SKUs are assigned to the forward area based on their frequency of access and are stored according to a dedicated storage policy (StorageAssignment), the picker routing is determined by a TSP heuristic (PickSequencing) and orders are batched based on the capacity of the pick equipment (BatchingPolicy). 8 T. Sprock et al. Figure 5. The system model for the Storage Department design problem provides a model to integrate all of the design subproblems into a complete system specification. The output of the behaviour layer is, again, a set of alternative partial designs in which both structure and behaviour are specified, using the DSL and reference architecture. Some of the original structural alternatives may have been discarded. The designer also may have circled back to the structure layer to add some new structural alternatives. The last layer of the design hierarchy searches for the best combination of control policies that work well for the structure and equipment of the forward area that have been fixed in the prior design steps (see, e.g. Petersen and Aase 2004; Won and Olafsson 2005; Chen et al. 2010). In this subsystem, the storageController is configured with a set of decision support strategies for storage slot assignment, pick sequencing and batching. At each layer of the design hierarchy, the performance metrics are estimated by Monte Carlo sampling 100 orders and batching them according to the pick equipment capacity (see, e.g. Petersen and Schmenner 1999; Roodbergen, Vis, and Taylor Jr 2015). In this use case, the time required to pick 100 orders is used as a proxy for the throughput of the system, and the average time for a single tour is used as a proxy for the service level, or cycle time, a system realises. Representative pick lists are generated by sampling SKUs according to their frequency of access, and based on the remaining assumptions of the proxy model, the duration of a pick tour is determined and converted into the different metrics used to evaluate the candidate designs. The variable costs of owning and operating the pick equipment resources are calculated as the present value of the product of the time it takes to pick all orders over the planning horizon and the loaded wage of a picker and the number of pickers. The capital cost of the pick and storage equipment is defined as the investment cost determined according to the Rules of Thumb by TranSystems (2010). 4.2 Structure screening The first layer of the design hierarchy (Figure 6) uses the mean time per stop to evaluate the trade-off between the height of the storage equipment and the percentage of SKUs stored in the forward area. Then the design hierarchy evaluates the impact on the mean time per stop for various shape factors for the candidate configurations of the forward area found in the first step (Figure 6(b)). To evaluate the performance of each of candidate design, a reuseable analysis method has been developed to generate a simulation model (Figure 3) from the system model in Figure 5, e.g. International Journal of Production Research (a) 9 (b) Figure 6. The mean travel time per stop is a proxy metric for labour efficiency for each candidate structural design for the forward pick area. (a) The structural design decisions evaluate the trade-off between height of the storage units, percentage of SKUs, and mean travel time per stop. (b) The shape of the forward pick area impacts the mean travel time per stop. [ pick N etwor k, storageN etwor k] = configureFacility(cr oss Aisle, Shape, AisleSet) The performance measure of interest, in this case, the mean travel time per stop of a picking tour, is a proxy for labour efficiency. Each of the points in Figure 6 represents a different configuration of the forward area, and the green highlighted points indicate configurations of the forward pick area that fulfil ad-hoc design screening rules for the mean time per stop and the footprint of the area; e.g. less than 20s/stop and 20, 000 f t 2 , respectively. Figure 6(b) plots the mean travel time per stop against the shape factor for one of the forward pick area designs in Figure 6, e.g. the minimum mean travel time is achieved at 2 levels high and 10% of SKUs in the forward area. In general, any number of designs can be selected from Figure 6 for further exploration, but the search process must balance between exploration of new designs and exploitation of good designs. This analysis shows the trade-off between a wide area with a larger number of short aisles and a long area with fewer longer aisles (Figure 6(b)). The graph shows that the longer the aisles in the forward area, and therefore the fewer aisles, the lower the mean travel time per stop of a pick tour for this problem. Based on these characteristics of the pick area, an expert may evaluate the candidate designs in Figure 6(a) and (b) based on how they well they meet the design requirements and then select a set of storage department designs to be further refined in the next level. 