## 7 Sensitivity Analysis and Numerical Results
### Instance 1: FOQ Ordering Policy  
The following assumptions are considered for Instance 1:  
* The initial level of inventory for products is zero in the case of launching a new product into the market. In this case, the first order will be launched at the beginning of January and delivered at the beginning of June (LT = 5 months).
* Based on historical data from previous years and experience, the manager forecasts monthly sales at the beginning of the first year for the next 2 years.
* The supplier defines the FOQ for each product. Since the FOQ is not unique for each product, the unit price depends on the ordered quantity.
* At the beginning of every month, customers from all countries send stock level reports to the company's logistics manager. This report represents the prescribed form and format in an Excel spreadsheet.
* The delivery lead time is five months. The quantity ordered at the beginning of February is in stock at the beginning of July.
* At the beginning of the first year, there are no realized inputs of stock for launched orders from the previous periods.  
Instance 1 is analysed for two separate cases. Case 1 considers FOQ policy with deterministic demand, where the forecasted sale is equal to the realized sale. Case 2 reflects  
Figure 5: Pseudocode for planned order quantity.  
According to Case 2 (Figure 8), the variable Realized sales is presented as the variable Sales forecast, which is changed randomly in the range of \(\pm\)20% for each period of time horizon \(T\), as it is presented by Equation (8).  
For Case 2, the total number of planned orders and received deliveries is the same as for Case 1. From the company manager's point of view, forecasted sales never deviate more than \(\pm\)20%. This stochastic demand generates very similar values of the objective functions \(J^{1}\) and \(J^{2}\) as for Case 1, concerning the average level of inventories and stock-outs (Figure 9).  
Figure 8: Elements of the spreadsheet model for Case 2: FOQ policy with stochastic demand.  
Figure 9: Dynamic of accumulation for Case 2: FOQ policy with stochastic demand.  
The total number of planned orders is 14, and the total number of received deliveries is 11. As shown in Figures 6 and 8 and Table 2, at the beginning of the first year, the columns Stock level report, Realized input of stock and Realized sales are empty because there are no launched orders from the previous year for delivery in the first five months of time horizon \(T\). For Case 1, the model shows that the planned average level of inventory for the product in the warehouse (63,000 units) is greater than the realized average level of stock in time horizon \(T\) = 24 months (45,595 units) for 17,405 units, according to the objective function (15). In addition, except for the first five months, the value of the objective function (16) is zero, without stock-out situations.  
If we compare the numerical results of Case 1 and Case 2 for FOQ ordering policy (Table 2), it can be appointed that the differences between the values of the objective functions are small, even in Case 2, when the realized sales are randomly changed in the range of \(\pm\)20%. An insignificant deviation of the objective functions results for Cases 1 and 2 confirms that the model is sensitive and stable. One of the main questions related to future research, also significant from a company perspective, can be: \"What will happen with the Total number of orders, Stock-outs, and Costs, if the business environment is unstable and uncertainty is higher, e.g., if realized sales vary more than \(\pm\)30% or \(\pm\)50%?\".