The present work deals with the multi-product straight pipeline scheduling problem. The considered straight pipeline system is used to transport refined petroleum products from a single source (refinery with storage tanks) to a single destination (distribution center). The main objective is to find a sequence of batches which aims to maximize the total volume to be transported via the pipeline, while meeting the daily customer demands over a fixed time horizon. Each batch contains only one product with a volume between its upper and lower bounds. Constraints related to inventory levels, batch settling periods and forbidden sequences between pairs of products must be respected, and pipeline stoppage periods should also be handled. A Mixed Integer Linear Programming (MILP) model and a Greedy Randomized Adaptive Search Procedure (GRASP)-like algorithm are proposed to tackle the problem under study. The MILP model is based on the discharging time axis with continuous representation for both time and volume formulation. The GRASP-like algorithm is composed of a construction method and an improvement procedure. The construction method generates a new sequence of batches in a random way with the use of a repair process to obtain an initial solution that satisfies all demands. Then, the improvement procedure is attempted to increase the fill rate of pipeline using volume optimization operators without change the sequence of products. A set of instances was generated from a real case study in order to validate the proposed approach. The performance of our approach is benchmarked against the MILP model (solved using Gurobi Solver), and the numerical experiments proved that the proposed approach obtains very competitive results both in term of solution quality and CPU time.