4.3 Behaviour screening There may be several candidate structures for the storage department, and the next set of decisions focus on specifying the behaviour of the department. For this layer of the design hierarchy, this use case will focus on selecting an appropriate fleet of picking vehicles (Figures 7 and 8), where each point specifies a different pick equipment type, a combination of capacity and vertical and horizontal speeds, and the size of the fleet for a single structural candidate selected from the results of the structural design phase. In practice, there may be several candidates selected in the first level, and a portfolio of candidate resource sets (and the associated trade-off curves) is generated for each. The metrics that support the decision-making in this step are the throughput and the service level achieved by an equipment type and fleet size, as well as the realised capital and variable costs (Figures 7 and 8). Note that only the Pareto-optimal design alternatives are shown in Figures 7 and 8 – there are many other designs evaluated which are dominated by those shown in the figures. There are two different ways the points of the design space can be selected to be evaluated on this level of the hierarchy. The Latin Hypercube sampling method generates a diverse collection of candidate equipment classes, which reflects a design process that selects equipment from a predefined catalogue of options. The genetic algorithm produces a Pareto set of the ‘best’ combinations of equipment attributes (Figures 7 and 8), which in practice then can be used to find equipment with similar configurations in a catalogue, or in cases where a custom solution is required, can be used to draft a requirements specification. The analysis models for this layer of the design hierarchy show that the time required to complete 100 orders decreases with increasing investment cost, and that the average time per tour decreases with increasing variable cost (Figures 7 and 8). For each level of investment cost the time per tour can be decreased by increasing the variable cost, e.g. using more pickers or working overtime. This depicts the trade-off between shorter pick cycle time and shorter, less efficient tours which results 10 T. Sprock et al. (a) (b) Figure 7. Trade-off between the time that is required to clear out 100 orders, and the variable and capital cost for an equipment configuration (type and fleet size). (a) Pareto set of resource options produced by the genetic algorithm. (b) Candidate resource types generated Latin Hypercube Sampling. The green points form the Pareto portfolio of resource options. (a) (b) Figure 8. Trade-off between average time per tour, and the variable and capital cost for an equipment configuration. (a) Pareto set found by Genetic Algorithm. (b) Points chosen by Latin Hypercube Sampling, where the green points indicate the equipment selection is on the Pareto frontier. in a lower system throughput. By studying the graphs generated on this layer of the design hierarchy, an expert can choose equipment configurations that are promising for the forward pick area. 4.4 Control screening On the final layer of the design hierarchy, the designs selected in the behavioural layer are elaborated with more detailed control policies. Object-oriented methods, such as the strategy pattern, encapsulate each control algorithm as an object and provide a standardised interface to the analysis tool. This standardised interface enables interoperability between the system model and the analysis model and allows the seamless exchange of storage, slotting, routing and batching policies. However, there remains additional work to define a canonical set of control policies that the warehouse needs to implement and a corresponding library of plug-and-play analysis components that enable the designer to evaluate the relative effectiveness each control algorithm. 5. Conclusions and discussion As is true with other complex DELS, there is a need for a comprehensive engineering design methodology for warehouses that consists of a common model of the system, a common design process and a library of tools and techniques used to perform the design process. The research reported here makes progress on addressing this need by augmenting an existing design process developed in McGinnis (2012) with a hierarchical design method that decomposes the design and optimisation process into subproblems that can be solved with tailored analysis models. This research also makes progress on developing a common semantic framework, a reference architecture, for warehouse design that provides the foundation for developing International Journal of Production Research 11 libraries of reusable modelling components and analysis tools as well as a pathway to integrating the solutions into a final system specification. While this approach is used extensively in other engineering disciplines where model-based design is more routine, hierarchical design is a relatively unexplored method in the warehouse literature. Therefore, there are several related open questions that may impact the overall applicability of the methodology, including: (1) Is there only one, or a single best design hierarchy? (2) How are surrogates or approximations selected, and can they be reused across