THIS PAPER DEALS WITH THE PROBLEMS FACED WITH THE DESIGNING AND PLANNING OF A SPORTING FIXTURE CONSIDERING CORRECT REFEREE ASSIGNMENTS. A NON-LINEAR BINARY PROGRAM MODEL IS PROPOSED TO SOLVE THE PROBLEMS, WHICH AIMS TO MINIMIZE THE SUMS OF THE DIFFERENCES THAT EXIST BETWEEN THE REQUIREMENTS OF EACH MATCH AND THE QUALITY OF THE REFEREE ASSIGNED ACHIEVING THE DESIGN OF THE MOST ADEQUATE REFEREE FOR EACH MATCH. THE EFFICIENCY OF THE PROPOSED MODEL IS PROVED USING SOME REAL DATA OBTAINED FROM VARIOUS FIXTURES FOR SPORTS SUCH AS SOCCER, VOLLEYBALL, AND BASKETBALL. THE MATHEMATICAL MODEL IS SOLVED BY USING CPLEX 12.7.0., WHICH ALLOWS THE AUTOMATIC LINEARIZATION OF THE PROBLEMS. THE RESULTS OBTAINED DEMONSTRATE THE EFFICIENCY OF THE PROPOSED METHODOLOGY FOR TACKLING PROBLEMS, AS WELL AS ITS EXTENSION TO OTHER SPORTING DISCIPLINES, WHICH REQUIRE A SIMILAR TYPE OF PLANNING. SIMILARLY, GIVEN THE ROBUST NATURE OF THE PROPOSED MODEL, IT IS POSSIBLE TO IMPLEMENT OTHER OBJECTIVE FUNCTIONS IN ACCORDANCE WITH THE REQUIREMENTS OF EACH LEAGUE.

PURPOSE: WE CONSIDER A REAL CASE STUDY OF A VEHICLE ROUTING PROBLEM WITH A HETEROGENEOUS FLEET AND TIME WINDOWS (HFVRPTW) FOR A FRANCHISE COMPANY BOTTLING COCA-COLA PRODUCTS IN COLOMBIA. THIS STUDY AIMS TO DETERMINE THE ROUTES TO BE PERFORMED TO FULFILL THE DEMAND OF THE CUSTOMERS BY USING A HETEROGENEOUS FLEET AND CONSIDERING SOFT TIME WINDOWS. THE OBJECTIVE IS TO MINIMIZE THE DISTANCE TRAVELED BY THE PERFORMED ROUTES. DESIGN/METHODOLOGY/APPROACH: WE PROPOSE A TWO-PHASE HEURISTIC ALGORITHM. IN THE PROPOSED APPROACH, AFTER AN INITIAL PHASE (FIRST PHASE), A GRANULAR TABU SEARCH IS APPLIED DURING THE IMPROVEMENT PHASE (SECOND PHASE). TWO ADDITIONAL PROCEDURES ARE CONSIDERED TO HELP THAT THE ALGORITHM COULD ESCAPE FROM LOCAL OPTIMUM, GIVEN THAT DURING A GIVEN NUMBER OF ITERATIONS THERE HAS BEEN NO IMPROVEMENT. FINDINGS: COMPUTATIONAL EXPERIMENTS ON REAL INSTANCES SHOW THAT THE PROPOSED ALGORITHM IS ABLE TO OBTAIN HIGH-QUALITY SOLUTIONS WITHIN A SHORT COMPUTING TIME COMPARED TO THE RESULTS FOUND BY THE SOFTWARE THAT THE COMPANY CURRENTLY USES TO PLAN THE DAILY ROUTES. ORIGINALITY/VALUE: WE PROPOSE A NOVEL METAHEURISTIC ALGORITHM FOR SOLVING A REAL ROUTING PROBLEM BY CONSIDERING HETEROGENEOUS FLEET AND TIME WINDOWS. THE EFFICIENCY OF THE PROPOSED APPROACH HAS BEEN TESTED ON REAL INSTANCES, AND THE COMPUTATIONAL EXPERIMENTS SHOWN ITS APPLICABILITY AND PERFORMANCE FOR SOLVING NP-HARD PROBLEMS RELATED WITH ROUTING PROBLEMS WITH SIMILAR CHARACTERISTICS. THE PROPOSED ALGORITHM WAS ABLE TO IMPROVE SOME OF THE CURRENT SOLUTIONS APPLIED BY THE COMPANY BY REDUCING THE ROUTE LENGTH AND THE NUMBER OF VEHICLES.

