International Journal of Mathematical and Computational Methods W. Wongsinlatam et al. http://www.iaras.org/iaras/journals/ijmcm A Mixed Integer Linear Programming for Maximizing Effectiveness of Case Assignment in Court of Justice using Metaheuristic Optimization W. WONGSINLATAM1, K. PIMPILA2, A. WONGPHAT3, AND S. BUCHITCHON4* 1 Faculty of Applied Science and Engineering, Khon Kaen University, Nong Khai Campus, Nong Khai, 43000, THAILAND E-mail address : [email protected] 2 Faculty of Education, Rajabhat Phetchabun University, Phetchabun, 67000, THAILAND E-mail address : [email protected] 3 Faculty of Science and Technology, Rajabhat Mahasarakham University, Mahasarakham, 44000, THAILAND E-mail address : [email protected] 4 Faculty of Integrated Social Sciences, Khon Kaen University, Nong Khai Campus, Nong Khai, 43000, THAILAND *Corresponding author E-mail address : [email protected] Abstract: - It is known that litigation is time consuming. However, justice delayed is justice denied. The effectiveness of judicial system depends on the efficient and timely manner of court case operation. Court case assignment in Thailand is currently operated in a random assignment norm. However, the increasing number of cases in the court of justice contributes as a building block to the reputation of time consuming operating system. Selecting the right cases to be assigned to the available efficient judge in the area is a vital need for judicial operation. Therefore, major challenges with respect to court case assignment are to determine the right case to be assigned to the right efficient judge in the field and to allocate appropriate time for delivering the court decision in order to maximize the effectiveness of the judicial system. In this article, the selected math model is a mixed integer linear programming that is developed to analyze and solve the problem. A metaheuristic algorithm with polynomially bounded computational complexity is proposed to address the issue. Furthermore, results of extensive computational experiments to empirically evaluate its effectiveness to find an optimal solution are reported. Key-Words: - Justice administration, Case assignment, Mixed integer programming, Assignment problem, Metaheuristic method, NP-hard problem 1 Introduction However, the increasing number of cases in the Justice administration and case assignment court of justice contributes as a building block to the are routine works in judicial system. However, the reputation of time consuming operating system. In effectiveness of such work represents as a goal of the last decade, caseload in the court of Thailand has judicial system which is to ensure the rule of law. dramatically increased. This is due to the change in The ‘rule of law’ means that the administration of constitutional law which requires a full quorum of justice and other exercise of public authority must judges – generally a team of two - to be seated at a be predictable and consistent [1]. hearing. It is known that litigation is time Several proposals have been made to consuming. The effectiveness of judicial system increase system efficiency including case depends on the efficient and timely manner of court management, court-annexed mediation, and digital case operation. Court case assignment in Thailand is audio testimony recording system [2]. Case currently operated in a random assignment norm. assignment is one of the most significant tools in ISSN: 2367-895X 415 Volume 1, 2016 International Journal of Mathematical and Computational Methods W. Wongsinlatam et al. http://www.iaras.org/iaras/journals/ijmcm case management to improve efficiency of judicial high quality calcium carbonate slurry, supplied to system. It is proposed in this paper that selecting the European paper manufacturers. Christodoulos A. right cases to be assigned to the available efficient Floudas [6] applied the scheduling of chemical judge in the area is a vital need for judicial processing systems based on MILP approaches operation. Therefore, major challenges with respect which improved the computational efficiency in the to court case assignment are to determine the right solution of MILP problems. However, the use of case to be assigned to the right efficient judge in the MILP model in juridical problem is still limited. field and to allocate appropriate time for delivering Metaheuristic optimizations purpose is to the court decision in order to maximize the find optimal solution for NP-hard problem which effectiveness of the judicial system. solves the local minima problem to find the global In mathematics, mathematical modelling minima that solve several practical optimization transforms the real problem into the objective problems. The algorithm of metaheuristic methods function with constrained or unconstrained is made of a random number that moves in a wide optimization problems to find an exact solution or feasible solution to solve several optimization optimal solution. The mathematical modelling is problem. The metaheuristic method reduces the time being used in several fields of science