Application of Dynamic Value Stream Mapping in Warehousing Context

Uncertainty within supply chains increases the risk of not meeting objectives. Warehouses can absorb some of these uncertainties, by accumulating inventory. This accumulation has led many to consider warehouses as a source of waste in supply chains. Hence, there is limited research that seeks improving intrinsic warehouse efficiency; particularly in the context of Lean concepts and Value Stream Mapping (VSM). Since, warehouses seek to absorb uncertainty in supply chain by holding inventory; this uncertainty absorption may introduce variability to warehousing function itself. Therefore a methodology is required, which can capture the embodied dynamic within warehousing function. This paper reflects Lean concepts and, in particular, VSM to warehousing context and introduces some methods and guidelines to assure the proper application of VSM in what is an uncertain and dynamic system. In this paper, warehousing function is formulated based on some abstract processes which vary on their output status. This formulation facilitates identifying value-adding activities as one of the most substantial steps, yet confusing in application of VSM in warehousing context. The suggested methods enable fundamental statistical/mathematical analysis, which leverage VSM to a more dynamic evaluation tool. Application of the introduced approach will facilitate the decision making process for warehouse systems evaluation and improvement. The resultant methodology is applied to a factual case and this serves to demonstrate its practical application. It is worth mentioning that the findings applications, which can be termed ‘dynamic VSM’, are not limited to warehouses but can also be applied to any dynamic environment with non-deterministic processes.


Introduction
If supply chains are considered as distribution networks, then warehouses represent the main nodes of those networks.Hence, warehouses can exert a substantial leverage on supply chain service quality (Gray, Karmarkar, & Seidmann, 1992).This crucial role emphasizes the importance of study in the field of warehouse performance evaluation.Since warehouses like other industrial facilities perform series of coupled processes, the evaluation method should also fit this complex structure.Thus, an approach is necessary which can capture the holistic dynamic interaction among processes while also analysis them individually.
There is a close alignment between performance evaluation and improvement and Lean tools and methods.In short, 'Lean' seeks to improve the performance of operations by eliminating waste (Detty & Yingling, 2000;Hofer, Eroglu, & Rossiter Hofer, 2012;Liker & Convis, 2011;Pavnaskar, Gershenson, & Jambekar, 2003;Womack & Jones 2003).VSM is one of the better known Lean tools in the implementation of Lean concepts to production and more recently service industries.VSM is useful in the visualization of core value chain processes, which assists managers in identifying opportunities to achieve required objective.This map provides a high level view of the interdependencies and interactions across different processes as resources, products, or information passes each stage of the stream.This comprehensive illustration enables analysis and evaluation of process chain with respect to desired key performance indicators (KPIs).These VSM properties, and also the promising results that have been achieved by VSM implementation in manufacturing industries, make VSM a promising candidate for warehouse performance evaluation, too.Therefore, this research aims to investigate the application of VSM in a warehousing context, as well as the modifications that might be necessary.

