To address the multi-objective transportation problem with multi-choice costs and stochastic supply and demand, it becomes necessary to introduce a framework that takes into account the complexity and uncertainty implicit in modern logistics and supply chain management. By assigning appropriate weights to these objectives, organizations can express their preferences and priorities, thus allowing the decision-making process to be more optimized. This weighted approach ensures that the transportation network is optimized in a way that aligns with the specific goals of the organization, be it cost minimization, service level maximization, or a strategic balance between the two. The model takes into account the stochastic nature of supply and demand, recognizing that real-world conditions are rarely stable. Supply and demand can vary unpredictably due to factors like market fluctuations, seasonality, or unexpected disruptions. In essence, this model represents a holistic approach to transportation optimization, addressing not only the typical cost considerations but also the need for flexibility and adaptability in the face of uncertainty. By employing weights to the multiple objectives and accounting for stochastic supply and demand, organizations can design transportation systems that are not only cost-effective but also agile and responsive, ultimately bolstering their competitiveness in today’s ever-evolving business landscape. This paper’s main goal is to find the best way to choose cost coefficients for a transportation problem with multiple options. It uses a clever mathematical technique called Lagrange’s interpolating polynomial to minimize the overall cost. It also deals with the challenge of unpredictable supply and demand, treating it as an exciting part of the problem-solving process. In simpler terms, the paper aims to find an efficient way to transport goods even when factors like supply and demand keep changing. We used Lingo 18 software to find the best solution to our transportation problem. To show how it works, we applied our method to a real-world logistics challenge.