## 3 Inventory Location Identification Framework in MSR
### Indentification of Inventory Location  
Each stock item has a unique tag, and this study uses tags to denote stock items in the same sense. Once the measurement distance is set, the RFID reader scans the stock from the top-left to the bottom-right of the MSR (the tag scanning sequence of the RFID reader will be described in detail in this section) by moving from one zone to another. Note that the RFID reader looks straight ahead at the target zone and would be positioned perpendicular to the reference tag in each zone when scanning. The RFID reader keeps its predetermined measurement distance when scanning stocks and also keeps a constant recognition speed while moving in zones in order to improve identification accuracy. Figure 3 depicts an example where three stocks are loaded in each MSR zone consisting of \(i\) columns and \(j\) rows. To improve the accuracy of item location identification, items are loaded on one line within each zone, as shown in Figure 3. \(Rc_{ij}\) denotes the zone of the \(i\)-th column and the \(j\)-th row in the rack, that is, \(Rc_{11}\) and \(Rc_{21}\) denote zones A and B, respectively. The red circles represent the reference tags attached to the center of each zone, and the green rectangle represents the stock item with its unique tag. Reference tags A and B, which are attached to \(Rc_{11}\) and \(Rc_{21}\), respectively, are used as the location identifiers of the stock items {A1, A2, A3} in \(Rc_{11}\) and the stock items {A4, A5, A6} in \(Rc_{21}\), respectively. The items located in each zone are identified by the following Algorithm 1. Figure 3: MSR with reference tags and stocks. ```
Index: \(i\): Index of column (\(i\) = 1,.., \(I\)) \(j\): Index of row (\(j\) = 1,..., \(J\)) \(N\): Number of the item loaded in each zone of the MSR \(c\): Index of the radio-wave generation of the RFID reader in the \(j\)-th row (\(c\) = 1,..., \(C\)) Parameters: \(J_{cj}\) = A set of recognized tags when the RFID reader generates the \(c\)-th radio wave (i.e., the RFID reader performs the \(c\)-th scanning) in the \(j\)-th row of the rack \(R_{ij}\) = A set of recognized tags in which only one reference tag exists among \(J_{cj}\). (Note that only the first recognized \(R_{ij}\) has to be selected if there are several \(R_{ij}\)) \(G_{ij}\) = [Decision value] A set of identified item locations in \(R_{cij}\) Method: Step 1: Set \(T\) according to the distance between two adjacent reference tags attached to the MSR. Step 2: Calculate \(Rh\) according to Equation (2) and set the measurement distance of the RFID reader within \(Rh\). Step 3: Set the tag recognition interval of the RFID reader, recognizing speed, and \(\theta\). Step 4: Set \(i\) = 1 and \(j\) = 1, scan the tag information of the stock, and distinguish \(R_{ij}\) among \(J_{cj}\). Step 5: Set \(G_{ij}=R_{ij}\). Step 6: Exclude the reference tags and \(G_{i-1j}\) from \(R_{ij}\): \(R_{ij}\) = \(R_{ij}-G_{i-1j}\) - reference tags. \(\textit{While}\ c\) = \(C\)do \(c\) = \(c\) + 1  Exclude \(J_{cj}\) from \(R_{ij}\): \(R_{ij}-J_{cj}\) If the number of stocks in \(R_{ij}\) = \(N\), then let \(i\) = \(i\) + 1 and go to Step 5. \(\}\) Step 7: If \(i\) = \(I\), then let \(j\) = \(j\) + 1, \(i\) = 1, \(c\) = 1, and go to Step 5. Stopping rule: If \(i\) = \(I\) and \(j\) = \(J\), then the algorithm terminates. ```  
**Algorithm 1** Inventory location identification  
In step 4 of the algorithm, the scanning sequence is as follows. As shown in Figure 3, the RFID reader scans the tag information of the stock by visiting zones in sequence from \(R_{c11}\) to \(R_{c41}\) for the first row with a constant tag recognition speed and interval. If there is no recognizable stock after the RFID reader completes scanning \(R_{c41}\), the RFID reader scans the stock's tag information for the second row in the same direction (i.e., from \(R_{c12}\) to \(R_{c42}\)). The recognized stock tag information is then temporarily stored in the LS database.