Applied Mathematical Sciences, Vol. 14, 2020, no. 14, 669 - 677 HIKARI Ltd, / www.m-hikari.com https://doi.org/10.12988/ams.2020.912157 Optimal Predictive Algorithm for the Pickup and Delivery Problem with Time Windows and Scheduled Lines: Innovative Routing Transport Systems F. Nahayo 1 and M. Bigirimana 2 1 Research University Laboratory in Applied Statistics Modeling and Engineering ”LURMISTA”, Institute of Applied Statistics ”ISTA” University of Burundi, Burundi 2 Research University Laboratory in Applied Statistics Modeling and Engineering ”LURMISTA”,University of Burundi, Burundi This article is distributed under the Creative Commons by-nc-nd Attribution License. Copyright © 2020 Hikari Ltd. Abstract This paper concerns the Pickup and Delivery Problem with Time Windows and Scheduled Lines ”PDPTW-SL” by modeling it mathe- matically on the one hand with the help of dynamic programming, on the other hand, it presents two optimal predictive methods of com- binatorial optimization intended to solve it and which must provide stable and high accuracy solutions. The Pickup and Delivery Problem with Time Windows and Scheduled lines aims at routing a given set of vehicles to transport freight requests from their origins to their corre- sponding destinations, where the requests can use scheduled passenger transportation services during a stump of their journeys. We describe the PDPTW-SL as a mixed-integer program. Computational results on a set of small-size instances provide a clear understanding of the benefits of preprocessing step and valid inequalities using scheduled line services as a part of freights journey. Keywords: Dynamic programming, Pickup and Delivery Problem, Rout- ing and Scheduling, Transport Systems, Combinatorial optimization