Sankar Kumar Roy

Bio: Sankar Kumar Roy is an academic researcher from Vidyasagar University. The author has contributed to research in topics: Transportation theory & Fuzzy logic. The author has an hindex of 24, co-authored 109 publications receiving 1637 citations.

Analysis of inventory control model with shortage under time-dependent demand and time-varying holding cost including stochastic deterioration

Abstract: In this paper, a deterministic inventory control model with deterioration is developed. Here, the deterioration rate follows stochastic deterioration, especially Weibull distribution deterioration. A time-dependent demand approach is introduced to show the applicability of our proposed model and to be up-to-date with respect to time. The main purpose of the paper is to investigate the optimal retailer’s replenishment decisions for deteriorating items including time-dependent demand for demonstrating more practical circumstances within economic-order quantity frameworks. Keeping in mind the criterion of modern era, we consider that the holding cost is totally dependent on time, and shortages are allowed for this model. Subject to the formulated model, we minimize the total inventory cost. The mathematical model is explored by numerical examples to validate the proposed model. A sensitivity analysis of the optimal solution with regard to important parameters is also carried out to elaborate the quality, e.g., stability, of our result and to possibly modify our model. The paper ends with a conclusion and an outlook to future studies.

Conic scalarization approach to solve multi-choice multi-objective transportation problem with interval goal

Abstract: This paper explores the study of multi-choice multi-objective transportation problem (MCMTP) under the light of conic scalarizing function. MCMTP is a multi-objective transportation problem (MOTP) where the parameters such as cost, demand and supply are treated as multi-choice parameters. A general transformation procedure using binary variables is illustrated to reduce MCMTP into MOTP. Most of the MOTPs are solved by goal programming (GP) approach, but the solution of MOTP may not be satisfied all times by the decision maker when the objective functions of the proposed problem contains interval-valued aspiration levels. To overcome this difficulty, here we propose the approaches of revised multi-choice goal programming (RMCGP) and conic scalarizing function into the MOTP, and then we compare among the solutions. Two numerical examples are presented to show the feasibility and usefulness of our paper. The paper ends with a conclusion and an outlook on future studies.

Multi-objective two-stage grey transportation problem using utility function with goals

Abstract: Multi-Objective Goal Programming is applied to solve problems in many application areas of real-life decision making problems. We formulate the mathematical model of Two-Stage Multi-Objective Transportation Problem (MOTP) where we design the feasibility space based on the selection of goal values. Considering the uncertainty in real-life situations, we incorporate grey parameters for supply and demands into the Two-Stage MOTP, and a procedure is applied to reduce the grey numbers into real numbers. Thereafter, we present a solution procedure to the proposed problem by introducing an algorithm and using the approach of Revised Multi-Choice Goal Programming. In the proposed algorithm, we introduce a utility function for selecting the goals of the objective functions. A numerical example is encountered to justify the reality and feasibility of our proposed study. Finally, the paper ends with a conclusion and an outlook to future investigations of the study.

Management Models and Industrial Applications of Linear Programming

Abstract: (1962). Management Models and Industrial Applications of Linear Programming. Journal of the Operational Research Society: Vol. 13, No. 3, pp. 274-275.

Solving Fuzzy Job-Shop Scheduling Problem Using DE Algorithm Improved by a Selection Mechanism

Abstract: The emergence of fuzzy sets makes job-shop scheduling problem (JSSP) become better aligned with the reality. This article addresses the JSSP with fuzzy execution time and fuzzy completion time (FJSSP). We choose the classic differential evolution (DE) algorithm as the basic optimization framework. The advantage of the DE algorithm is that it uses a special evolutionary strategy of difference vector sets to carry out mutation operation. However, DE is not very effective in solving some instances of FJSSP. Therefore, we propose a novel selection mechanism augmenting the generic DE algorithm (NSODE) to achieve better optimization results. The proposed selection operator adopted in this article aims at a temporary retention of all children generated by the parent generation, and then selecting N better solutions as the new individuals from N parents and N children. Various examples of fuzzy shop scheduling problems are experimented with to test the performance of the improved DE algorithm. The NSODE algorithm is compared with a variety of existing algorithms such as ant colony optimization, particle swarm optimization, and cuckoo search. Experimental results show that the NSODE can obtain superior feasible solutions compared with solutions produced by several algorithms reported in the literature.