WE CONSIDER A REAL CASE STUDY OF A VEHICLE ROUTING PROBLEM WITH A HETEROGENEOUS FLEET AND TIME WINDOWS (HFVRPTW) FOR A FRANCHISE COMPANY BOTTLING COCA-COLA PRODUCTS IN COLOMBIA. THIS STUDY AIMS TO DETERMINE THE ROUTES TO BE PERFORMED TO FULFILL THE DEMAND OF THE CUSTOMERS BY USING A HETEROGENEOUS FLEET AND CONSIDERING SOFT TIME WINDOWS. THE OBJECTIVE IS TO MINIMIZE THE DISTANCE TRAVELED BY THE PERFORMED ROUTES. WE PROPOSE A TWO-PHASE HEURISTIC ALGORITHM. IN THE PROPOSED APPROACH, AFTER AN INITIAL PHASE (FIRST PHASE), A GRANULAR TABU SEARCH IS APPLIED DURING THE IMPROVEMENT PHASE (SECOND PHASE). TWO ADDITIONAL PROCEDURES ARE CONSIDERED TO HELP THAT THE ALGORITHM COULD ESCAPE FROM LOCAL OPTIMUM, GIVEN THAT DURING A GIVEN NUMBER OF ITERATIONS THERE HAS BEEN NO IMPROVEMENT. COMPUTATIONAL EXPERIMENTS ON REAL INSTANCES SHOW THAT THE PROPOSED ALGORITHM IS ABLE TO OBTAIN HIGH-QUALITY SOLUTIONS WITHIN A SHORT COMPUTING TIME COMPARED TO THE RESULTS FOUND BY THE SOFTWARE THAT THE COMPANY CURRENTLY USES TO PLAN THE DAILY ROUTES.

THIS PAPER PROPOSES A NEW HEURISTIC ALGORITHM FOR THE CAPACITATED LOCATION-ROUTING PROBLEM (CLRP), CALLED GRANULAR VARIABLE TABU NEIGHBORHOOD SEARCH (GVTNS). THIS HEURISTIC INCLUDES A GRANULAR TABU SEARCH WITHIN A VARIABLE NEIGHBORHOOD SEARCH ALGORITHM. THE PROPOSED ALGORITHM IS EXPERIMENTALLY COMPARED ON THE BENCHMARK INSTANCES FROM THE LITERATURE WITH SEVERAL OF THE MOST EFFECTIVE HEURISTICS PROPOSED FOR THE SOLUTION OF THE CLRP, BY TAKING INTO ACCOUNT THE CPU TIME AND THE QUALITY OF THE SOLUTIONS OBTAINED. THE COMPUTATIONAL RESULTS SHOW THAT GVTNS IS ABLE TO OBTAIN GOOD AVERAGE SOLUTIONS IN SHORT CPU TIMES, AND TO IMPROVE FIVE BEST KNOWN SOLUTIONS FROM THE LITERATURE. THE MAIN CONTRIBUTION OF THIS PAPER IS TO SHOW A SUCCESSFUL NEW HEURISTIC FOR THE CLRP, COMBINING TWO KNOWN HEURISTIC APPROACHES TO IMPROVE THE GLOBAL PERFORMANCE OF THE PROPOSED ALGORITHM FOR WHAT CONCERNS BOTH THE QUALITY OF THE SOLUTIONS AND THE COMPUTING TIMES REQUIRED TO FIND THEM.

