THE HIERARCHICAL NETWORK DESIGN PROBLEM CONSISTS OF LOCATING A MINIMUM COST BI-LEVEL NETWORK ON A GRAPH. THE HIGHER LEVEL SUB-NETWORK IS A PATH VISITING TWO OR MORE NODES. THE LOWER LEVEL SUB-NETWORK IS A FOREST CONNECTING THE REMAINING NODES TO THE PATH. WE OPTIMALLY SOLVE THE PROBLEM USING AN AD HOC BRANCH AND CUT PROCEDURE. RELAXED VERSIONS OF A BASE MODEL ARE SOLVED USING AN OPTIMIZATION PACKAGE AND, IF BINARY VARIABLES HAVE FRACTIONAL VALUES OR IF SOME OF THE RELAXED CONSTRAINTS ARE VIOLATED IN THE SOLUTION, CUTTING PLANES ARE ADDED. ONCE NO MORE CUTS CAN BE ADDED, BRANCH AND BOUND IS USED. THE METHOD FOR FINDING VALID CUTTING PLANES IS PRESENTED. FINALLY, WE USE DIFFERENT AVAILABLE TEST INSTANCES TO COMPARE THE PROCEDURE WITH THE BEST KNOWN PUBLISHED OPTIMAL PROCEDURE, WITH GOOD RESULTS. IN NONE OF THE INSTANCES WE NEEDED TO APPLY BRANCH AND BOUND, BUT ONLY THE CUTTING PLANES.

SE INTRODUCE UN PROBLEMA DE RECOLECCIÓN DE LECHE CON LA MEZCLA. UNA EMPRESA RECOGE LECHE DE LAS GRANJAS, Y CADA GRANJA PRODUCE UNA DE LAS TRES POSIBLES CUALIDADES DE LA LECHE. LOS INGRESOS AUMENTAN CON LA CALIDAD, Y HAY UN REQUISITO MÍNIMO EN LA PLANTA PARA CADA CALIDAD. DIFERENTES CUALIDADES DE LA LECHE SE PUEDEN MEZCLAR EN LOS CAMIONES, REDUCIENDO LOS INGRESOS, PERO TAMBIÉN LOS COSTOS DE TRANSPORTE, LO QUE RESULTA EN UN MAYOR BENEFICIO. SE PROPONE UN MODELO MIXTO DE PROGRAMACIÓN ENTERA, UN NUEVO CORTE Y UN ALGORITMO DE RAMIFICACIÓN Y CORTE PARA RESOLVER INSTANCIAS DE TAMAÑO MEDIO. UNA HEURÍSTICA DE TRES ETAPAS ESTÁ DISEÑADA PARA GRANDES INSTANCIAS. SE PRESENTA LA EXPERIENCIA COMPUTACIONAL PARA CASOS DE PRUEBA Y UN CASO REAL DE GRAN TAMAÑO

