Development of a decision support system for supplier evaluation and order allocation

This study aims to develop models and generate a decision support system (DSS) for the improvement of supplier evaluation and order allocation decisions in a supply chain. Supplier evaluation and order allocation are complex, multi criteria decisions. Initially, an analytic hierarchy process (AHP) model is developed for qualitative and quantitative evaluation of suppliers. Based on these evaluations, a goal programming (GP) model is developed for order allocation among suppliers. The models are integrated into a DSS that provides a dynamic, flexible and fast decision making environment. The DSS environment is tested at the purchasing department of a manufacturer and feedbacks are obtained.     

A multi-objective robust possibilistic model for technology portfolio optimization considering social impact and different types of financing

With respect to limited financial resources, prioritization of technology fields in order to be supported financially is a matter of paramount significance that governmental organizations, such as “Technology Development Funds (TDFs)”, face with. Innovation and technology development, as the cornerstone of the economic development of countries, requires making decisions in terms of assigning the best-suited form of financial resources mainly by governments. Accordingly, this study addresses a multi-objective portfolio optimization problem in a multi-period setting with the aim of maximizing the created jobs – as a key factor in social welfare – as well as intended profit while minimizing the risk of inappropriate portfolio selection. To formulate the proposed mathematical model, different financing methods, technology readiness levels (TRL), and return on investment (ROI) associated with each technological project are taken into account. Afterward, to deal with the uncertainty arisen from fuzzy parameters, the Multi-Objective Robust Possibilistic Programming approach (MORPP) is applied, the performance of which is examined under several computational tests. Finally, to illustrate the performance of the proposed model and its applicability in practice, the computational results are shown through a real case study in Iran Innovation & Prosperity Fund (IIPF). The results show that selecting small and medium-sized enterprises (SMEs) for being financed, is the best option when increasing job creation is considered in portfolio optimization. Furthermore, the comparison of the MORPP model results with the deterministic model shows that the solutions obtained from the robust possibilistic approach outweighed the deterministic model.     

Solving multiple objective quasi-convex goal programming problems by linear programming

This study presents a novel means of resolving multiple objective goal programming (GP) problems with quasi-convex linear penalty functions. The proposed method initially expresses a quasi-convex function by the maximum operator of two convex functions, then solves it via a linear programming technique. The proposed method does not contain any zero–one variables; nor does it require dividing the multi-objective quasi-convex GP problem into large sub-problems as in conventional methods. Some illustrative examples are provided.     

A two-phase approach for multi-objective programming problems with fuzzy coefficients

In this study, a two-phase procedure is introduced to solve multi-objective fuzzy linear programming problems. The procedure provides a practical solution approach, which is an integration of fuzzy parametric programming (FPP) and fuzzy linear programming (FLP), for solving real life multiple objective programming problems with all fuzzy coefficients. The interactive concept of the procedure is performed to reach simultaneous optimal solutions for all objective functions for different grades of precision according to the preferences of the decision-maker (DM). The procedure can be also performed to obtain lexicographic optimal and/or additive solutions if it is needed. In the first phase of the procedure, a family of vector optimization models is constructed by using FPP. Then in the second phase, each model is solved by FLP. The solutions are optimal and each one is an alternative decision plan for the DM.     

Variable neighborhood search for multi-objective resource allocation problems

The Resource Allocation Problem (RAP) is a classical problem in the field of operations management that has been broadly applied to real problems such as product allocation, project budgeting, resource distribution, and weapon-target assignment. In addition to focusing on a single objective, the RAP may seek to simultaneously optimize several expected but conflicting goals under conditions of resources scarcity. Thus, the single-objective RAP can be intuitively extended to become a Multi-Objective Resource Allocation Problem (MORAP) that also falls in the category of NP-Hard. Due to the complexity of the problem, metaheuristics have been proposed as a practical alternative in the selection of techniques for finding a solution. This study uses Variable Neighborhood Search (VNS) algorithms, one of the extensively used metaheuristic approaches, to solve the MORAP with two important but conflicting objectives—minimization of cost and maximization of efficiency. VNS searches the solution space by systematically changing the neighborhoods. Therefore, proper design of neighborhood structures, base solution selection strategy, and perturbation operators are used to help build a well-balanced set of non-dominated solutions. Two test instances from the literature are used to compare the performance of the competing algorithms including a hybrid genetic algorithm and an ant colony optimization algorithm. Moreover, two large instances are generated to further verify the performance of the proposed VNS algorithms. The approximated Pareto front obtained from the competing algorithms is compared with a reference Pareto front by the exhaustive search method. Three measures are considered to evaluate algorithm performance: D1_R, the Accuracy Ratio, and the number of non-dominated solutions. The results demonstrate the practicability and promise of VNS for solving multi-objective resource allocation problems.     