IN THIS PAPER, WE PROPOSE A HYBRID GRANULAR TABU SEARCH ALGORITHM TO SOLVE THE MULTI-DEPOT VEHICLE ROUTING PROBLEM (MDVRP). WE ARE GIVEN ON INPUT A SET OF IDENTICAL VEHICLES (EACH HAVING A CAPACITY AND A MAXIMUM DURATION), A SET OF DEPOTS, AND A SET OF CUSTOMERS WITH DETERMINISTIC DEMANDS AND SERVICE TIMES. THE PROBLEM CONSISTS OF DETERMINING THE ROUTES TO BE PERFORMED TO FULFILL THE DEMAND OF THE CUSTOMERS BY SATISFYING, FOR EACH ROUTE, THE ASSOCIATED CAPACITY AND MAXIMUM DURATION CONSTRAINTS. THE OBJECTIVE IS TO MINIMIZE THE SUM OF THE TRAVELING COSTS RELATED TO THE PERFORMED ROUTES. THE PROPOSED ALGORITHM IS BASED ON A HEURISTIC FRAMEWORK PREVIOUSLY INTRODUCED BY THE AUTHORS FOR THE SOLUTION OF THE CAPACITATED LOCATION ROUTING PROBLEM (CLRP). THE ALGORITHM APPLIES A HYBRID GRANULAR TABU SEARCH PROCEDURE, WHICH CONSIDERS DIFFERENT NEIGHBORHOODS AND DIVERSIFICATION STRATEGIES, TO IMPROVE THE INITIAL SOLUTION OBTAINED BY A HYBRID PROCEDURE. COMPUTATIONAL EXPERIMENTS ON BENCHMARK INSTANCES FROM THE LITERATURE SHOW THAT THE PROPOSED ALGORITHM IS ABLE TO PRODUCE, WITHIN SHORT COMPUTING TIME, SEVERAL BEST SOLUTIONS OBTAINED BY THE PREVIOUSLY PUBLISHED METHODS AND NEW BEST SOLUTIONS.

THIS PAPER ADDRESSES THE CAPACITATED LOCATION-ROUTING PROBLEM (CLRP) IN WHICH THE AIM IS TO DETERMINE THE DEPOTS TO BE OPENED, THE CUSTOMERS TO BE ASSIGNED TO EACH OPEN DEPOT, AND THE ROUTES TO BE PERFORMED TO FULFILL THE DEMAND OF THE CUSTOMERS. THE OBJECTIVE IS TO MINIMIZE THE SUM OF THE COST OF THE OPEN DEPOTS, OF THE USED VEHICLE COSTS, AND OF THE VARIABLE COSTS ASSOCIATED WITH THE DISTANCE TRAVELED BY THE PERFORMED ROUTES. IN THIS PAPER, A GRANULAR TABU SEARCH (GTS) WITH DIFFERENT DIVERSIFICATION STRATEGIES WITHIN A ITERATED LOCAL SEARCH (ILS) IS PROPOSED TO SOLVE THE CLRP. A SHAKING PROCEDURE IS APPLIED WHENEVER THE BEST SOLUTION FOUND SO FAR IS NOT IMPROVED FOR A GIVEN NUMBER OF ITERATIONS. COMPUTATIONAL EXPERIMENTS ON BENCHMARK INSTANCES TAKEN FROM THE LITERATURE SHOW THAT THE PROPOSED APPROACH IS ABLE TO OBTAIN, WITHIN SHORT COMPUTING TIMES, HIGH QUALITY SOLUTIONS ILLUSTRATING ITS EFFECTIVENESS.

IN THIS WORK, WE INTRODUCE A HYBRID METAHEURISTIC APPROACH FOR THE 3L-CVRP. THE PROPOSED APPROACH USES AN INITIAL SOLUTION OBTAINED BY A MODIFIED CLARK & WRIGHT ALGORITHM CONSIDERING THE PACKING CONSTRAINTS BY A GRASP SCHEME. THEN, A GRANULAR TABU SEARCH (GTS) ALGORITHM IS EMPLOYED TO IMPROVE THE INITIAL SOLUTION, MEANWHILE THE GRASP APPROACH VALIDATES THE PACKING CONSTRAINTS DURING THE SEARCH PROCESS. THE PROPOSED ALGORITHM HAS BEEN COMPARED WITH THE MOST EFFECTIVE ALGORITHMS PROPOSED FOR THE 3L-CVRP. COMPUTATIONAL RESULTS SHOW THE EFFECTIVENESS OF THE PROPOSED APPROACH.

