A data-driven mathematical model to design a responsive-sustainable pharmaceutical supply chain network: a Benders decomposition approach

The pharmaceutical supply chain is unique to other supply chains due to certain characteristics. Medicine is classified as a valuable asset, and any minor disruption in its supply chain can result in significant crises. So, this work develops a novel multi-objective model to configure a responsive sustainable pharmaceutical supply chain network by considering Cap-and-Trade policy, different manufacturing technologies selections, and different transportation modes selections. The model seeks to minimize the overall costs, environmental harms, and travel times for dissatisfied clients, whose requests must be answered by distribution centers constructed in other locations to maximize the chain's responsiveness. This study is highly beneficial in practical applications where finding the optimal location of nodes that satisfy multiple constraints is critical. Moreover, it increases the efficiency of resource allocation, reduces travel time and cost, and determines the optimal flow of products between nodes. Furthermore, time series-based machine learning algorithms are conducted to forecast the demand for medicine to decrease the possibility of a shortage of pharma supply in the supply chain network. By examining several methods, it is revealed that the Prophet model has superior performance to other models. So, this method is utilized to forecast demand. The goal attainment method is first used to solve small problem instances to meet the suggested model. However, this method was inefficient for solving large-sized examples. As a result, Bender's decomposition solution approach is used. The presented decision model's efficacy is evaluated against a real-life case study. Moreover, a sensitivity analysis is done on important parameters to offer insightful managerial information. The sensitivity analysis results show that the third objective function (which represents overall travel times for unmet clients) increases as demand rises. This indicates that unsatisfied demand has increased. Moreover, with a 20% increase in demand, the overall travel time increases by 49%. So, pharmacies can use prediction tools to avoid crises and plan for the future. Furthermore, based on the findings of this work, estimating the precise amount of demand for each period is impactful in diminishing shortage.