sub-domains or are they sub-domain specific? (3) How can we most effectively search the design space and select candidate solutions from each layer of the hierarchy? (4) And finally, how do we deploy the solution of this design process? These last two questions are discussed below in more detail. When it comes to selecting the best candidate system solutions to carry forward to the next design layer, many systems engineering design methodologies rely on requirements specifications to guide the selection process. However, there may be other methods, such as value-driven methods (Hazelrigg 2012) that incorporate stakeholder preferences and expert knowledge into the design process. Finally, in modern warehouse design, it is not sufficient to select the best system design, but rather a complete roundtrip design methodology requires the behavioural specifications and control algorithms to be deployed in the warehouse management and control systems. Moreover, deployable control algorithms often feature complex layers of rules that need to be debugged and fine-tuned, which is significantly different from deploying a static rule or algorithm. This gap between design and deployment is large, but a model-driven, object-oriented design approach narrows the gap. Object-oriented system models are partial solutions to the software design needs, a starting point for further refining the system model to incorporate software specific details. Acknowledgements The authors thank the anonymous referees for their valuable comments and suggestions that helped improved the paper. Disclosure statement No potential conflict of interest was reported by the authors. Funding This research was supported by The Boeing Company, Fraunhofer Institute of Material Flow and Logistics, and TU Dortmund University. ORCID Timothy Sprock http://orcid.org/0000-0002-7276-7636 References Apple, James M., Russell D. Meller, and John A. White. 2010. “Empirically-based Warehouse Design: Can Academics Accept Such an Approach.” 11th International Material Handling Research Colloquium – 2010. Milwaukee, Wisconsin: Material Handling Industry of America. Baker, Peter, and Marco Canessa. 2009. “Warehouse Design: A Structured Approach.” European Journal of Operational Research 193 (2): 425–436. Batarseh, Ola, Edward Huang, and Leon F. McGinnis. 2015. “Capturing Simulation Tool and Application Domain Knowledge for Automating Simulation Model Creation.” Journal of Simulation 9 (1): 1–15. Batarseh, Ola, and Leon F. McGinnis. 2012. “System Modeling in SysML and System Analysis in Arena.” In Proceedings of the 2012 Winter Simulation Conference, 258. IEEE. Biswas, S., and Y. Narahari. 2004. “Object Oriented Modeling and Decision Support for Supply Chains.” European Journal of Operational Research 153 (3): 704–726. Chen, Chien-Ming, Yeming Gong, René De Koster, and Jo A. E. E. Van Nunen. 2010. “A Flexible Evaluative Framework for Order Picking Systems.” Production and Operations Management 19 (1): 70–82. Cloutier, Robert J., and Dinesh Verma. 2007. “Applying the concept of patterns to systems architecture.” Systems Engineering 10 (2): 138–154. Coad, Peter, and Edward Yourdon. 1991. Object-oriented Design. Vol. 92. Englewood Cliffs, NJ: Yourdon Press. Dallari, Fabrizio, Gino Marchet, and Marco Melacini. 2009. “Design of Order Picking System.” The International Journal of Advanced Manufacturing Technology 42 (1–2): 1–12. 12 T. Sprock et al. Koster, De, Tho Le-Duc René, and Kees Jan Roodbergen. 2007. “Design and Control of Warehouse Order Picking: A Literature Review.” European Journal of Operational Research 182 (2): 481–501. Estefan, Jelf A. 2007. “Survey of Model-Based Systems Engineering (MBSE) Methodologies.” Incose MBSE Focus Group 25: 8. Friedenthal, Sanford, Alan Moore, and Rick Steiner. 2014. A Practical Guide to SysML: The Systems Modeling Language. Waltham, MA: Morgan Kaufmann. Gray, Ann E., Uday S. Karmarkar, and Abraham Seidmann. 1992. “Design and Operation of an Order-consolidation Warehouse: Models and Application.” European Journal of Operational Research 58 (1): 14–36. Gu, Jinxiang, Marc Goetschalckx, and Leon F. McGinnis. 2010. “Research on Warehouse Design and Performance Evaluation: A Comprehensive Review.” European Journal of Operational Research 203 (3): 539–549. Hassan, Mohsen M. D. 2010. “A Framework for Selection of Material Handling Equipment in Manufacturing and Logistics Facilities.” Journal of Manufacturing Technology Management 21 (2): 246–268. Hazelrigg, George A. 2012. Fundamentals of Decision Making for Engineering Design and Systems Engineering. Washington, DC: George Hazelrigg. Heragu, Sunderesh S., L. Du, Ronald J. Mantel, and Peter C. Schuur. 2005. “Mathematical Model for Warehouse Design and Product Allocation.” International Journal of Production Research 43 (2): 327–338. Huang, Edward, Randeep Ramamurthy, and Leon F. McGinnis. 2007. “System and Simulation Modeling Using SysML.” In Proceedings of the 2007 Winter Simulation Conference, 796–803. Washington, DC: IEEE Press. Kim, Jinho, and K. J. Rogers. 