THE COLLECTION, TRANSPORT, AND FINAL DISPOSAL OF HOSPITAL WASTE MAY CAUSE CONTAMINATION AND DISEASE IF IMPROPERLY HANDLED. THEREFORE, SUCH RESIDUES ARE HAZARDOUS TO THE HEALTH OF WASTE COLLECTORS. THESE WASTES ARE GENERATED BY PUBLIC AGENCIES, SUCH AS HOSPITALS, FAMILY HEALTH CENTERS, DIALYSIS CENTERS, AND PRIVATE HEALTHCARE PROVIDERS. IN THIS STUDY, A MIXED-INTEGER LINEAR PROGRAMMING MODEL IS PROPOSED FOR MONTHLY CUSTOMER SCHEDULING AND ROUTE ASSIGNMENT. THE PROPOSED APPROACH WAS FULFILLED ACCORDING TO CUSTOMERS? COLLECTION FREQUENCY, TRUCK CAPACITY, AND CUSTOMER GEOGRAPHICAL LOCATION. THE PROPOSED MATHEMATICAL MODEL SUCCESSFULLY BALANCED THE NUMBER OF CUSTOMERS AND THE WORKLOAD DURING EACH DAY. THE EFFECTIVENESS OF THE PROPOSED MODEL WAS TESTED ON DATA OBTAINED FROM A WASTE COLLECTION COMPANY. THE MODEL HAS BEEN IMPLEMENTED IN AMPL LANGUAGE, AND THE PERFORMANCE OF COMMERCIAL SOLVERS, GUROBI AND CPLEX, TO OBTAIN AN OPTIMAL SOLUTION WERE TESTED. THE RESULTS SHOW THE EFFICIENCY OF THE PROPOSED APPROACH TO BALANCE THE WORKLOAD CONCERNING PREVIOUS SCHEDULING IS DONE AD HOC AT THE COMPANY. THE USE OF THE FORMULATED MODEL PROVIDES AN AUTOMATIC PROCEDURE THAT WAS PREVIOUSLY PERFORMED MANUALLY. THE METHODOLOGY CAN BE ADAPTED TO OTHER COMPANIES WITH SIMILAR REQUIREMENTS.

SOME OF THE COMPLEX LOGISTICAL PROBLEMS FACED BY COMPANIES COMBINE THE NEEDS FOR STRATEGIC AND TACTICAL DECISIONS CONCERNING THE INTERRELATED ISSUES OF CLUSTERING, SCHEDULING, AND ROUTING. VARIOUS STRATEGIES CAN BE USED TO SOLVE THESE PROBLEMS. WE PRESENT A PROBLEM OF THIS TYPE, INVOLVING A COMPANY WHOSE FUNDAMENTAL OBJECTIVE IS THE COMMERCIALIZATION OF ITS PRODUCT IN THE DOMESTIC MARKET. THE PAPER FOCUSES ON A MODEL OF AND METHOD FOR A SOLUTION TO THE PROBLEM OF SCHEDULING VISITS TO CUSTOMERS, TAKING INTO ACCOUNT THE RELATIONSHIP WITH OTHER PHASES OF PRODUCT MARKETING. THE MODEL IS NONLINEAR, INVOLVES BINARY AND CONTINUOUS VARIABLES, AND SOLVED HEURISTICALLY. COMPUTATIONAL EXPERIMENTS SHOW THAT THE PROPOSED SOLUTION PERFORMED VERY WELL FOR BOTH REAL-LIFE AND THEORETICAL INSTANCES.

THIS PAPER INTRODUCES THE MULTI-DEPOT MULTI-TRAVELLING SALESMAN PROBLEM WITH SPLIT AND DELIVERY DEMAND (MMTSP-SD). THE PROBLEM HAS BEEN FORMULATED AS A FLEXIBLE OPTIMISATION MODEL THAT CONSIDERS FOUR KEY PERFORMANCE INDICATORS (KPIS): THE MINIMISATION OF THE ROUTE DISTANCE, THE MINIMUM DAILY DEMAND TO SATISFY SIMILAR DEMAND BETWEEN CREWS, AND THE EQUIVALENT KILOMETRES TRAVELLED BETWEEN CREWS. THE EFFICIENCY OF THE PROPOSED APPROACH HAS BEEN TESTED IN THREE TYPES OF INSTANCES ADAPTED FROM A GREEN AREA MAINTENANCE COMPANY DEDICATED TO THE MANAGEMENT OF ANY VEGETATION, CUTTING GRASS OR WEEDS AND/OR COLLECTING LEAVES, WATERING, OR FERTILISING, AMONG MANY OTHER SERVICES. THE RESULTS CONFIRM THE EFFICIENCY OF THE PROPOSED APPROACH AND THE POSITIVE IMPACT IN DETERMINING THE DIFFERENT PERFORMANCE MEASURES THAT ARE CONSIDERED.

