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The pharmaceutical industry is one of the most essential areas of health in any country. It is defined as a system of processes, operations and organizations involved in discovering, developing and producing drugs. The supply chain in the pharmaceutical field is one of the most important strategic issues in the pharmaceutical and health-care industries. The purpose of this study is to reduce the total cost of the supply chain network and reduce the amount of distribution scheduling.

In this study, the authors designed a drug supply chain network with uncertainty-related corruption. The optimal number and location of potential facilities, the optimal allocation of flow between facilities, the optimal routing of vehicles and the optimal amount of inventory in production and distribution center warehouses were determined to achieve these two objective functions.

In evaluating the small sample size problem, it was found that the comprehensive benchmarking method was more efficient than the other methods in obtaining the mean index of the first objective function. The utility function method has also proved its efficiency in obtaining the mean of the second objective function indices, the spacing index and the computational time. Because of the inefficiency of GAMS software in resolving size issues, the modified NSGA II and MOPSO algorithms with modified priority-based encryption have been used. First, using the Taguchi method, the initial parameters of the metaheuristic algorithms are adjusted, and then, 15 sample problems are designed in larger sizes. To avoid generating random data, five problems were equally designed, and the averages of objective functions and metrics of met heuristic algorithms (number of efficient solutions, maximum expansion index, spacing index and computational time) were analyzed as the basis of evaluation and comparison. Therefore, using all the indicators and results of the NSGA II algorithm is recommended.

In this research, a biobjective modeling approach is proposed to minimize the total costs of the supply chain network (construction costs, storage costs and product transportation costs between centers) and advertising costs and to minimize distribution and transportation scheduling across each level of the supply chain network.

Adsorption parameters (e.g. Langmuir constant, mass transfer coefficient and Thomas rate constant) are involved in the design of aqueous-media adsorption treatment units. However, the classic approach to estimating such parameters is perceived to be imprecise. Herein, the essential features and performances of the ant colony, bee colony and elephant herd optimisation approaches are introduced to the experimental chemist and chemical engineer engaged in adsorption research for aqueous systems. Key research and development directions, believed to harness these algorithms for real-scale water treatment (which falls within the wide-ranging coverage of the Sustainable Development Goal 6 (SDG 6) ‘Clean Water and Sanitation for All’), are also proposed. The ant colony, bee colony and elephant herd optimisations have higher precision and accuracy, and are particularly efficient in finding the global optimum solution. It is hoped that the discussions can stimulate both the experimental chemist and chemical engineer to delineate the progress achieved so far and collaborate further to devise strategies for integrating these intelligent optimisations in the design and operation of real multicomponent multi-complexity adsorption systems for water purification.