Solving a Special Case of the Generalized Assignment Problem Using the Modified Differential Evolution Algorithms: A Case Study in Sugarcane Harvesting

We proposed and created a methodology to solve a real-world problem, which is a special case of the generalized assignment problem. The problem consists of assigning drivers to harvesters, which will then be assigned to harvest sugarcane in order to maximize daily profit. A set of drivers have various levels of experience. Therefore, a different capability to harvest sugarcane leads to a range of daily wages. Each harvester has different operating years and engine size, which affects its fuel consumption rate and capacity to harvest sugarcane, respectively. Assigning a worker to a harvester can improve the fuel consumption and efficiency of the harvester. We developed a mathematical model to reflect this problem and to solve it to find the maximum outcome using Lingo v.11 commercial optimization software. Since Lingo v.11 is limited to solving only small-size test instances, for medium to large test instances, four modified differential evolution (MDE) algorithms were used to solve the problem: MDE-1, MDE-2, MDE-3, and MDE-4. MDE-2 was found to be the best proposed heuristics because it has intensification and diversification ability. MDE has been tested with the case study. We tried to increase the daily profit by implementing three strategies: (1) change all harvesters that are more than five years old, (2) train drivers to reach maximum capacity, and (3) a combination of 1 and 2. Each strategy has a different investment. The breakeven point (number of days) to return the investment was calculated from the increase of daily profit. The computational results show that strategy 2 is the best because it has the quickest rate of investment return rate. However, this strategy has a disadvantage, since it is possible that drivers may leave the company if they have been highly trained. Moreover, strategy 1 has an acceptable break-even point at 392 days.

[1]  Kyungbae Park,et al.  Dynamics from open innovation to evolutionary change , 2016 .

[2]  Kanchana Sethanan,et al.  Improved differential evolution algorithms for solving generalized assignment problem , 2016, Expert Syst. Appl..

[3]  Rapeepan Pitakaso,et al.  Differential evolution algorithm for simple assembly line balancing type 1 (SALBP-1) , 2015 .

[4]  Marshall L. Fisher,et al.  A generalized assignment heuristic for vehicle routing , 1981, Networks.

[5]  Yeong-Dae Kim,et al.  Algorithms for a two-machine flowshop problem with jobs of two classes , 2020, Int. Trans. Oper. Res..

[6]  Kanchana Sethanan,et al.  A differential evolution algorithm for the capacitated VRP with flexibility of mixing pickup and delivery services and the maximum duration of a route in poultry industry , 2017, J. Intell. Manuf..

[7]  J. Yun,et al.  The Effect of Open Innovation on Technology Value and Technology Transfer: A Comparative Analysis of the Automotive, Robotics, and Aviation Industries of Korea , 2018, Sustainability.

[8]  Lale Özbakir,et al.  Bees algorithm for generalized assignment problem , 2010, Appl. Math. Comput..

[9]  Richard M. Soland,et al.  A branch and bound algorithm for the generalized assignment problem , 1975, Math. Program..

[10]  Marcin Wozniak,et al.  Hybrid neuro-heuristic methodology for simulation and control of dynamic systems over time interval , 2017, Neural Networks.

[11]  G. van Straten,et al.  Optimal control of nitrate in lettuce by a hybrid approach: differential evolution and adjustable control weight gradient algorithms , 2003 .

[12]  John E. Beasley,et al.  A genetic algorithm for the generalised assignment problem , 1997, Comput. Oper. Res..

[13]  Sang-Oh Shim,et al.  Innovative Production Scheduling with Customer Satisfaction Based Measurement for the Sustainability of Manufacturing Firms , 2017 .

[14]  Mohamed Haouari,et al.  Optimization-Based Very Large-Scale Neighborhood Search for Generalized Assignment Problems with Location/Allocation Considerations , 2016, INFORMS J. Comput..

[15]  Ibrahim H. Osman,et al.  Heuristics for the generalised assignment problem: simulated annealing and tabu search approaches , 1995 .

[16]  Sang-Oh Shim,et al.  Heuristic algorithms for two-machine re-entrant flowshop scheduling problem with jobs of two classes , 2017 .

[17]  Raknoi Akararungruangkul,et al.  Modified Differential Evolution Algorithm Solving the Special Case of Location Routing Problem , 2018, Mathematical and Computational Applications.

[18]  Sang-Oh Shim,et al.  Multi-level job scheduling under processing time uncertainty , 2018, Comput. Ind. Eng..

[19]  Marcin Wozniak,et al.  Bio-inspired methods modeled for respiratory disease detection from medical images , 2018, Swarm Evol. Comput..

[20]  Marcin Wozniak,et al.  Polar Bear Optimization Algorithm: Meta-Heuristic with Fast Population Movement and Dynamic Birth and Death Mechanism , 2017, Symmetry.

[21]  Juan A. Díaz,et al.  A Tabu search heuristic for the generalized assignment problem , 2001, Eur. J. Oper. Res..

[22]  Alan R. McKendall,et al.  A tabu search heuristic for a generalized quadratic assignment problem , 2017 .

[23]  Martin W. P. Savelsbergh,et al.  A Branch-and-Price Algorithm for the Generalized Assignment Problem , 1997, Oper. Res..

[24]  Mohamed Haouari,et al.  Exact Solution Methods for a Generalized Assignment Problem with Location/Allocation Considerations , 2016, INFORMS J. Comput..

[25]  Kanchana Sethanan,et al.  Differential evolution algorithms for scheduling raw milk transportation , 2016, Comput. Electron. Agric..

[26]  Xian Wei,et al.  An Improved Whale Optimization Algorithm Based on Different Searching Paths and Perceptual Disturbance , 2018, Symmetry.

[27]  Moustafa Elshafei,et al.  A dynamic programming algorithm for days-off scheduling with sequence dependent labor costs , 2008, J. Sched..

[28]  Marcin Wozniak,et al.  Adaptive neuro-heuristic hybrid model for fruit peel defects detection , 2018, Neural Networks.

[29]  María Auxilio Osorio Lama,et al.  Logic cuts for multilevel generalized assignment problems , 2003, Eur. J. Oper. Res..

[30]  Sang-Oh Shim,et al.  Technology for Production Scheduling of Jobs for Open Innovation and Sustainability with Fixed Processing Property on Parallel Machines , 2016 .

[31]  J. P. Kelly,et al.  Tabu search for the multilevel generalized assignment problem , 1995 .

[32]  John M. Wilson,et al.  A hybrid tabu search/branch & bound approach to solving the generalized assignment problem , 2010, Eur. J. Oper. Res..

[33]  Sasitorn Kaewman,et al.  Methodology to Solve the Combination of the Generalized Assignment Problem and the Vehicle Routing Problem: A Case Study in Drug and Medical Instrument Sales and Service , 2018, Administrative Sciences.

[34]  Sasitorn Kaewman,et al.  Differential Evolution Algorithm for Multilevel Assignment Problem: A Case Study in Chicken Transportation , 2018, Mathematical and Computational Applications.

[35]  Seyedali Mirjalili,et al.  Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems , 2015, Neural Computing and Applications.

[36]  Reuven Cohen,et al.  An efficient approximation for the Generalized Assignment Problem , 2006, Inf. Process. Lett..

[37]  Kanchana Sethanan,et al.  Modified differential evolution algorithm for simple assembly line balancing with a limit on the number of machine types , 2016 .

[38]  Benavídes Rodríguez,et al.  Selección de cepas nativas de bacterias aerobias formadoras de endospora como promotoras de crecimiento vegetal con enfasis en su capacidad antagonista contra Xanthomonas campestris pv. vitians del cultivo de lechuga , 2019 .