2005. “An Object-oriented Approach for Building a Flexible Supply Chain Model.” International Journal of Physical Distribution & Logistics Management 35 (7): 481–502. Lemaignan, Severin, Ali Siadat, Jean-Yves Dantan, and Anatoli Semenenko. 2006. “MASON: A Proposal for an Ontology of Manufacturing Domain.” In IEEE Workshop on Distributed Intelligent Systems: Collective Intelligence and its Applications. DIS 2006, 195-200. Prague: IEEE. McGinnis, L. 2010. “The Future of Modeling in Material Handling Systems.” In 11th International Material Handling Research Colloquium – 2010. Milwaukee, WI: Material Handling Industry of America. McGinnis, L. 2012. “An Object Oriented and Axiomatic Theory of Warehouse Design.” In 12th International Material Handling Research Colloquium – 2012. Gardanne: Material Handling Industries of America. McGinnis, Leon, Michael Schmidt, and Detlef Spee. 2014. “Model Based Systems Engineering and Warehouse Design.” In Efficiency and Innovation in Logistics, edited by Uwe Clausen, Michael ten Hompel and J. Fabian Meier, 161–178. Cham: Springer International. McLean, Charles Robert, Y. Tina Lee, Guodong Shao, Frank Riddick, and S. Leong. 2005. Shop Data Model and Interface Specification. Gaithersburg, MD: US Department of Commerce, Technology Administration, National Institute of Standards and Technology. Mönch, Lars, Peter Lendermann, Leon F. McGinnis, and Arnd Schirrmann. 2011. “A Survey of Challenges in Modeling and Decisionmaking for Discrete Event Logistics Systems.” Computers in Industry 62 (6): 557–567. Narayanan, S., D. A. Bodner, U. Sreekanth, T. Govindaraj, L. F. McGinnis, and C. M. Mitchell. 1998. “Research in Object-oriented Manufacturing Simulations: An Assessment of the State of the Art.” IIE Transactions 30 (9): 795–810. OMG. 2012. “OMG Systems Modeling Language (OMG SysML) Version 1.3.” http://www.omg.org/spec/SysML/1.3/. Petersen, Charles G., and Gerald Aase. 2004. “A Comparison of Picking, Storage, and Routing Policies in Manual Order Picking.” International Journal of Production Economics 92 (1): 11–19. Petersen, Charles G., and Roger W. Schmenner. 1999. “An Evaluation of Routing and Volume-based Storage Policies in an Order Picking Operation.” Decision Sciences 30 (2): 481–501. Roodbergen, Kees Jan, Iris F. A. Vis, and G. Don Taylor Jr. 2015. “Simultaneous Determination of Warehouse Layout and Control Policies.” International Journal of Production Research 53 (11): 3306–3326. Rouwenhorst, Bart, B. Reuter, V. Stockrahm, G. J. Van Houtum, R. J. Mantel, and W. H. M. Zijm. 2000. “Warehouse Design and Control: Framework and Literature Review.” European Journal of Operational Research 122 (3): 515–533. Schönherr, Oliver, and Oliver Rose. 2009. “First Steps Towards a General SysML Model for Discrete Processes in Production Systems. In Proceedings of the 2009 Winter Simulation Conference, 1711-1718. Austin, TX: IEEE. SeBok, v. 1.6. 2016a. “Applying Life Cycle Processes: Life-cycle Process Recursion.” Accessed June 4 2016. http://sebokwiki.org/wiki/ Applying_Life_Cycle_Processes SeBok, v. 1.6. 2016b. “System Life Cycle Process Models: Iterative.” Accessed August 12 2016. http://sebokwiki.org/wiki/System_ Life_Cycle_Process_Models:_Iterative. Smith, Stephen F, and Marcel A. Becker. 1997. “An Ontology for Constructing Scheduling Systems.” In Working Notes of 1997 AAAI Symposium on Ontological Engineering, AAAI Technical Report SS-97-06, Palo Alto, California, 120-127. Sobieszczanski-Sobieski, Jaroslaw, and Raphael T. Haftka. 1997. “Multidisciplinary Aerospace Design Optimization: Survey of Recent Developments.” Structural Optimization 14 (1): 1–23. Sprock, Timothy. 2015. “A Metamodel of Operational Control for Discrete Event Logistics Systems (DELS).” PhD thesis. Atlanta, GA: Georgia Institute of Technology. Sprock, Timothy, and Leon F. McGinnis. 2014. “Simulation Model Generation of Discrete Event Logistics Systems (DELS) Using Software Patterns.” In Proceedings of the 2014 Winter Simulation Conference. Savannah, GA: IEEE Press. Subrahmanyam, Sriram, Joseph F. Pekny, and Gintaras V. Reklaitis. 1994. “Design of Batch Chemical Plants Under Market Uncertainty.” Industrial & Engineering Chemistry Research 33 (11): 2688–2701. International Journal of Production Research 13 Thiers, George. 2014. “A Model-based Systems Engineering Methodology to Make Engineering Analysis of Discrete-event Logistics Systems More Cost-accessible.” PhD thesis, Atlanta, GA: Georgia Institute of Technology. Thiers, George, and Leon McGinnis. 2011. “Logistics Systems Modeling and Simulation.” In Proceedings of the 2011 Winter Simulation Conference, 1531-1541. Phoenix, AZ: IEEE. TranSystems. 2010. “Rules of Thumb – Warehousing and Distribution Guidelines.” Technical report. Brussel, Van, Jo Wyns Hendrik, Paul Valckenaers, Luc Bongaerts, and Patrick Peeters. 1998. “Reference Architecture for Holonic Manufacturing Systems: PROSA.” Computers in industry 37 (3): 255–274. Won, J., and S. Olafsson. 2005. “Joint Order Batching and Order Picking in Warehouse Operations.” International Journal of Production Research 43 (7): 1427–1442. Wysk, Richard A., and Jeffrey S. Smith. 1995. “A Formal Functional Characterization of Shop Floor Control.” Computers & Industrial Engineering 28 (3): 631–643.