Fuzzy Multi-objective Mixed-integer Programming Research Articles

A New Decision Framework of Online Multi-Attribute Reverse Auctions for Green Supplier Selection under Mixed Uncertainty

In order to realize the “dual carbon” goal proposed for the world and to seek the low-carbon and sustainable development of the economy and society, the green supply chain management problem faced by Chinese enterprises and governments is particularly important. At the same time, how to quickly and efficiently select the suitable green supplier is the most basic and critical link in green supply chain management, as well as an important issue that Chinese government and enterprises must face in the process of green material procurement. In addition, there are various uncertainties emerging in the current market environment that hinder the green suppliers and the buyer to make the efficient decisions. Therefore, in order to find a more suitable and efficient method for green supplier selection, from the standpoint of the buyer, a new decision framework of online multi-sourcing, multi-attribute reverse auction (OMSMARA), which effectively improves the procurement efficiency and reduces procurement costs and risks, is proposed under the mixed uncertainty. Specifically, the main innovation work includes three aspects: Firstly, the trapezoidal fuzzy numbers are applied to describe the uncertain bidding attribute values by the green suppliers. Secondly, the hesitant fuzzy sets theory is introduced to characterize the buyer’s satisfaction degrees of the bidding evaluation attribute information, and the attribute weights are determined by using the hesitant fuzzy maximizing deviation method. Thirdly, a fuzzy multi-objective mixed integer programming model is proposed to solve the green supplier selection and quantity allocation question in OMSMARA. A numerical example is given to demonstrate the feasibility and effectiveness of the proposed decision framework, and the sensitivity analysis and comparison analysis further show the robustness and reliability of the proposed solution method.

Fuzzy multi-objective optimization for multi-site integrated production and distribution planning in two echelon supply chain

This paper addresses an integrated production and distribution planning problem for a two-echelon supply chain network comprising of multiple manufacturers serving multiple selling locations. A novel fuzzy multi-objective mixed integer programming model is formulated considering multi-product, multi-period, and multi-site manufacturing environment. Minimization of total cost, delivery time, and backorder level are the three fuzzy objectives represented by piecewise linear membership function. Three important production and distribution aspects viz. capacity of the heterogeneous transportation, backordering for unfulfilled demand, and set-up cost/time for different products at manufacturing site are incorporated in an integrated manner to represent closeness to the real-life problem. An illustrative example inspired from a real-world case of an automobile industry is taken to demonstrate analytical results of the proposed approach. The outcome of the research indicates the practical applicability of the approach. Sensitivity analysis on objective function values is conducted for analyzing the effect of change in aspiration levels of objective function values on decision maker’s satisfaction level.

Application of Two-Phase Fuzzy Optimization Approach to Multiproduct Multistage Integrated Production Planning with Linguistic Preference under Uncertainty

This paper tackles the challenges for a production planning problem with linguistic preference on the objectives in an uncertain multiproduct multistage manufacturing environment. The uncertain sources are modelled by fuzzy sets and involve those induced by both the epistemic factors of process and external factors from customers and suppliers. A fuzzy multiobjective mixed integer programming model with different objective priorities is proposed to address the problem which attempts to simultaneously minimize the relevant operations cost and maximize the average safety stock holding level and the average service level. The epistemic and external uncertainty is simultaneously considered and formulated as flexible constraints. By defining the priority levels, a two-phase fuzzy optimization approach is used to manage the preference extent and convert the original model into an auxiliary crisp one. Then a novel interactive solution approach is proposed to solve this problem. An industrial case originating from a steel rolling plant is applied to implement the proposed approach. The numerical results demonstrate the efficiency and feasibility to handle the linguistic preference and provide a compromised solution in an uncertain environment.

Multiproduct vendor selection with volume discounts as the fuzzy multi-objective programming problem

Vendor selection in supply chain is a multi-criteria problem that involves a number of quantitative and qualitative factors. This paper deals with a concrete problem of flour purchase by a company that manufactures bakery products. The selection process is driven by the price, reliability and quality objectives of the buyer and is subject to the capacity constraints of the vendors in the situation where all suppliers offer several kinds of flour (multiproduct situation). Vendors often offer quantity discounts, i.e. the purchasing price of flour depends on the quantity ordered. The multiproduct situation complicates the mathematical formulation of the problem and in this context it is much more convenient to consider the discounts of the money volume of business with every vendor. This problem has been solved using an integration of analytic hierarchy process (AHP), weighted sum model (WSM) and fuzzy multi-objective mixed-integer programming to define the optimum quantities among the selected suppliers.

A new approach for long term planning of solid waste management systems using fuzzy global criterion

Recent studies regarding solid waste management system planning frequently emphasize that both socioeconomic and environmental impacts have to be considered simultaneously. While the total elimination of environmental risks is impossible, the analytical concern actually rests upon the concept of the minimization of both environmental risks and costs in an efficient management system. But uncertainty plays an important role in decision making. The related impreciseness/fuzziness of environmental risks were rarely taken into account in previous models. This paper illustrates a new approach, using fuzzy global criterion technique, to show how the concept of fuzzy environmental resources can be incorporated into an optimization process and create a set of more flexible optimal planning alternatives. A fuzzy multiobjective mixed integer programming model for long term planning of metropolitan solid waste management systems is applied as a method for generating such alternatives. The practical implementation of this approach is assessed by a case study in the City of Kaohsiung in Taiwan.