Literature Review
Generally the research in warehousing can be divided to two fields; design and performance evaluation, with the former topic commanding a broader foundation of research.In this context, design refers to physical design, equipment selection, as well as operational design.Evaluation refers the assessment of the performance of existing designs with respect to various key performance metrics.Since this current research focuses on performance evaluation, only the literature in that area is reviewed.However complexity of warehousing systems made researchers, in either topic, to narrow down the scope of research, and study warehouse design or evaluation topics partially, such as individual analysis of layout or operational policies.Interested readers can find design topics in related literatures (Berg & Zijm, 1999;J. Gu, Goetschalckx, & McGinnis, 2007; J. X.Gu, Goetschalckx, & McGinnis, 2010;Rouwenhorst et al., 2000a) One of the very first studies in warehouse evaluation proposes the application of 'zero-based analysis.This approach suggests to divide resource consumption to three parts; necessary work, losses and cost.The former refers to required resources in ideal case, losses are expressed as a percentage of the necessary work and the later are monetary units.So, 'zero based analysis develops a reference system in the form of utopian loss-free system such that the reference point is only dependent on the product.The main drawback of this approach is inability to evaluate time-based or quality of service parameters.In addition, the scope of mentioned study is limited to the manual processes.Thus, this approach may have shortcomings on its application to those warehousing processes which require multiple resource type (Henrik, Mats, & Lars, 1994) As mentioned, this research aims to investigate the application of VSM in warehousing context for the purpose of warehouse evaluation.Hence, the literatures regarding VSM application in warehousing is critically reviewed.There is a large volume of literature concerning Lean and specifically the application of VSM in manufacturing industries and more recently supply chain, but limited and scarce in warehousing (Ben Naylor, Naim, & Berry, 1999;Bozer, 2012).When VSM is applied to supply chains, warehouses are generally represented as an inventory 'black box'.This approach neglects to reflect any detailed information in regards to warehouse performance.However, in order to have a lean supply chain, warehouses, as one of the main entities in logistic networks, should be lean as well (Jones, Hines & Rich, 1997) (Bozer, 2012) In context of applying lean concepts in logistics management, Myerson suggests considering warehouse function as assembly line constituting several activities.Thus, warehouse efficiency can be improved by some general guidelines such as improving tools and equipment availability (Myerson, 2012).
Mustafa introduces a framework to apply Lean concepts in warehouses.The proposed framework is limited to some theoretical guidelines without providing enough details regarding implementation of Lean tools and techniques.Moreover the guidelines are not generic enough without formal representation which makes it hard to apply them in different situations (Mustafa, 2015).
Garcia carried out one of the earliest applications of VSM in warehousing (Frank C. Garcia, 2013).In the mentioned paper, the scope is limited to unit-load warehouses, however a significant proportion of industrial warehouses operate under-unit-load, which actually requires more considerations in VSM application due to changing the unit of operation in warehousing processes.Moreover, some inconsistencies exist in the published VSM, such as different work in progress units among different stages.The importance of unit consistency in evaluation of process chains and how to achieve it in warehousing context is well discussed in section 2.
In another work, Dotoli advocates analyzing warehouse operations in three steps with different methods (Dotoli, Epicoco, Falagario, Costantino, & Turchiano, 2015).In first step, the Unified Modelling Language (UML) is used to describe the warehouse logistics.Then in the next step, VSM is applied to identify non value-adding tasks.In the final step, a mathematical formulation assists on ranking all identified types of wastes which were termed in that paper anomaly.The paper more focuses on ranking anomalies and hence it does not map KPI values as a basis for comparison.Additionally, the research scope is limited to production warehouses, and other types of warehouses are shown as work-in-progress (WIP) boxes without including detailed information about their operational performance.
Bozer attempted to analysis the reflection of some lean concepts in warehousing after investigating lean application in couple of case studies (Bozer, 2012).However the analysis and discussion of value-adding and non-value-adding activities, in the mentioned report, is one of the most important works in this area, but it is not easy to generalize some of the concluded results to all warehouse types.For example, Bozer defines any increment of inventory above a determined minimum level, as warehouse inefficiency.If the study scope is narrowed down to the warehouse, and not whole supply chain, this argument cannot be true for warehouses which their inbound and outbound activities are dictated from the supply chain.Consider, if customer order reduces considerably after receiving new supply consignment, inventory level will exceed the determined Then, it is recommended that the warehousing objectives should be defined with respect to the introduced enabler abstract processes.This is an important step for utilizing Lean concepts by application of VSM in warehousing.Considering a pool of possible processes and sub-processes, the warehousing function, , can be represented as it shown in ( 1) and ( 2).