IN THE FIELD OF WATER MANAGEMENT, DESALINATION INDUSTRY HAS FACED VARIOUS ECONOMIC AND ENVIRONMENTAL CHALLENGES. RENEWABLE ENERGIES AND THE INCORPORATION OF OPERATIONAL STRATEGIES SUCH AS DEMAND-SIDE MANAGEMENT HAVE BEEN ABLE TO CONTRIBUTE WITH THE AIM OF FACING THEM. NONETHELESS, IT IS NECESSARY TO CONTINUE STUDYING DEMAND-SIDE MANAGEMENT FOR WATER SUPPLY SYSTEMS EMPHASISING IT AS A STRATEGIC TOOL TO MAKE OPERATIONAL DECISIONS. THIS ARTICLE PRESENTS A METHODOLOGY BASED ON A NOVEL MIXED-INTEGER LINEAR PROGRAMMING MODEL IN ORDER TO PROGRAM THE OPERATION OF A SEAWATER REVERSE OSMOSIS DESALINATION PLANT WITH ONE PUMPING STATION FOR A DESERTIC REMOTE AGRICULTURAL ZONE, IN ACCORDANCE WITH THE PRINCIPLES OF DEMAND-SIDE MANAGEMENT. A PHOTOVOLTAIC SOLAR PLANT CONNECTED TO THE GRID IS CONSIDERED AS A RENEWABLE ENERGY SOURCE. THE MATHEMATICAL MODEL AIMS TO ESTABLISH THE OPTIMAL HOURLY OPERATING LOAD OF THE SYSTEM THAT MINIMISES THE DAILY MARGIN OF PURCHASED ELECTRICITY COSTS MINUS SALES INCOME OF GENERATED ELECTRICITY. THE CASE STUDY WHERE THE METHODOLOGY IS TESTED IS AN AGRICULTURAL AREA IN NORTHERN CHILE. THE PROPOSED METHODOLOGY IN THIS PAPER ESTABLISHES THE BASIS FOR FUTURE RESEARCH AND INDUSTRIAL APPLICATIONS, CONSIDERING THAT IT CAN BE GENERALISED TO OTHER GEOGRAPHICAL SITUATIONS, AS WELL AS BEING MODIFIABLE TO BE ADAPTED FOR MORE COMPLEX WATER SUPPLY SYSTEMS AND/OR OTHER RENEWABLE ENERGY SOURCES.

IN THIS ARTICLE, WE PRESENT AN EASY TO IMPLEMENT ALGORITHMIC APPROACH THAT IMPROVES THE COMPUTATIONAL PERFORMANCE OF THE MILLER?TUCKER?ZEMLIN (MTZ) MODEL FOR THE ASYMMETRIC TRAVELING SALESMAN PROBLEM (ATSP) BY EFFICIENTLY GENERATING VALID INEQUALITIES FROM FRACTIONAL SOLUTIONS. COMPUTATIONAL EXPERIMENTS SHOW THAT THE PROPOSED APPROACH ENHANCES CONSIDERABLY THE PERFORMANCE OF MTZ-BASED FORMULATIONS REPORTED IN THE LITERATURE. BY ADDING FACET-DEFINING INEQUALITIES OF THE UNDERLINE ATSP-POLYTOPE, THE NUMBER OF NODES IN THE BRANCH-AND-BOUND TREE IS DRASTICALLY REDUCED, AND THE CONVERGENCE OF THE MTZ-TYPE FORMULATIONS IS ACCELERATED. WE ALSO EXTEND THIS IDEA TO SOLVE THE MULTIPLE ASYMMETRIC TRAVELING SALESMAN PROBLEM (MATSP). THIS APPROACH CAN HELP PRACTITIONERS TO SOLVE REAL-LIFE PROBLEMS TO NEAR OPTIMALITY USING A STANDARD OPTIMIZATION SOLVER AND MAY BE USEFUL TO SOLVE A VARIETY OF ROUTING PROBLEMS THAT USE MTZ-TYPE OF SUBTOUR ELIMINATION CONSTRAINTS.

WE ADDRESS THE P-CABLE-TRENCH PROBLEM. IN THIS PROBLEM, P FACILITIES ARE LOCATED, A TRENCH NETWORK IS DUG AND CABLES ARE LAID IN THE TRENCHES, SO THAT EVERY CUSTOMER OR DEMAND IN THE REGION IS CONNECTED TO A FACILITY THROUGH A CABLE. THE DIGGING COST OF THE TRENCHES, AS WELL AS THE SUM OF THE CABLE LENGTHS BETWEEN THE CUSTOMERS AND THEIR ASSIGNED FACILITIES, ARE MINIMIZED. WE FORMULATE AN INTEGER PROGRAMMING MODEL OF THE PROBLEM USING MULTICOMMODITY FLOWS THAT ALLOWS FINDING THE SOLUTION FOR INSTANCES OF UP TO 200 NODES. WE ALSO PROPOSE TWO LAGRANGEAN RELAXATION-BASED HEURISTICS TO SOLVE LARGER INSTANCES OF THE PROBLEM. COMPUTATIONAL EXPERIENCE IS PROVIDED FOR INSTANCES OF UP TO 300 NODES.