THIS INVESTIGATION PRESENTS A NEW MATHEMATICAL MODEL TO SOLVE THE VEHICLE ROUTING PROBLEM WITH BACKHAULS AND TIME WINDOWS (VRPBTW). IN THIS PROBLEM, CUSTOMERS ARE DIVIDED INTO TWO SUBSETS, FOR DELIVERY AND COLLECTION. EACH VEHICLE LEAVES THE WAREHOUSE TO DELIVER MERCHANDISE TO LINEHAULS CUSTOMERS. SUBSEQUENTLY, IT MAKES A COLLECTION OF MERCHANDISE TO BACKHAULS CUSTOMERS AND RETURNS TO THE DEPARTURE WAREHOUSE. IN THIS PROPOSAL, THE OBJECTIVE IS TO MINIMIZE THE TOTAL DISTANCE, SATISFYING ALL RESTRICTIONS. IN ADDITION, THE NUMBER OF VEHICLES TO MAKE THE ROUTE IS MINIMIZED. THE MODEL HAS BEEN EVALUATED BASED ON ARTIFICIAL DATA ADAPTED FROM THE LITERATURE, WHICH INCLUDES DEMAND FOR 10, 15, 20 AND 30 NODES. THE COMPUTATIONAL RESULTS CONTRIBUTE TO VALIDATE THE APPROACH AND SCALE THE PROBLEM FOR FUTURE WORK.

THIS PAPER CONSIDERS THE PROBLEM OF GENERATING PERSONALISED ROUTES FOR PEOPLE ATTENDING MUSIC FESTIVALS CONSIDERING TIME WINDOWS. THE OBJECTIVE IS TO MAXIMISE THE ATTENDEES? SATISFACTION BY CONSIDERING ELEMENTS SUCH AS THE DESIRE TO SEE SOME ARTISTS OF A FESTIVAL PROGRAM, THE TIME WINDOWS, AND THE DISTANCE BETWEEN EACH STAGE. THE PROPOSED MATHEMATICAL MODEL DETERMINES WHICH ARTISTS AN ATTENDEE SHOULD SEE AMONG THE MANY OPTIONS A MUSIC FESTIVAL OFFER. THE MORE SATISFIED AN ATTENDEE IS, THE MORE READILY THEY WILL RETURN TO THE EVENTS, IMPROVING LOGISTICS IN MUSICAL EVENTS. THE PROPOSED FORMULATION IS BASED ON THE WELL-KNOWN ORIENTEERING PROBLEM WITH TIME WINDOWS (OPTW). INSTANCES (ATTENDEES? PREFERENCES) ARE GENERATED FROM A SPECIFIC DAY OF LOLLAPALOOZA CHILE (2019), A FESTIVAL WITH SEVEN STAGES AND 120 ARTISTS DISTRIBUTED OVER THREE DAYS TO TEST THE EFFICIENCY OF THE PROPOSED METHODOLOGY. THE RESULTS ARE PROMINENT CONSIDERING THE DIVERSE TYPE OF ATTENDEES.

WE ADDRESS THE WELL-KNOWN DISTANCE CONSTRAINED CAPACITATED VEHICLE ROUTING PROBLEM (DCVRP) BY CONSIDERING EUCLIDEAN DISTANCES, IN WHICH THE AIM IS TO DETERMINE THE ROUTES TO BE PERFORMED TO FULFIL THE DEMAND OF THE CUSTOMERS BY USING A HOMOGENEOUS FLEET. THE OBJECTIVE IS TO MINIMISE THE SUM OF THE VARIABLE COSTS ASSOCIATED WITH THE DISTANCE TRAVELLED BY THE PERFORMED ROUTES. IN THIS PAPER, WE PROPOSE A METAHEURISTIC ALGORITHM BASED ON A PROBABILISTIC GRANULAR TABU SEARCH (PGTS) BY CONSIDERING DIFFERENT NEIGHBOURHOODS. IN PARTICULAR, THE PROPOSED ALGORITHM SELECTS A NEIGHBOURHOOD BY USING A PROBABILISTIC DISCRETE FUNCTION, WHICH IS MODIFIED DYNAMICALLY DURING THE SEARCH BY FAVOURING THE MOVES THAT HAVE IMPROVED THE BEST SOLUTION FOUND SO FAR. A SHAKING PROCEDURE IS APPLIED WHENEVER THE BEST SOLUTION FOUND SO FAR IS NOT IMPROVED FOR A GIVEN NUMBER OF ITERATIONS. COMPUTATIONAL EXPERIMENTS ON BENCHMARK INSTANCES TAKEN FROM THE LITERATURE SHOW THAT THE PROPOSED APPROACH IS ABLE TO OBTAIN HIGH QUALITY SOLUTIONS, WITHIN SHORT COMPUTING TIMES.

