**8. Sensitivity Analyses**

To show the impact of various known inventory parameters on the average profit (*TP*), production time (*t*1), selling price (*p*), and cycle length (*T*), sensitivity analyses are performed with respect to Example 2 by changing the parameters from −20% to 20%. Then, the obtained results of these analyses are depicted graphically in Figures 7–12.

**Figure 7.** Impact of *Co* on the optimal policy.

**Figure 8.** Impact of *h* on the optimal policy.

**Figure 9.** Impact of *cp* on the optimal policy.

**Figure 10.** Impact of *θ*<sup>1</sup> on the optimal policy.

**Figure 11.** Impact of *m* on the optimal policy.

**Figure 12.** Impact of *b* on the optimal policy.

From Figures 7–12, the following observations can be made:


## **9. Managerial Implications**

From the numerical and sensitivity analyses, a few advisories or awareness may be given to the manager of the manufacturing system of mixed products, which are presented below:


#### **10. Conclusions**

In this work, the concept of the mixing problem is implemented in the production inventory model for a liquid product with selling-price-dependent demand and a variable production rate under preservation technology. The mixing process is formulated mathematically by the system of differential equations. The non-linear average profit is maximized numerically by the meta-heuristic optimizers: differential evaluation and simulated annealing.

It may be concluded from the numerical result that, if the enterprise/organization applies the preservation facility, it will be more beneficial for them. From the sensitivity analyses, it can also be concluded that the demand parameters and different inventory costs have a significant negative impact on average profit.

As a practical implication, the concept of this proposed model can be applied in various industries, such as medicine, cosmetics, detergent, food industries, and so on. Although the concept of this model can be implemented in the various fields mentioned above, this work has some limitations. Firstly, there is no theoretical proof of the optimal policy of the proposed model. Secondly, under uncertainty, this model cannot be directly implemented in the such industrial sectors and, finally, the shortages case is not considered in this model.

Keeping the above limitations of the proposed model in mind, in the future, the concept of the mixing problem can be extended in other production inventory models, such as models with shortages, a production model with an imperfect production process, and a model with trade credit policy, among others. Finally, the concept of this work may

be extended in an uncertain environment-fuzzy, stochastic, fuzzy-stochastic, and interval environment, among others.

**Author Contributions:** Conceptualization, M.S.R., S.D., A.K.M., A.A.S., A.K.B., L.E.C.-B., G.T.-G. and A.C.-M.; Data curation, M.S.R., S.D. and L.E.C.-B.; Formal analysis, M.S.R., S.D., A.K.M., A.A.S., A.K.B., L.E.C.-B., G.T.-G. and A.C.-M.; Investigation, M.S.R., S.D., A.K.M., A.A.S., A.K.B., L.E.C.-B., G.T.-G. and A.C.-M.; Methodology, M.S.R., S.D., A.K.M., A.A.S., A.K.B., L.E.C.-B., G.T.-G. and A.C.- M.; Supervision, L.E.C.-B.; Validation, M.S.R., S.D., A.K.M., A.A.S., A.K.B., L.E.C.-B., G.T.-G. and A.C.-M.; Visualization, M.S.R.; Writing—original draft, M.S.R., S.D. and A.K.M.; Writing—review and editing, A.A.S., A.K.B., L.E.C.-B., G.T.-G. and A.C.-M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data is in the paper.

**Conflicts of Interest:** The authors declare no conflict of interest.
