THE VEHICLE ROUTING PROBLEM (VRP) IS CENTRAL TO LAST-MILE LOGISTICS, YET A GAP REMAINS WHEN PRODUCTS HAVE LATE RELEASE TIMES AND VEHICLES CAN BE RELOADED EN ROUTE VIA MOBILE SATELLITES THAT RENDEZVOUS WITH RELOADING VEHICLES AT CUSTOMER LOCATIONS. WE PROPOSE THE VRP WITH RELEASE TIMES AND RELOADING AT MOBILE SATELLITES (VRP-RT-RMS) AND DEVELOP TWO MIXED-INTEGER LINEAR PROGRAMMING FORMULATIONS: A THREE-INDEX (MILP-3) AND A TWO-INDEX (MILP-2). THE OBJECTIVE MINIMIZES TOTAL DISTANCE SUBJECT TO CAPACITY, ROUTE DURATION, SYNCHRONIZATION, AND TIME CONSTRAINTS. WE GENERATED 40 INSTANCES FROM REAL DATA (10 PER SIZE N E{10,15,20,25}). EN-ROUTE RELOADS SIMULTANEOUSLY REDUCE DISTANCE AND FLEET SIZE AND CAN RESTORE FEASIBILITY WHEN THE CLASSICAL VRP IS INFEASIBLE. TO CONTRAST THE CLASSICAL VRP WITH OUR VRP-RT-RMS, WE ANALYZED A PARTICULAR INSTANCE WITH N =10 CUSTOMERS: TOTAL DISTANCE DECREASED BY 7.26% AND THE NUMBER OF VEHICLES FELL FROM 5 TO 3. AS INSTANCE SIZE GROWS, MILP-2 SHOWS SUPERIOR SCALABILITY AND EFFICIENCY COMPARED WITH MILP-3. BEYOND THE TECHNICAL SCOPE, COORDINATING RELOADS IS PERTINENT TO URBAN OPERATIONS WITH LATE PRODUCT RELEASES, LOWERING KILOMETERS TRAVELED AND DELIVERY TIMES.

THE VEHICLE-ROUTING PROBLEM (VRP) REPRESENTS A CRITICAL CHALLENGE IN LOGISTICS, ENCOMPASSING NUMEROUS VARIATIONS, SUCH AS TIME WINDOW CONSIDERATIONS, MULTI-DEPOT SYSTEMS, TWO-ECHELON ROUTING ASPECTS, AND SATELLITE LOCATIONS (SL). SLS ARE INTERMEDIATE FACILITIES THAT SUPPORT CROSS-DOCKING, STORAGE, AND TRANSSHIPMENT OPERATIONS. HOWEVER, INCONSISTENCIES IN DEFINING ?SATELLITE? HAVE HINDERED PRECISE RESEARCH AND IMPLEMENTATION. THIS STUDY PRESENTS A SYSTEMATIC REVIEW OF THE USE OF SATELLITES FOR VRP, EMPLOYING THE PRISMA METHODOLOGY TO ENSURE A COMPREHENSIVE AND REPRODUCIBLE ANALYSIS. THE FINDINGS INDICATE THAT ABOUT 50% OF THE REVIEWED PAPERS INCLUDE A PATH-SPLITTING VARIANT. AT THE SAME TIME, THERE IS A NOTABLE GAP IN ADDRESSING RANDOM DEMANDS AND PICKUP AND DELIVERY WITHIN CROSS-DOCKING ENVIRONMENTS. A MAJOR LIMITATION IS THE LACK OF A WELL-KNOWN PUBLIC DATASET, AS ABOUT 50% OF THE DATASETS ARE CREATED OR ADAPTED FOR SPECIFIC STUDIES. ADDITIONALLY, THE ANALYSIS REVEALS SIGNIFICANT GAPS IN DATASET STANDARDIZATION AND THE INTEGRATION OF DYNAMIC ROUTING UNDER UNCERTAINTY. THESE FINDINGS UNDERSCORE THE POTENTIAL OF SATELLITE-BASED SYSTEMS TO OPTIMIZE URBAN LOGISTICS AND SUPPLY CHAINS WHILE POINTING TO CRITICAL AVENUES FOR FUTURE RESEARCH.