WE PROPOSE A META-HEURISTIC ALGORITHM FOR ADDRESSING A REAL CASE OF VEHICLE ROUTING PROBLEM WITH A HETEROGENEOUS FLEET AND TIME WINDOWS. OUR PROPOSAL CONSISTS OF GENERATING AN INITIAL FEASIBLE SOLUTION USING THE SOLUTION OF A TRAVELLING SALESMAN PROBLEM AND, SUBSEQUENTLY, REFINING IT THROUGH SIMULATED ANNEALING. IN THIS WORK, WE EVALUATE THE SUITABILITY OF OUR DEVELOPMENT TO PLANNING THE DISTRIBUTION OF A REGIONAL DISTRIBUTION CENTRE OF A FOOD COMPANY TO CUSTOMERS WITHIN THE URBAN PERIMETER OF CALI, COLOMBIA. FOLLOWING THE COMPANY S CUSTOMER SATISFACTION GOALS, OUR PRIMARY AIM IS TO ROUTE TO REACH A SERVICE LEVEL OF 95% WHILE REDUCING OPERATIONAL COSTS. OUR RESULTS ON OUR REAL CASE STUDY SHOW THAT OUR META-HEURISTIC ALGORITHM FINDS BETTER ROUTES THAN CURRENT ONES, IN TERMS OF COSTS AND SERVICE LEVELS, IN A RELATIVELY SHORT TIME.

IN THIS PAPER, A TWO-PHASE HYBRID ALGORITHM TO ADDRESS THE PROBLEM OF SCHEDULING VISITS TO CUSTOMERS AND THE VEHICLE ROUTING PROBLEM OF MEDICATION DELIVERY TO HIGHLY DEPENDENT PATIENTS IS PROPOSED. IN THE FIRST PHASE, THE ISSUE OF DAILY SCHEDULING FOR A CLUSTER OF CUSTOMERS IS SOLVED VIA A FLEXIBLE MATHEMATICAL OPTIMIZATION MODEL APPLIED TO DIFFERENT SCENARIOS. THE SOLUTION OBTAINED IN THE FIRST PHASE GENERATES CLUSTERS OF PATIENTS AND A FREQUENCY ROUTING PROBLEM THAT CONSIDERS DELIVERY PERIODICITY, LOCATION, DEMAND, SERVICE TIMES, TRAVEL TIMES, AND DAILY LOAD-BALANCING CONSTRAINTS. IN THE SECOND PHASE, A HYBRID METAHEURISTIC APPROACH INCLUDING THE SYNERGY AND CONSTANT ITERATION BETWEEN SIMULATED ANNEALING AND A RECORD-TO-RECORD ALGORITHM IS APPLIED TO IMPROVE THE INITIAL SOLUTION OBTAINED IN THE FIRST PHASE. THE EFFECTIVENESS OF THE PROPOSED ALGORITHM IS VALIDATED WITH REAL DATA OBTAINED FROM A PILOT PROJECT IN CHILE. THE RESULTS ARE PROMISING AND DEMONSTRATE THE EFFICIENCY OF THE PROPOSED METHODOLOGY.