A FREE PATH (WITH NO PRESET EXTREME NODES) IS LOCATED ON A NETWORK, IN SUCH A WAY AS TO MINIMIZE THE COST AND MAXIMIZE THE TRAFFIC CAPTURED BY THE PATH. TRAFFIC BETWEEN A PAIR OF NODES IS CAPTURED IF BOTH NODES ARE VISITED BY THE PATH. APPLICATIONS ARE THE DESIGN OF THE ROUTE AND LOCATIONS OF MAILBOXES FOR A LOCAL PACKAGE DELIVERY COMPANY, OR THE DESIGN OF BUS OR SUBWAY LINES, IN WHICH THE SHAPE OF THE ROUTE AND THE NUMBER OF STOPS IS DETERMINED BY THE SOLUTION OF THE OPTIMIZATION PROBLEM. THE PROBLEM ALSO APPLIES TO THE DESIGN OF AN OPTICAL FIBER NETWORK INTERCONNECTING WIFI ANTENNAS IN A UNIVERSITY CAMPUS. WE PROPOSE TWO MODELS AND AN EXACT SOLUTION METHOD. COMPUTATIONAL EXPERIENCE IS PRESENTED FOR UP TO 300 NODES AND 1772 ARCS, AS WELL AS A PRACTICAL CASE FOR THE CITY OF CONCEPCIÓN, CHILE.

THE ELECTORAL MAP REPRESENTATIVENESS OF THE BINOMIAL VOTING SYSTEM USED IN CHILE HAS ALWAYS HAD PROBLEMS IN THE ELECTIONS. ALTHOUGH THE REFORM OF THE YEAR 2015 FIXED A PORTION OF THE DISTORTIONS, THIS SYSTEM STILL HAS ISSUES WITH THE ACCORDANCE BETWEEN THE VOTING AND THE PARLIAMENTARY SEATS. UNDER THIS CIRCUMSTANCE, A MATHEMATICAL PROGRAMMING MODEL IS PROPOSED WHICH DEFINES THE DISTRICT DISTRIBUTION AND SEAT ASSIGNMENT IN THE LOWER HOUSE OF CHILE, OBTAINING SIGNIFICANT IMPROVEMENTS IN THREE REPRESENTATIVENESS INDICATORS. THE IMPLICATIONS OF THIS REDISTRIBUTION AT THE LEVEL OF POLITICAL ANALYSIS ARE IMPORTANT; HOWEVER, THEY ARE NOT CONSIDERED IN THIS PAPER.

IN MANY REAL-WORLD SITUATIONS, THE BENEFICIARIES OF A DISTRIBUTION SYSTEM MAY BE GROUPED INTO CLUSTERS, REQUIRING A TRANSPORTATION STRUCTURE TO SERVE EACH CLUSTER OF BENEFICIARIES EFFICIENTLY. FOR INSTANCE, IN PUBLIC SERVICES, SUCH AS HEALTH, EDUCATION, AND EMERGENCIES, DELIVERY TASKS RELY ON THE LOCAL AUTHORITY OF EACH DISTRICT OR CLUSTER. IN THIS CONTEXT, A TWO-LEVEL DISTRIBUTION SYSTEM NAMED THE TWO-LEVEL GENERALIZED MEDIAN TOUR PROBLEM (TLGMTP) IS INTRODUCED. THE FIRST LEVEL ADDRESSES PRODUCT DISTRIBUTION USING A SPECIALIZED VEHICLE, STARTING AND ENDING AT A DEPOT AND VISITING SOME CLUSTERS. IN THIS MANNER, PRODUCTS ARE DELIVERED TO ONE OR MORE NODES BELONGING TO THE VISITED CLUSTERS. THE SECOND LEVEL COMPRISES SMALLER VEHICLES THAT START THEIR TRIPS FROM THE NODES BELONGING TO THE FIRST LEVEL AND TRANSPORT THE PRODUCTS TO ONE OR MORE NODES LOCATED IN A NON-VISITED CLUSTER, ENSURING THAT ALL NON-VISITED CLUSTERS OF THE FIRST LEVEL ARE VISITED IN THE SECOND LEVEL. THEN, THE NON-VISITED NODES IN EACH CLUSTER MUST REACH A NODE IN THE SAME CLUSTER TO COLLECT THEIR PRODUCTS. IN THIS STUDY, WE PRESENT, MODEL, AND SOLVE THE TLGMTP TO MINIMIZE THE TOTAL TRANSPORTATION COSTS. WE DEVELOP THREE MATHEMATICAL FORMULATIONS AND SOLVE THEM USING A BRANCH-AND-CUT ALGORITHM. EXHAUSTIVE COMPUTATIONAL EXPERIMENTS INVOLVING TESTS AND REAL-WORLD INSTANCES ARE PRESENTED TO SHOW THE EFFICIENCY AND ADVANTAGES OF THE PROPOSED METHODOLOGY.

