## 3 Presentation of the Proposed Model
### Sub-Modules of the Presented Model
#### 3.3.7 Efficiency Analysis Module  
The assessment of the storage processes' efficiency can be performed in terms of different criteria, including (a) the duration of picking, (b) the route of picking, and (c) resource consumption (human labor, costs, transport). The developed system as a criterion of efficiency adopts the duration of order-picking. To evaluate the effectiveness of the picking process that results from the applied model of product distribution in the warehouse, it is important to apply a model that allows high precision so as to reflect the processes occurring in a real warehouse. According to the picking lists, a picking route was planned using a model applied in the majority of medium-sized companies that have their warehouses, i.e., determining the order-picking route based on the closest point to the current location of a warehouse employee. This model also contemplates the need to intervene in the order of products on a picking table in the event of the risk that a smaller product can be crushed by a larger one--sensitivity to stacking. The model can be implemented in most of the conventional warehouses, i.e., those where the products are stored in rows in the storage area. There can be many parameters of the racks; however, all the racks must be the same, which is important because of a matrix-parametric description of warehouse structure. The number of storage levels is irrelevant; the warehouse may have several levels of storage ([PERSON], 2019). Incidence matrix was used to describe the structure. Accordingly, the structure of the warehouse storage surface can be expressed as an incidence matrix \(W\) (16). \[W=\left[ \begin{array}{cccccc}r_{11}&r_{12}&\ldots&r_{1y}&\cdots&r_{1M}\\ r_{21}&r_{22}&\ldots&r_{2y}&\cdots&r_{2M}\\ \vdots&\vdots&\ddots&\vdots&\ddots&\vdots\\ r_{x1}&r_{x2}&\cdots&r_{xy}&\cdots&r_{xM}\\ \vdots&\vdots&\vdots&\vdots&\ddots&\vdots\\ r_{N1}&r_{N2}&\cdots&r_{Ny}&\cdots&r_{NM}\end{array} \right] \tag{16}\]  
For the precision of further considerations, the following notation is used \(r_{xy}\equiv r(x,y)\). The \(W\) matrix along with the parameters describing the structure of the warehouse fully reflects its real dimensions. Based on the \(W\) matrix, a \(D\) matrix was constructed that mirrors access time from packaging area \(r(0,1)\) to each rack located in the storage area. Before completing the values in matrix \(D\) it is necessary to fill in the \(W\) matrix. The movement time from the packaging area to the first product on the picking list has been described by formula (17). \[ \begin{array}{l}t(x,y,p)\ =\ t_{lp}\ (D_{lr}(y)\cdot(x-c_{l}(x))\ +\ d_{cr}c_{l}(x))\\ +t_{lp}\ (D_{ur}(y)\cdot(y-c_{w}(y))\ +\ d_{cr}c_{w}(y))\ +\ t_{a}\ +\ t(p) \end{array}  \tag{17}\]For further calculations, in the paper, the time of lifting and lowering forks \(t(p)\) on a given storage level was assumed based on the technical data of a standard high storage forklift truck. Besides, this requires a time correction \(t_{p}\) if the rack is facing the packaging zone, because it will not be necessary to travel an extra distance equal to the width of the corridor between the rows. Therefore, the correction takes the forms of equation (18). \[If\ W\ (x,y-1)\ \ =\ \ 0\ then\ t(x,y,p)_{new}\ =\ t\ (x,y,p)-\ t_{lp}\ (D_{wr}+d_{cr}) \tag{18}\]  
After completing the entire \(D\) matrix with the access times to a given spot, it is important to exclude the values with access times to spots that are not storage spots (are aisles). Racks with the shortest access time will be used to store key goods. To analyze the total picking time, it is important to determine each time the movement time around the warehouse for each item on the picking list. Due to a large number of combinations, it is impossible to generate a matrix containing these times. In such a case it would be necessary to generate as many matrices as there are coordinates defining the location of a product. The subsequent part of the algorithm for defining picking time can be described in the following steps.