= {( , )}; є{1, … ,5} Where: K: number of all sub-processes : Process i : Sub-process k For example; Warehouse A is assigned (from supply chain level) to change the status of items as follows; warehouse-able items, stored items, picked items, dispatched items, while warehouse B is assigned only the first and last of these activities.If is assumed as the membership value of storing process, it will be 1 and 0 respectively for warehouse A and warehouse B.
To distinguish value-adding from non-value adding activities within in each abstract process class, here, it is suggested to define those activities as non-value adding, if they perform after the item transits to the required status from that abstract process class.So, each sub-process of a process should be analyzed with respect to its abstract process and thus a value-adding activity in one process can be non-value-adding in another.Value-adding activities are generally recognizable, but sometimes non value-adding activities and waste are intertwined with value-added activities, making it difficult to clearly distinguish them from each other.Therefore some of these ambiguities will be discussed further.
Because of the long history of considering inventory as source of waste in Lean, it may seem bizarre not to consider warehouse inventory as waste.Basically, in finished goods warehouses, storing the items and carrying some inventory levels, let's term it dedicated capacity, is the main role of warehouse, such that inventory assists to absorb the risk of demand variation in the supply chain.Hence, it can't be so true to consider any level of inventory, even equal or less than dedicated capacity, as warehouse waste or inefficiency.Moreover, as explained, if warehouse does not have control over its inbound or outbound flows, changes in these flows may lead to inventory accumulation which exceeds the warehouse dedicated capacity.However, in the context of supply chain analysis, this exceeded inventory is waste and could happen due to inefficiency in so many forms such as poor supply planning.But, in the context of warehousing, the mentioned case of exceeded inventory from dedicated capacity is not due to warehouse inefficiency.In other word, the inventory accumulation, as waste in lean concept, can be in two forms; warehouse waste or supply chain waste.Warehouse waste is generated due to in-efficiency in warehousing operations whereas supply chain ones generated due to in-efficiency in supply chain planning level.However the supply chain waste could accumulate in warehouse, but these wastes should not be considered as warehouse waste.This research aims to apply Lean concepts by application of VSM in warehouse which its role is well defined in supply chain level.Hence, only that level of inventory, which occurs due to internal warehousing processes inefficiency, is suggested to be considered as warehouse waste.
As with manufacturing systems, most transportation between processes can be considered to be non-value-adding activity.In the current literature, picking and storing are considered to be the most time and cost consuming processes in warehousing, as a function of travel distance.Since, this paper suggests defining value-adding activities as those which directly change the item status, the travel of a picker from its dwell point to a storage module to pick items can be considered non-value-adding.Some examples of different picking/storing policies support this argument.Consider double command storing/picking process; the operator in first part of travel, stores the items in storage modules and in the way back to dwell point, picks the orders For SKU-based processes, since they already operate based on SKU, there is no need to convert the process operational unit.In regards to not SKU-based processes, these may operate in three general conditions as follows; 1-Input SKU, output not-SKU: In this case, the number of inputs can be used to formulate process parameters as a function of SKU.
2-Input not SKU, output SKU: In this case, output number can be used to formulate process parameters as a function of SKU.
3-Input not SKU, output not-SKU: Here either 'expected' or 'Min-Max frontier' strategies can be utilized to estimate the average or a range for the number of SKUs in the process.The explanation of these strategies is given in section 2.2.1.
Up to this point all processes types could be converted to SKU base.It is worth noting that process parameters can vary from one operation to another.For example, the process parameters which are employed to measure typical process outcomes in VSMs are operation time, failure rate, resource and required consumables.Sometimes, the process parameter is a standalone KPI itself, such as process time.But, generally process KPIs are functions of process parameters.As shown in a generic representation in (4), is a function which maps the process parameter to a KPI.In general, each specific KPI can be calculated based on a specific function and specific process parameter(s).