THIS PAPER PROPOSES A TRACTABLE MODEL FOR THE DESIGN OF A RAPID TRANSIT SYSTEM. TRAVEL COST IS MINIMIZED AND TRAFFIC CAPTURE IS MAXIMIZED. THE PROBLEM IS MODELED ON AN UNDIRECTED GRAPH AND CAST AS AN INTEGER LINEAR PROGRAM. THE IDEA IS TO BUILD SEGMENTS WITHIN BROAD CORRIDORS TO CONNECT SOME VERTEX SETS. THESE SEGMENTS CAN THEN BE ASSEMBLED INTO LINES, AT A LATER STAGE. THE MODEL IS SOLVED BY BRANCH-AND-CUT WITHIN THE CPLEX FRAMEWORK. TESTS CONDUCTED ON DATA FROM CONCEPCIÓN, CHILE, CONFIRM THE EFFECTIVENESS OF THE PROPOSED METHODOLOGY.

MOBILE DENTAL CLINICS (MDCS) ARE SUITABLE SOLUTIONS FOR SERVICING PEOPLE LIVING IN RURAL AND URBAN AREAS THAT REQUIRE DENTAL HEALTHCARE. MDCS CAN PROVIDE DENTAL CARE TO THE MOST VULNERABLE HIGH-SCHOOL STUDENTS. HOWEVER, SCHEDULING MDCS TO VISIT PATIENTS IS CRITICAL TO DEVELOPING EFCIENT DENTAL PROGRAMS. HERE, WE STUDY A MOBILE DENTAL CLINIC SCHEDULING PROBLEM THAT ARISES FROM THE REAL-LIFE LOGISTICS MANAGEMENT CHALLENGE FACED BY A SCHOOL-BASED MOBILE DENTAL CARE PROGRAM IN SOUTHERN CHILE. THIS PROBLEM INVOLVES SCHEDULING MDCS TO TREAT HIGH-SCHOOL STUDENTS AT PUBLIC SCHOOLS WHILE CONSIDERING A FAIRNESS CONSTRAINT AMONG DISTRICTS. SCHOOLS ARE CIRCUMSCRIBED INTO DISTRICTS, AND BY PROGRAM REGULATIONS, AT LEAST 50% OF THE STUDENTS IN EACH DISTRICT MUST RECEIVE DENTAL CARE DURING THE FRST SEMESTER. FAIRNESS PREVENTS SOME DISTRICTS FROM WAITING MORE TIME TO RECEIVE DENTAL CARE THAN OTHERS. WE MODEL THE PROBLEM AS A PARALLEL MACHINE SCHEDULING PROBLEM WITH SEQUENCE-DEPENDENT SETUP COSTS AND BATCH DUE DATES AND PROPOSE A MATHEMATICAL MODEL AND A GENETIC ALGORITHM-BASED SOLUTION TO SOLVE THE PROBLEM. OUR COMPUTATIONAL RESULTS DEMONSTRATE THE EFECTIVENESS OF OUR APPROACHES IN OBTAINING NEAR-OPTIMAL SOLUTIONS. FINALLY, DENTAL PROGRAM MANAGERS CAN USE THE METHODOLOGIES PRESENTED IN THIS WORK TO SCHEDULE MOBILE DENTAL CLINICS AND IMPROVE THEIR OPERATIONS.

