Fuzzy Multi-objective Integer Linear Programming Research Articles

On optimisation over the integer efficient set in fuzzy linear multicriteria programming

The problem of optimising a linear function over the efficient set of a multiobjective linear programming problem is an important field of research and has some applications in multiple objective decision making. The main difficulty of this problem is that its feasible domain is non-convex and not described explicitly. The main purpose of this paper is to describe an efficient and finite new algorithm which provides a global R-optimal solution of the problem of optimising a fuzzy linear function over the efficient set of a fuzzy multiobjective integer linear programming (FMOILP) problem without having to search all integer R-efficient solutions. All the parameters of the considered problem are characterised by trapezoidal fuzzy numbers. The proposed approach is based first on the concept of comparison of fuzzy numbers by using ranking function and on an extension of Jorge's algorithm onto fuzzy numbers. Finally a numerical illustration is included for illustration.

A rolling horizon approach for material requirement planning under fuzzy lead times

This paper proposes a fuzzy multi-objective integer linear programming (FMOILP) approach to model a material requirement planning (MRP) problem with fuzzy lead times. The objective functions minimise the total costs, back-order quantities and idle times of productive resources. Capacity constraints are included by considering overtime resources. Into the crisp MRP multi-objective model, we incorporate the possibility of occurrence of each uncertain lead time using fuzzy numbers. Then FMOILP is transformed into an auxiliary crisp mixed-integer linear programming model by a fuzzy goal programming approach for each fuzzy lead time combination. In order to defuzzify the set of solutions associated with each fuzzy lead time combination, a solution method based on the centre of gravity concept is addressed. Model validation with a numerical example is carried out by a novel rolling horizon procedure where uncertain lead times are updated during each planning period according to the centre of gravity obtained. For illustration purposes, the proposed solution approach is satisfactorily compared to a rolling horizon approach in which lead times are allocated when the possibility of occurrence is established at one.

A weighted possibilistic programming approach for sustainable vendor selection and order allocation in fuzzy environment

This paper focused on the analysis of imprecise information in terms of many critical parameters for a multi-objective multi-item vendor selection-order allocation problem with price-breaks. We used both quantitative and qualitative criteria taking into account the economic, technological, social, environmental factors, and the price-breaks that were offered on order quantity following ‘all-unit discount schedule.’ We developed an optimization model that integrated fuzzy multi-objective integer linear programming and analytic hierarchy process techniques. A weighted possibilistic programming approach was presented to solve the optimization model, which simultaneously minimized (maximized) the best scenario, the likeliest scenario, and the worst scenario for the imprecise objective functions thereby avoiding situations that may force the solution process to divert. The integrated model and the solution approach were tested on the data set of an industrial case study. A detailed performance analysis and comparisons were done to show superiority of the proposed methodology over the existing related fuzzy programming approaches.

Material Requirement Planning under Fuzzy Lead Times

This paper proposes a fuzzy multi-objective integer linear programming approach to model a material requirement planning (MRP) problem with fuzzy lead times. We incorporate to the crisp MRP model the possibility of occurrence of each one of the possible lead times. Then, an objective function that maximizes the possibility of occurrence of the lead times is considered. By combining this objective with the initials of the MRP model, decision makers can play with their risk attitude of admitting lead times that improve the other objectives but have a minor possibility of occurrence.

A fuzzy optimization approach for procurement transport operational planning in an automobile supply chain

We consider a real-world automobile supply chain in which a first-tier supplier serves an assembler and determines its procurement transport planning for a second-tier supplier by using the automobile assembler’s demand information, the available capacity of trucks and inventory levels. The proposed fuzzy multi-objective integer linear programming model (FMOILP) improves the transport planning process for material procurement at the first-tier supplier level, which is subject to product groups composed of items that must be ordered together, order lot sizes, fuzzy aspiration levels for inventory and used trucks and uncertain truck maximum available capacities and minimum percentages of demand in stock. Regarding the defuzzification process, we apply two existing methods based on the weighted average method to convert the FMOILP into a crisp MOILP to then apply two different aggregation functions, which we compare, to transform this crisp MOILP into a single objective MILP model. A sensitivity analysis is included to show the impact of the objectives weight vector on the final solutions. The model, based on the full truck load material pick method, provides the quantity of products and number of containers to be loaded per truck and period. An industrial automobile supply chain case study demonstrates the feasibility of applying the proposed model and the solution methodology to a realistic procurement transport planning problem. The results provide lower stock levels and higher occupation of the trucks used to fulfill both demand and minimum inventory requirements than those obtained by the manual spreadsheet-based method.

An iterative goal programming approach for solving fuzzy multiobjective integer linear programming problems

This paper presents an iterative goal programming approach for solving fuzzy multiobjective integer linear programming problems. These problems involve fuzzy parameters in the right-hand side of the constraints. The concept of α-level set of these fuzzy parameters is introduced with the definition of their membership function. A solution algorithm is described in sequential steps to solve the formulated model. The suggested approach in this paper is mainly based on the iterative goal programming technique together with Gomory cuts. An illustrative numerical example is given to clarify the theory and the solution algorithm.

Solving a special class of large-scale fuzzy multiobjective integer linear programming problems

We present a method useful in solving a special class of large-scale multiobjective integer problems depending on the decomposition algorithm. These problems involve fuzzy parameters on the right-hand side of the independent constraints. The presented solution method is based upon a combination of the decomposition algorithm coupled with the weighting method together with the branch-and-bound method. An illustrative numerical example is given to clarify the theory and the method discussed in this paper.