KPI = ( )
Depending on the process parameter type (fixed, constant, variable), some further manipulation is required in order to formulating process parameters to SKU base, which is explained in section 2.2.1, 2.2.2 and 2.2.3.

Processes with Variable Parameters
For this process type, two methods are suggested; 'expected' and 'Min-Max frontier'.These approaches, as mentioned, can also be utilized when the number of operational units in a process is not determined.
Expected: Sometimes upon close examination of the historical data, a pattern can be observed and thus it may be possible to map the variable parameter to a probabilistic distribution function.The process parameter may then be represented as a function of some other variables as shown in (5).
PP: Process parameter defined as random variable PP ~ D; PP has the probability distribution D P(PP = pp): Probability that the PP has a particular value of pp.
= ( , ., ., ) In the 'expected' approach, it is suggested to use an 'expected value' of the variable process parameter to estimate the related KPIs as shown in ( 6) to (10).refers to the set of all possible values for .^ and ^ are respectively the estimated values for and .
It is worth noting that the benefits of this approach are not limited to the estimation of variable process parameters.This approach enables broad range of statistical analysis of KPIs.For example, if the modal value of a process parameter is more desirable than its expected value, KPIs can be easily interpreted with respect to the probability distribution function of the parameter.
Another advantage of this approach is that it enables one to analysis the occurrence chance of an acceptable KPI.For example, sometimes smaller values of PP guarantee meeting the desirable KPI.In this case, by utilizing the probability cumulative function(F(a)), the probability of meeting the desired KPI can be formulated as shown in (11).Thus, this approach enables one to capture the dynamic nature of a process, such that, scenarios may be developed and tested based upon different possible process outcomes.As mentioned, the order picking process is a good example of a process with variable process time and many researches have formulated the picking time as a function of travel distance (de Koster et al., 2007) By adjusting these generic formulas to warehouse specific conditions, the expected travel distance (accordingly process time) can be formulated.Generally, the picking time, , can be a function of many parameters, such as; : picking aisles length, : picking aisles width , : picking aisles height , T: number of aisles, dw: dwell point position, D: dock position, s: demand skewness, : order size, : order diversity.Hence, the picking time and its estimated value can be presented as follows: = ( , , , , , , , , ) , ≈ ( ) The abovementioned parameters for the picking process can be divided into two general categories; deterministic and non-deterministic.Some parameters are fixed, such as the number of aisles whereas some parameters, such as order diversity or order size, may vary from one order to another.These non-deterministic parameters introduce variability to the process time.As mentioned, observing historical data can reveal order profile patterns, which can then be mapped to a probability distribution function.Hence, the chance of receiving different order sizes with different diversity can be formulated.As shown in ( 12), the expected value is formulated based on two elements.First element is the probability of receiving orders with specific size and diversity as a function of non-deterministic parameters.The second element is the accordance picking time with respect to the received specific order and deterministic parameters.The order diversity can range from one to maximum order size.The former represents a single order line, whilst the later indicates one single item per SKU in the order.
( )= ∑ ( , ) × ( , , ℎ , , , , , , ) Min-Max frontier: If the explained 'expected' approach is not applicable, or for ease of calculation, Min-Max frontier approach is suggested.In this approach the possible minimum and maximum values of variable process parameters should be estimated.These thresholds constitute a feasible range for the variable parameters and accordingly for the process KPIs, as represented in a generic form in ( 13) and ( 14).
Recalling the picking process, considering the furthest and closest storage modules, the longest and shortest travel distances (consequently process times), can be obtained.Although this approach determines some thresholds and not one specific value for the variable parameter, it nevertheless provides an acceptable insight from variable process parameter to interpret the related KPI.

Processes with Fixed Parameters
Since in this process type, process parameters are a direct function of the number of operational units, , it is quite straight forward to formulate KPIs when a process is aligned to a SKU base.The generic form of this approach is shown in ( 15) and ( 16).

Processes with Constant Parameters
If the number of operational units is constant, , KPIs can be calculated on a SKU base by using the constant process parameter; as shown in ( 17) and ( 18).

= μ ×
; μ: constant coefficient (17) If the number of operational units is variable, the 'expected' or 'min-max frontier' approach can be applied to estimate the number of operational units and from that, the relevant KPI can be calculated.In case of variable number of operational units, the variable parameter is .
The generic representation of applying 'Expected' method to estimate KPI, when the operational unit is variable, is shown in ( 19)-( 22).Consider the case that fork lifts carry different SKU numbers from docks to a stacking area with constant carrying time.If historical data reveals that carrying SKUs follows a uniform distribution with definable minimum and maximum SKUs, using the distribution parameters the expected number of carrying SKUs can be considered for estimating process parameters/KPIs.
As mentioned, 'Min-Max frontier' can also be utilized to estimate the variable number of operational unit, .In this approach the maximum and minimum number of operational inputs is considered, which provides a range for process parameters and accordingly KPIs as shown in ( 23)-( 25).
If the 'min-max frontier' approach is applied to more than one process, the possible combination of min and max values for all processes should be taken to account and the corresponding global min and max should be chosen for the KPI.For example, consider that 'min-max frontier' approach is applied to estimate process time of storing and picking process, and .The storing and picking process time , and 3 , can sit within the ranges given below, by considering the effective parameters; such as furthest and closest storing/picking modules, maximum and minimum order size and diversity.

4
< 2 < 12 , 5 < 3 < 12 Hence, by application of the 'min-max' strategy on these two processes, their total process time, , results in the below range.= {9, 16, 17, 24} → 9 < < 24 Utilizing explained methods in 2.2, all warehousing processes can be formulated in such a way that all types of processes can be measured with an identical scale unit, the SKU.

