**4. Results**

#### *4.1. Numerical Results*

The objective is to make the production plane, where the number of workstations, workers, and production time cycle are required. The production rate of the system is depending upon the production rate of machines, which is kept in such a way that there are no shortages in the system. The systems of equations generated from the proposed model consisting non-linear equations. There are numerous techniques used to find the optimal solution of non-linear models e.g., interior point optimization (IPO), particle swarm optimization (PSO), pattern search (PS), genetic algorithm (GA), min-max optimization (MMO) etc. Analytically, the methodology is proceeded to search the optimal and global solutions. The proposed model is solved with global optimal result and solution as given in Table 4. The total minimum cost of production is obtained as \$478,491, which is optimal and better as compared to PSO, PS, and GA as evidence. The possible optimal production plan for the manufacturing of parts A, B, and C as a solution consider the production cycle time in days (5.4, 5.76, 5.76), machine (9, 8, 7) at the first stage, and (7, 6, 6) at the final stage of sugar processing, respectively. The number of labors as an indirect decision variable are calculated as (32, 29, 25) and (17, 15, 15) for first and final stage of production.

A special case is considered to solve the proposed research model by taking constant production rate of the sugar processing firm. This analysis is important to understand the importance of the controllable production rate by comparing the results. The main objective is to minimize the total cost of production. The proposed research model is solved by using the solution algorithm developed by considering constant production rates of the machines located at first stage and final stage of the production system, i.e., <sup>ε</sup>*ja* = (140, 150, 160) and <sup>ε</sup>*jc* = (120, 130, <sup>140</sup>). The comparative results on the basis of the *TCsj* is represented in Table 5 and Figure 2 to show the evaluation of the controllable production rate. It is found that the total cost of production in case of variable production rate is optimal as compared to the special case by taking constant production rate. The total cost of processing is minimum in case of variable production rate i.e., \$478,491 as compared to special case. In addition, the machines required for the production of products at constant production rate required more machines to fulfill the demand. This result provides an important justification for the transformation of the proposed model into a traditional system, considering a constant production rate for the production system.

Theoretically, the study is a proactive approach for the decision-makers to take advantage of the controllable production rate to avoid excess production of agri-product against fluctuating demand with the minimum optimal cost of Agri-SCM. The solution of the research is provided by incorporating a controllable production rate for flexible manufacturing, inventory level control, optimal carbon emission, and best resource utilization to cope with the fluctuating demand. The research is effective for agricultural businesses to understand the role of controllable production rate for cleaner production.


**Table 4.** The optimal result of the production model with solution for the processing of sugar.

**Table 5.** Sensitivity analysis of the SCM with respect to key parameters.


#### *4.2. Sensitivity Analysis*

The sensitivity analysis of the proposed model is necessary to check the limitation and variation of the system by changing the important factors and parameters. The objective of the proposed model

as total cost of agri-processing over short run along is showing a good variation depending upon the change in labor cost, reworking cost, carbon cost, and inspection cost. A sensitivity analysis is necessary to show the e ffects of varying data on the final objective of the model, i.e., the total profit. Di fferent experiments are also required to test the proposed production model in di fferent situations. There are eight parameters considered as performance indicators for the sensitivity of the proposed model, and the results of the analysis for the SQP technique are given as in Table 5 and also presented graphically in Figure 2.

The sensitivity provides a detailed analysis of the largest e ffects of the parameters (changes of −50%, −25%, +25% and 50%) on the objective function. This analysis is conducted as follows.


**Figure 2.** The sensitivity of total cost of Agri-SCM with respect to the cost parameters.