and in finding the exact solution or the good solution in technology. The objective function is generally the problem. Popular methods for assignment being formed in convex programming, nonlinear problem includes; Ant Colony Optimization (ACO) programming, and stochastic programming. The [7]; Tabu Search (TS) [8]; Particle Swarm new trend of objective function is interested in Optimization (PSO) [9]; and Firefly Algorithm (FA) forming the mixed integer linear programming. The [10]. mixed integer linear programming (MILP) is In this paper, the practical problem in popular in the problem of assignment because the juridical area is being used as assignment problem. objective function of minimize or maximize Selecting the right cases to be assigned to the optimization in MILP is more effective than the available efficient judge in the area is a vital need linear or nonlinear programming. MILP is a mixed for judicial operation. Therefore, major challenges of the several forms of programming which with respect to court case assignment are to combined the binary integer programming with determine the right case to be assigned to the right linear programming. efficient judge in the field and to allocate This research uses the metaheuristic method appropriate time for delivering the court decision in for assignment problem of the court case and order to maximize the effectiveness of the judicial coordination of justice team. The objective of system. The objective function is used the MILP assignment problem includes N cases that must be optimization model of case analysis and assigned to N teams where each team has the examination. The goal of this proposed model is to competence to do all cases. However, due to maximize the overall effectiveness in identifying the personal ability, case specification or other reasons, perpetrator of the crime. each team may spend different time for minimize or The rest of the paper proceeds as follows: maximize with the objective of assignment problem. Section 2 is an introduction to assignment problem In planning the working system in an of the case assignment in court of justice. The organization, the coordination of workers and tasks objective function uses the MILP optimization by is a major consideration that reflects the efficiency using two metaheuristic optimizations. The of the company. The Mixed integer programming computational results and discussion about the (MIP) was used in the examination proctor effectiveness of the proposed metaheuristic assignment problem by Takeshi Koide where staffs algorithms in finding an optimal are provided in are assigned for examinations as proctors in the Section 3. Finally, section 4 summarizes our regular examination period [3]. Julia Rieck et al. [4] conclusions. applied the project scheduling problems subject to general temporal constraints using MILP model and domain-reducing processing techniques. The models 2 The Case Assignment in the Court used CPLEX 12.1 software to solve lower and upper bounds for resource requirements at particular of Justice points in time. David Bredström et al. [5] used MILP model for barge transport planning on the 2.1 The definition of problem river Rhine. The planning solved the supply chain management of Omya’s production of Norwegian ISSN: 2367-895X 416 Volume 1, 2016 International Journal of Mathematical and Computational Methods W. Wongsinlatam et al. http://www.iaras.org/iaras/journals/ijmcm Nomenclature 2.2 The formulation of problem C index set for cases assignment. {1,2,...,n } The MILP model formulation for the above P index set for justice panel. {1,2,..., m} problem is as follows: nm c each case assignment. cC∈ . maximize ZT=∑∑µi ⋅ ij (1) effective rate for case assignment. ij=11 = µc L lower bounds on justice time. Constraints: c n upper bounds on justice time. Uc ∑Tij ≤ MT; ∀ jm≤ (2) MT maximum time for justice deadline. i=1 T− XU ⋅≤0; ∀ i≤≤ nj, m (3) T assignment of case c to the right justice. ij ij i cj T− XL ⋅≥0; ∀ i≤≤ nj, m (4) X an binary decision variable. ij ij i ij m ∑ X ij ≤1; ∀ in≤ (5) To define the problem, consider the j=1 following scenario: A set Cn= {}1,2,.., of n cases 1, if case i is selected to justice j; X ij = has been filed to the court of justice where a set 0, otherwise; Pm= {}1,2,.., of m are available justice panels ∀≤ i nj, ≤ m (6) forming justice teams. If case cC∈ is selected for We assume that the effectiveness rate of a justice team, at least Lt time units must be spent µµ µ to deliver the court decision. Also, the maximum cases administration are 12, ,.., n , respectively. amount of time to be spent on each case cC∈ must The objective function according equation (1) for not exceed U be time units since spending more the above problem is defined to the overall t effectiveness of the judicial procedure. The than this time would distort justice. constraint in equation (2) is the total time spent on a To simplify the presentation of our approach sequential of case does not exceed the maximum to develop and solve a mathematical model for this allowable time MT for each justice team.