THE USE OF PUBLIC BICYCLE SYSTEMS HAS GAINED GREAT IMPORTANCE IN EUROPEAN COUNTRIES AND AROUND THE GLOBE; THIS HAS LED TO THE NEED TO SEEK ADVANCED TECHNIQUES TO HELP DECISION MAKING. A PUBLIC BICYCLE SYSTEM CONSISTS OF A SET OF POINTS WHERE YOU CAN PICK UP AND DELIVER BICYCLES; A HEADQUARTERS WHERE A GROUP OF VEHICLES TAKING LEFTOVER BIKES AND TRANSPORTED TO THE POINTS WHERE A DEFICIT (THE DEMAND EXCEEDS SUPPLY) EXISTS. ONE OF THE MAJOR PROBLEMS THAT ARISE IN SYSTEMS OF PUBLIC BIKE IS BALANCED, WHICH INVOLVES SENDING BIKES FROM THE POINT WHERE AN OFFER (BICYCLES LEFT OVER) TO THE POINT WHERE THERE IS A DEMAND (BIKES MISSING) OCCURS. THE WAY TO MODEL THIS PROBLEM IS WITH AN ADAPTATION OF THE VEHICLE ROUTING PROBLEM WITH PICKUP AND DELIVERY (VRPPD), ALLOWING EACH ROUTE MAKE PARTIAL DELIVERIES TO CUSTOMERS AND LIMITING THE NUMBER OF CUSTOMERS TO VISIT BY EACH ROUTE. IN THIS PAPER AN INTEGER LINEAR PROGRAMMING MODEL IS INTRODUCED AND A METAHEURISTIC BASED ON GRANULAR TABU SEARCH TO FIND A LOCAL OPTIMUM. INSTANCES FROM 15 TO 500 CUSTOMERS ADAPTED FROM THE LITERATURE ARE USED. THE COMPUTATIONAL RESULTS SHOW THAT THE PROPOSED ALGORITHM FINDS SOLUTIONS IN SHORT COMPUTATIONAL TIME.

TIS PAPER ADDRESSES A METHOD TO SOLVE A MULTI-PERIOD PORTFOLIO SELECTION ON THE STOCK MARKET. TE PORTFOLIO PROBLEM SEEKS AN INVESTOR TO TRADE STOCKS WITH A FNITE BUDGET AND A GIVEN INTEGER NUMBER OF STOCKS TO HOLD IN A PORTFOLIO. TE TRADE MUST BE PERFORMED THROUGH A STOCKBROKER THAT CHARGES ITS RESPECTIVE TRANSACTION COST AND HAS ITS MINIMUM REQUIRED TRADE AMOUNT. A MATHEMATICAL MODEL HAS BEEN PROPOSED TO DEAL WITH THE CONSTRAINED PROBLEM. TE OBJECTIVE FUNCTION IS TO FND THE BEST RISK-RETURN RATE; THUS, SHARPE RATIO AND TREYNOR RATIO ARE USED AS OBJECTIVE FUNCTIONS. TE RETURNS ARE THE SAME FOR THESE RATIOS, BUT THE RISKS ARE NOT SHARPE CONSIDERING COVARIANCE AND TREYNOR SYSTEMATICAL RISK. TE RETURNS ARE PREDICTED USING A NEURAL NET WITH LONG-SHORT-TERM MEMORY (LSTM). TIS NEURAL NET IS COMPARED WITH SIMPLE FORECASTING METHODS THROUGH MEAN ABSOLUTE PERCENTAGE ERROR (MAPE). COMPUTATIONAL EXPERIMENTS SHOW THE QUALITY PREDICTION PERFORMED BY LSTM. TE HETEROSKEDASTIC RISK IS ESTIMATED BY GENERALIZED AUTOREGRESSIVE CONDITIONAL HETEROSKEDASTICITY (GARCH), ADJUSTING THE VARIANCE FOR EVERY PERIOD; THIS RISK MEASURE IS USED IN SHARPE RATIO. TE EXPERIMENT CONTEMPLATES A WEEKLY PORTFOLIO SELECTION WITH 5 AND 10 STOCKS IN 122 WEEKLY PERIODS FOR EACH CHILEAN MARKET RATIO. TE BEST PORTFOLIO IS SHARPE RATIO WITH TEN STOCKS, PERFORMING A 62.28% REAL RETURN BEATING THE MARKET, REPRESENTED BY THE SELECTIVE STOCK PRICE INDEX (IPSA). EVEN THE WORST PORTFOLIO, TREYNOR RATIO, OVERCOMES THE IPSA CUMULATIVE YIELD WITH TEN STOCKS.