An interactive possibilistic programming approach for a multi-objective closed-loop supply chain network under uncertainty

In this article, we first propose a closed-loop supply chain network design that integrates network design decisions in both forward and reverse supply chain networks into a unified structure as well as incorporates the tactical decisions with strategic ones (e.g., facility location and supplier selection) at each period. To do so, various conflicting objectives and constraints are simultaneously taken into account in the presence of some uncertain parameters, such as cost coefficients and customer demands. Then, we propose a novel interactive possibilistic approach based on the well-known STEP method to solve the multi-objective mixed-integer linear programming model. To validate the presented model and solution method, a numerical test is accomplished through the application of the proposed possibilistic-STEM algorithm. The computational results demonstrate suitability of the presented model and solution method.     

Applying fuzzy multi-objective linear programming to project management decisions with the interactive two-phase method

The aim of this paper is to develop an interactive two-phase method that can help the Project Manager (PM) with solving the fuzzy multi-objective decision problems. Therefore, in this paper, we first revisit the related papers and focus on how to develop an interactive two-phase method. Next, we establish to consider the imprecise nature of the data by fulfilling the possibilistic programming model, and we also assume that each objective work has a fuzzy goal. Finally, for reaching our objective, the detailed numerical example is presented to illustrate the feasibility of applying the proposed approach to PM decision problems at the end of this paper. Results show that our model can be applied as an effective tool. Furthermore, we believe that this approach can be applied to solve other multi-objective decision making problems.     

Integrated product line design and supplier selection: A multi-objective optimization paradigm

Product line design is commonly used to provide higher product variety for satisfying diversified customer needs. To reduce the cost and development time and improve quality of products, companies quite often consider sourcing. Conventionally, product line design and supplier selection are dealt with separately. Some previous studies have been attempted to consider product line design and supplier selection simultaneously but two shortcomings were noted. First, the previous studies considered several objectives as a single objective function in the formulation of optimization models for the integrated problem. Second, positions of product variants to be offered in a product line in competitive markets are not clearly defined that would affect the formulation of marketing strategies for the product line. In this paper, a methodology for integrated product line design and supplier selection is proposed to address the shortcomings in which a multi-objective optimization model is formulated to determine their specifications and select suppliers for maximizing the profit, quality and performance as well as minimizing the cost of the product line. In addition, joint-spacing mapping is introduced to help estimate market share of products and indicate positions of product variants. The proposed methodology can provide decision makers with a better tradeoff among various objectives of product line design, and define market positions of product variants explicitly. The results generated based on the methodology could help companies develop product lines with higher profits, better product quality and larger market share to be obtained. A case study of a product line design of notebook computers was performed to illustrate the effectiveness of the proposed methodology. The results have shown that Pareto optimal product line designs and the specifications of product variants can be determined. Suppliers of components and modules can be selected with considerations of minimum sourcing cost, and maximum performance and quality of product variants. Prices and positions of the product variants can also be determined.     

矿山产能分配的变量模糊线性规划模型

针对矿山资源开采过程中产能不确定的分配问题,引入了模糊结构元素理论。将产能用结构元表示,并利用结构元加权序将模糊数比较转化为单调函数比较,将含有模糊变量的线性规划问题等价转化为经典线性规划问题。以某矿山为例,建立矿山产能分配的变量模糊线性规划模型,并进行求解。结果表明：实现了将实际问题中的模糊事件进行精确表达,原问题的求解更简便。得到矿山产能取得最大可能利润时的可能分配。应用结构元加权序求解的线性规划模型优于结构元元序的。     

Supplier selection model with contingency planning for supplier failures

We consider the optimal allocation of demand across a set of suppliers given the risk of supplier failures. We assume items sourced are used in multiple facilities and can be purchased from multiple suppliers with different cost and reliability characteristics. Suppliers have production flexibility that allows them to deliver a contingency quantity in case other suppliers fail. Costs considered include supplier fixed costs and variable costs per unit, while failure to deliver to a demand point results in a particular financial loss. The model utilizes the decision tree approach to consider all the possible states of nature when one or more suppliers fail, as well as expand the traditional transportation problem. Unlike other supplier selection models, this model considers contingency planning in the decision process, minimizing the total network costs. This results in a base allocation to one or more of the available suppliers and a state of nature specific delivery contingency plan from the suppliers to each demand point. A numerical example, as well as sensitivity analysis, is presented to illustrate the model and provide insights.     

