Atul Tiwari

Assignment Problem (AP), as extensively discussed in operations research, industrial engineering and computational mathematics has been addressed under different headings and using different approaches. One of the approaches to solve an AP under uncertainty and in real world scenarios is using fuzzy theory. Fuzzy multi-objective linear programming usually deals with flexible aspiration levels that are indicative of optimality when considering all objectives or goals simultaneously with possible deviation in objectives or constraints in vague, imprecise and uncertain environment. Therefore in this study we propose an algorithm for solving multi-objective assignment problem (MOAP) with linear and nonlinear membership functions. The proposed model will give a compromised solution for best optimality and higher satisfaction level for parameters being considered in uncertain environment. The result obtained by using a linear membership function has been compared with the solution obtaine...

Travelling Salesman Problem (TSP), as extensively discussed in literature is an NP hard problem and among the most challenging problems in operations research, industrial engineering and computational mathematics, which has been deciphered and scrutinized under different headings and using different approaches e.g. Artificial Intelligence techniques, evolutionary algorithms and linear programming models under deterministic conditions. However, the information about real life processes is not always crisp but is often available as vague, uncertain and imprecise data. Fuzzy numbers finds application in handling vague terms, and therefore they can be suitably used to model real life scenarios involving vague parameters so as to obtain optimal solutions. Fuzzy multi-objective linear programming usually deals with flexible aspiration levels that are indicative of optimality when considering all objectives or goals simultaneously with possible deviation in objectives or constraints. Therefore in this study we develop a fuzzy multi-objective linear programming model with nonlinear membership functions for solving a multi objective TSP in order to simultaneously minimize the three parameters cost, distance and time. The importance of these parameters is assigned as weights to these objectives in the final model using AHP. The proposed model will give a compromised solution for best optimality and higher satisfaction level for the three parameters being considered in uncertain environment. The primary contribution of this study is a fuzzy mathematical model using nonlinear membership functions, more precisely the exponential functions to ensure an optimal solution in vague, imprecise and uncertain environment.

Purpose – Changes are inevitable in risky and uncertain business environments of today’s volatile supply chains. The concept of flexibility originates from this need to mitigate the ill-effects of risks and uncertainty in supply chains. In this paper, an attempt is made to present an exhaustive review on supply chain flexibility (SCF) and its implementation to gain strategic advantages. Design/methodology/approach – A citation analysis method is employed in this paper to discuss, analyse and apprehend the conceptual, empirical, analytical and simulation studies done in this field. In this paper, about 110 papers on flexibility from many reputed journals are examined to study and assimilate various aspects of flexibility. Findings – SCF embraces a unified process-based view including the core processes such as procurement, sourcing, distribution and logistics and mitigates uncertainty or risks involved. The review helps to assimilate the key knowledge about relevant practices in SCF ...

ABSTRACT Supply chain flexibility (SCF) is being viewed most important among the tools to counter and handle risks and uncertainties in today’s volatile markets. It may also be considered to plan strategies, in order to gain competitive edge over competitors. Recently extensive work is being reported in SCF focussing mainly on its multi dimensional aspects and implementation. However SCF is no free lunch and it may require huge investments to realise its potential benefits. ‘How much flexibility is required’, thus becomes the prime concern for firms willing to be flexible. This question is rarely discussed in the literature and in its scarcity, flexibility performance measurements remains untouched for risky and uncertain environments. Therefore measuring SCF is a prominent field where research needs to be focused. In this paper a mathematical model is proposed to evaluate supply chain flexibility at supplier buyer interface with an aim to attain robust supply in all possible scenarios. Further cost of procurement in view of flexibility is investigated in disastrous scenarios to support procurement decisions by managers. The paper contributes by analysing and evaluating SCF in environment of demand and lead time uncertainties and risks of major plant disruptions.

ABSTRACT Flexibility in supply chain is proved to be a way of countering uncertainties and planning strategies. In this paper an attempt is made to evaluate procurement flexibility at supplier buyer interface in disastrous scenarios. This can be considered to be an extension of research work carried out by Das and Abdel-Malek (2003). This paper contributes by analysing supply chain disruptions in extremely risky environments that are coupled with uncertainties in demand and lead times from downstream. These uncertainties are captured by a probability density functions, more precisely the normal distributions. A flexibility measure ψ is designed which not only ensures timely supply of material from the supplier but also ensures to maintain a continuous supply at minimal risk to buyer in case of complete disruptions at supplier's production sites. As this flexibility measure ψ varies from 0 to 1, it reflects a 0 to 100% flexibility of supplier from buyers' viewpoint.

Supplier selection is a multi-criteria decision making problem. It can critically influence the competitiveness in the entire supply chain network. It simultaneously takes into account several quantitative and qualitative factors. In this paper, a fuzzy approach is utilized for ...