THIS PAPER INTRODUCES AND STUDIES THE BI-OBJECTIVE INSULAR TRAVELING SALESMAN PROBLEM, WHERE A SET OF RURAL ISLANDS MUST BE SERVED USING A SINGLE BARGE FOLLOWING A SINGLE ROUTE. EACH ISLAND PRESENTS A NUMBER OF DOCKS FROM WHICH AT LEAST ONE DOCK MUST BE SELECTED FOR VISITING. ONE DISTINCTIVE FEATURE IS THAT THE FREIGHT TO BE COLLECTED FROM EACH DOCK OR NODE IS NOT KNOWN IN ADVANCE, SINCE THEY DEPEND ON A SET OF SELECTED DOCKS AT EACH ISLAND AND ON THE STRATEGY EMPLOYED TO ALLOCATE THE ISLAND DEMANDS AMONG THE VISITED DOCKS. IN CONTRAST TO OTHER SIMILAR PROBLEMS FOUND IN THE LITERATURE, PARTICULARLY THE GENERALIZED TRAVELING SALESMAN PROBLEM, TWO OBJECTIVE FUNCTIONS ARE AIMED TO BE MINIMIZED: MARITIME AND GROUND TRANSPORTATION COSTS. THE GROUND TRANSPORTATION COST INCURRED AT THE ISLANDS IS STRONGLY RELATED TO THE STRATEGY FOR TRANSPORTING THE FREIGHT TO THE SELECTED DOCKS INSIDE THE ISLANDS, WHICH IS A DISTINCT CHARACTERISTIC OF THE STUDIED PROBLEM. THE PROPOSED MIXED INTEGER PROGRAMMING MODEL IS SOLVED FOR A SET OF REAL INSTANCES FROM CHILE USING A WEIGHTED SUM APPROACH, DENOTING THE BI-OBJECTIVE NATURE OF THE PROBLEM. THIS PROBLEM FEATURE ALONG WITH THE OPTIMAL SOLUTION STRUCTURE ARE REVEALED AND ANALYZED, AND THE APPROPRIATENESS OF THE PROPOSED APPROACH IS HIGHLIGHTED FOR FREIGHT COLLECTION OR DISTRIBUTION DECISION MAKING IN INSULAR ZONES.

WE INTRODUCE, FORMULATE, AND SOLVE THE GENERALIZED MEDIAN TOUR PROBLEM, WHICH IS MOTIVATED IN THE HEALTH SUPPLIES DISTRIBUTION FOR URBAN AND RURAL AREAS. A REGION COMPRISES DISTRICTS THAT MUST BE SERVED BY A SPECIALIZED VEHICLE VISITING ITS HEALTH FACILITIES. WE PROPOSE A DISTRIBUTION STRATEGY TO SERVE THESE HEALTH FACILITIES EFFICIENTLY. A SINGLE TOUR IS DETERMINED THAT VISITS A SET OF HEALTH FACILITIES (NODES) COMPOSED OF DISJOINT CLUSTERS. THE TOUR MUST VISIT AT LEAST ONE FACILITY WITHIN EACH CLUSTER, AND THE UNVISITED FACILITIES ARE ASSIGNED TO THE CLOSEST FACILITY ON THE TOUR. WE MINIMIZE THE SUM OF THE TOTAL TOUR DISTANCE AND THE ACCESS DISTANCE TRAVELED BY THE UNVISITED FACILITIES. EFFICIENT FORMULATIONS ARE PROPOSED AND SEVERAL SOLUTION STRATEGIES ARE DEVELOPED TO AVOID SUBTOURS BASED ON BRANCH & CUT. WE SOLVE A SET OF TEST INSTANCES AND A REAL-WORLD INSTANCE TO SHOW THE EFFICIENCY OF OUR SOLUTION APPROACHES.