Type-2 fuzzy multi-objective DEA model: An application to sustainable supplier evaluation

In the last 10 years, sustainable supply chain management (SSCM) has become one of the important topics in business and academe. Sustainable supplier performance evaluation and selection play a significant role in establishing an effective SSCM. One of the techniques that can be used for evaluating sustainable supplier performance is data envelopment analysis (DEA). The conventional DEA methods require accurate measurement of both input and output variables present in the problem. In practice, the observed values of the input and output data present in real-world problems are often imprecise. To cope with this situation, fuzzy DEA models were constructed for expressing relative fuzzy efficiencies of decision-making units (DMUs). However, fuzzy DEA is still limited to fuzzy input/output data while some inputs and outputs might be affected by various factors of uncertainty and information granularity, meaning that they could be better modeled in terms of fuzzy sets of type-2. In this paper, we develop a multi-objective DEA model in a setting of type-2 fuzzy modeling to evaluate and select the most appropriate sustainable suppliers. In the proposed model, both efficiency and effectiveness are considered to describe the integrated productivity of suppliers. In sequel, chance constrained programming, critical value-based reduction methods and equivalent transformations are considered to solve the problem. A detailed case study is employed to show the advantages of the proposed model in terms of measuring effectiveness, efficiency and productivity in an uncertain environment expressed at different confidence levels. At the same time, the results demonstrate that the model is capable of helping decision makers to balance economic, social, and environmental factors when selecting sustainable suppliers.     

Comparative study of the applicability of fuzzy multi-objective linear programming models through cost-effective analysis for mold manufacturing

The mold-manufacturing process consists of prototype design, production, assembly, and testing. As products tend to vary, have short due dates, and life cycles, are highly precise and must be responsiveness to customers, production system planning is complex and the relationship between outsourcing capability and in-house capacity is crucial to mold-manufacturing. Differentiation of core operations vs. non-core operations in internal vs. external environments and time control are essential for mold manufacturing when planning production systems. To analyze the cost-effectiveness of capacity planning and its relationship to suppliers, this work applies a novel fuzzy multi-objective linear programming model. Considered factors are order quantity allocation, due dates, manufacturing quantity, capacity, defect rates, back-log, and the purchasing discount. The applicability of three fuzzy theories is assessed using total costs, punishment costs, and crashing costs. Implementation results demonstrate the potentials for cost-effective capacity planning and outsourcing, and identify the applicability of these fuzzy theories to a specific mold-manufacturing case.     

A multi-objective evolutionary algorithm to exploit the similarities of resource allocation problems

The complexity of a resource allocation problem (RAP) is usually NP-complete, which makes an exact method inadequate to handle RAPs, and encourages heuristic techniques to this class of problems for obtaining approximate solutions in polynomial time. Different heuristic techniques have already been investigated for handling various RAPs. However, since the properties of an RAP can help in characterizing other RAPs, instead of individual solution techniques, the similarities of different RAPs might be exploited for developing a common solution technique for them. Two RAPs of quite different nature, namely university class timetabling and land-use management, are considered here for such a study. The similarities between the problems are first explored, and then a common multi-objective evolutionary algorithm (a kind of heuristic techniques) for them is developed by exploiting those similarities. The algorithm is problem-dependent to some extent and can easily be extended to other similar RAPs. In the present work, the algorithm is applied to two real instances of the considered problems, and its properties are derived from the obtained results.     

A hybrid genetic and linear programming algorithm for two-agent order acceptance and scheduling problem

In this paper, the simultaneous order acceptance and scheduling problem is developed by considering the variety of customers’ requests. To that end, two agents with different scheduling criteria including the total weighted lateness for the first and the weighted number of tardy orders for the second agent are considered. The objective is to maximize the sum of the total profit of the first and the total revenue of the second agents’ orders when the weighted number of tardy orders of the second agent is bounded by an upper bound value. In this study, it is shown that this problem is NP-hard in the strong sense, and then to optimally solve it, an integer linear programming model is proposed based on the properties of optimal solution. This model is capable of solving problem instances up to 60 orders in size. Also, the LP-relaxation of this model was used to propose a hybrid meta-heuristic algorithm which was developed by employing genetic algorithm and linear programming. Computational results reveal that the proposed meta-heuristic can achieve near optimal solutions so efficiently that for the instances up to 60 orders in size, the average deviation of the model from the optimal solution is lower than 0.2% and for the instances up to 150 orders in size, the average deviation from the problem upper bound is lower than 1.5%.     

Interactive balance space approach for solving multi-level multi-objective programming problems

This paper studies a multi-level multi-objective decision-making (ML-MODM) problems with linear or non-linear constraints. The objective functions at each level are non-linear functions, which are to be maximized or minimized.This paper presents a three-level multi-objective decision-making (TL-MODM) model and an interactive algorithm for solving such a model. The algorithm simplifies three-level multi-objective decision-making problems by transforming them into separate multi-objective decision making problems at each level, thereby avoiding the difficulty associated with non-convex mathematical programming. Our algorithm is an extension of the work of Shi and Xia [X. Shi, H. Xia, Interactive bi-level multi-objective decision making, Journal of the Operational Research Society 48 (1997) 943-949], which dealt with interactive bi-level multi-objective decision-making problems, with some modifications in assigning satisfactoriness to each objective function in all the levels of the TL-MODM problem. Also, we solve each separate multi-objective decision making problem of the TL-MODM problem by the balance space approach.A new formula is introduced to interconnect the satisfactoriness and the proportions of deviation needed to reflect the relative importance of each objective function. Thus, we have the proportions of deviation including satisfactoriness.In addition, we present new definitions for the satisfactoriness and the preferred solution in view of singular-level multi-objective decision making problems that corresponds to the η-optimal solution of the balance space approach. Also, new definitions for the feasible solution and the preferred solution (η-optimal point) of the TL-MODM problem are presented. An illustrative numerical example is given to demonstrate the algorithm.     