Formulating Order-Based KPIs
Generally, it is more preferable to measure process KPIs with respect to the eventual objectives of a process chain.In the application of VSM to manufacturing systems, everything should be measured with respect to finished goods, for which specifications are predetermined.In the warehousing context customer order fulfilment is the main objective which the orders specifications are not known in advance and can vary from one order to another.This ambiguity was the main reason that the SKU was chosen as the common unit for process evaluation in section 2.2.1.Nevertheless, it is still preferable to interpret warehousing KPIs with respect to customer order profile.Hence, SKU-based KPIs must be transformed into order-based KPIs.It is again suggested to utilize either the expected or min-max approach for order profile estimation.Estimation of order profile is different to demand forecasting.In demand forecasting the total number of customer orders over a time period are forecasted.Whereas, order profiling seeks to find patterns within orders, such as order size or item diversity, respectively; , .
If 'Expected' approach is utilized, probability distribution functions, such as , , can be assigned to variable parameters of orders, such as order size and diversity, , .By estimating these parameters, as shown in ( 26), the proces in ( 27)-( 30In a simpl was 20 (as

As mentio based KPI approach p
In general interpretat parameters the estima the whole   The warehouse has a static time window in which to receive orders and after that 3 starts.Pickers pick required items and sort them in sorting matrix in preparation for shipment.Pareto-distribution with proper shape and scale parameters can also be a good estimator for picking process, by considering the storing policy, storage area configuration and other related parameters.

Produc
3 ~Pr(t) Analyzing the order profile, the order size varies from 3 to 11 SKU per order with average of 9, which larger orders are more common.Since the sorting area is small, hence arranging larger orders is not measurably longer than smaller orders; sorting process is almost identical free from order size.The sorting process can be converted to SKU base by considering its expected value of operational units.For the purpose of demonstration in this case study, the typical metrics in the VSM are primarily examined, such as process time; however other KPIs can also be easily formulated.The current state map of the described warehouse, with restructured SKU-based processes, is illustrated in Figure 5.In order to demonstrate order-based KPIs, the process parameters are divided to 9 (average order size), shown as the bottom line in Figure 5.

Discussion
As discussed earlier, the duration of stay of a SKU in the warehouse is not an indicator of warehouse inefficiency.
In this case study, from receiving to storing, all processes operate on push mode and only customer orders send a pull signal to trigger picking process.This makes picking as the decoupling point, and the pacemaker of the warehousing function.Hence, as illustrated in Figure .5, the stored items are shown in supermarket, instead of wrongly showing them as work in progress (WIP).The lead time in the supermarket indicates the time interval from receiving an order to picking it from the racks.In other words, lead times before the decoupling point indicates the SKU's waiting time to progress to successive process, whereas the cumulative values of lead times after decoupling point represent the order lead-time.
The total process time of each single SKU is expected to be 1.906 minutes.However, depending on non-deterministic process parameters, this value can vary.The variation of storing and picking process time and their transportation sub processes have led to a non-smooth process chain as captured and shown in the dynamic VSM representation in Figure .5.This variation sometimes results in either idle time or resource bottleneck.Upon closer inspection, sorting and picking tend to be the most time consuming processes, which is reasonable since the studied warehouse is a customer-facing warehouse.Moreover, since picking is the pacemaker it is a good candidate for improvement.Combining the storing and picking processes as one process may help to absorb some variation from both processes and providing the warehouse operates with greater stability.This approach promises to increase process efficiency as discussed in the literature and to warehouse managers in the exemplar organization concur that application of double command storing-picking process would improve efficiency and also create smoother flow.Demonstrating such a future state map is not in the scope of this paper but would follow the same procedures set out in this paper.

Conclus
The If PP ≤ a → KPI = g(pp ≤ a) ≤ b → KPI is acceptable, F(a) = P(PP ≤ a) F(a) = P(KPI ≤ b); the probability of meeting KPI(11) Figure 3. Impa Figure 5, instead of showing a single value for the estimated parameters, these are represented as distribution functions.For clarity, the adjusted Pareto diagrams are rotated 90 degrees and the dashed-lines show the expected values of each distribution.One may consider each value in the distribution function, for KPI estimation, by considering its corresponding probability.
SKU based ^= (PT 4 |order size=9) ≈0.56 minutes As an initial step to formulate different process types on SKU base, warehousing processes should be decomposed into all possible sub-processes.Utilization of given representation in (1) and (2) can facilitate this step considerably.The second step is to categorize all warehousing sub-processes into SKU-based/fixed, SKU-based/variable, SKU-based/ constant, not-SKU-based/ fixed, not SKU-based/variable, not SKU-based/constant.