Optimizing Batch Scheduling of Multiproduct Pipelines Using a Smooth Modeling Approach

The main method of delivering oil products is by the sequential operation of pipelines. Scheduling oil batches efficiently, considering intricate constraints, is typically a challenging problem that is not readily solvable. The present work developed a systematic approach for the optimization of batch scheduling. The model utilized a continuous- time representation with the objective of minimizing the total costs related to energy and oil mixing loss. The analysis included multiple constraints, including time frame, oil download, flow rate, and fluctuations in pressure caused by friction at various batch interface locations. By applying the penalty function approach, the original model was transformed into an unconstrained model. Smoothing was applied to the noncontinuous variables using the Dirac delta function and the maximum entropy function. A novel nonlinear programming (NLP) model was successfully devised to enhance the efficiency of oil product scheduling. A successive function approximation algorithm was used to solve the model, and the decision variables were modified to decrease the number of model decision variables and enhance the system's capacity to surpass the local optimum. Subsequently, the model was calculated to address a practical multiproduct pipeline scheduling problem. The model presented in this study identified 74 decision variables, which account for around 1% of the typical mixed integer linear programming (MILP) model. The method presented in this work has the capability to accurately obtain an enhanced solution, making it useful for real applications.