Multiple objective branch and bound for mixed 0-1 linear programming: Corrections and improvements for the biobjective case

This work addresses the correction and improvement of Mavrotas and Diakoulaki's branch and bound algorithm for mixed 0-1 multiple objective linear programs. We first elaborate the issues encountered by the original algorithm and then propose a corrected version for the biobjective case using an exact representation of the nondominated set associated with an appropriate update procedure. Then we introduce several improvements using better bound sets and branching strategies and finally present some experiments to study the effectiveness of our propositions.     

高效求解整数线性规划问题的分支算法

为了提高求解一般整数线性规划问题的效率,提出了一种基于目标函数超平面移动的分支算法。对于给定的目标函数整数值,首先利用线性规划松弛问题的最优单纯形表确定变量的上、下界,然后将变量的上、下界条件加入约束条件中对相应的目标函数超平面进行切割,最后应用分支定界算法中的分支方法来搜寻目标函数超平面上的可行解。通过对一些经典的数值例子的求解计算并与经典的分支定界算法进行比较,结果表明,该算法减少了分支数和单纯形迭代数,具有较大的实用价值。     

A goal programming model for joint decision making of inventory lot-size,supplier selection and carrier selection

In this paper, we address a problem in which a storage space constrained buyer procures a single product in multiple periods from multiple suppliers. The production capacity constrained suppliers offer all-unit quantity discounts. The late deliveries and rejections are also incorporated in sourcing. In addition, we consider transportation cost explicitly in decision making which may vary because of freight quantity and distance of shipment between the buyer and a supplier. We propose a multi-objective integer linear programming model for joint decision making of inventory lot-sizing, supplier selection and carrier selection problem. In the multi-objective formulation, net rejected items, net costs and net late delivered items are considered as three objectives that have to be minimized simultaneously over the decision horizon. The intent of the model is to determine the timings, lot-size to be procured, and supplier and carrier to be chosen in each replenishment period. We solve the multi-objective optimization problem using three variants of goal programming (GP) approaches: preemptive GP, non-preemptive GP and weighted max–min fuzzy GP. The solution of these models is compared at different service-level requirements using value path approach.     

Structured methodology for supplier selection and evaluation in a supply chain

Supply chain management (SCM) is one of the most important competitive strategies used by modern enterprises. The main aim of supply chain management is to integrate various suppliers to satisfy market demand. Meanwhile, supplier selection and evaluation plays an important role in establishing an effective supply chain. Traditional supplier selection and evaluation methods focus on the requirements of single enterprises, and fail to consider the entire supply chain. Therefore, this study proposes a structured methodology for supplier selection and evaluation based on the supply chain integration architecture.In developing the methodology for supplier selection and evaluation in a supply chain, enterprise competitive strategy is first identified using strengths weaknesses opportunities threats (SWOT) analysis. Based on the competitive strategy, the criteria and indicators of supplier selection are chosen to establish the supplier selection framework. Subsequently, potential suppliers are screened through data envelopment analysis (DEA). Technique for order preference by similarity to ideal solution (TOPSIS), a multi-attribute decision-making (MADA) method is adapted to rank potential suppliers. Finally, the Taiwanese textile industry is used to illustrate the application and feasibility of the proposed methodology.This study facilitates the improvement of collaborator relationships and the management of potential suppliers to help increase product development capability and quality, reduce product lifecycle time and cost, and thus increase product marketability.     

A two-phase optimization procedure for integer programming problems

This paper presents a simple two-phase method for optimizing integer programming problems with a linear or nonlinear objective function subject to multiple linear or nonlinear constraints. The primary phase is based on a variation of the method of steepest descent in the feasible region, and a hem-stitching approach when a constraint is violated. The secondary phase zeros on the optimum solution by exploring the neighborhood of the suboptimum found in the first phase of the optimization process. The effectiveness of this method is illustrated through the optimization of several examples. The results from the proposed optimization approach are compared to those from methods developed specially for dealing with integer problems. The proposed method is simple, easy to implement yet very effective in dealing with a wide class of integer problems such as spare allocation, reliability optimization, and transportation problems.