Determining the methods for fulfilling the continuously increasing customer expectations and maintaining competitiveness in the market while limiting controllable expenses is challenging. Our study thus identifies inefficiencies in the supply chain network (SCN). The initial goal is to obtain the best allocation order for products from various sources with different destinations in an optimal manner. This study considers two types of decision-makers (DMs) operating at two separate groups of SCN, that is, a bi-level decision-making process. The first-level DM moves first and determines the amounts of the quantity transported to distributors, and the second-level DM then rationally chooses their amounts. First-level decision-makers (FLDMs) aimed at minimizing the total costs of transportation, while second-level decision-makers (SLDM) attempt to simultaneously minimize the total delivery time of the SCN and balance the allocation order between various sources and destinations. This investigation implements fuzzy goal programming (FGP) to solve the multi-objective of SCN in an intuitionistic fuzzy environment. The FGP concept was used to define the fuzzy goals, build linear and nonlinear membership functions, and achieve the compromise solution. A real-life case study was used to illustrate the proposed work. The obtained result shows the optimal quantities transported from the various sources to the various destinations that could enable managers to detect the optimum quantity of the product when hierarchical decision-making involving two levels. A case study then illustrates the application of the proposed work.

In this article, a multiobjective multiproduct production planning (MOMPP) problem discussed for a hardware firm. The hardware firm produces various types of hardware locks and other items in a production run. The firm manager's objectives are minimizing the production cost and inventory holding cost while maximizing the net profit subject to some system constraints. The multiproduct production planning is solved with the last production run information precisely known to the decision-maker, and finally, the model is solved using the intuitionistic and neutrosophic programming approaches, respectively. Also, the multiproduct production planning problem is discussed for situations when the product information is vague. The interval-valued trapezoidal neutrosophic numbers used to define this Vagueness. The multiobjective multiproduct production planning problem under fuzziness is solved using the neutrosophic compromise programming. The stepwise solution procedures are discussed using the case study.

This study investigates the compromise allocation of multivariate stratified sampling with complete response and nonresponse. We have formulated a multivariate stratified sampling problem as a mathematical programming problem to estimate p-population means with complete response and nonresponse for a fixed cost. Then, the compromise allocations for sample designs are determined by implementing intuitionistic fuzzy programming using optimistic and pessimistic solution strategies. A simulation study is carried out using the Stratify R software program to demonstrate the complete solution process. In wildlife, agricultural and marketing-related surveys, the study could be helpful. Also, the national planning policies related to surveys in such cases this study could be helpful. This study is an attempt to solve the sampling optimization problem using the Lingo-18 optimization program.

The problem of transportation in real-life is an uncertain multi-objective decision-making problem. In particular, by taking into account the conflicting objectives, Decision-Makers (DMs) are looking for the best transport set up to determine the optimum shipping quantity subject to certain capacity constraints on each route. This paper presented a Multi-Objective Transportation Problem (MOTP) where the objective functions are considered as Type-2 trapezoidal fuzzy numbers (T2TpFN), respectively. Demand and supply in constraints are in multi-choice and probabilistic random variables, respectively. Also considered the “rate of increment in Transportation Cost (TC) and rate of decrement in profit on transporting the products from ith sources to jth destinations due to” (or additional cost) of each product due to the damage, late deliveries, weather conditions, and any other issues. Due to the presence of all these uncertainties, it is not possible to obtain the optimum solution directly, so first, we need to convert all these uncertainties from the model into a crisp equivalent form. The two-phase defuzzification technique is used to transform T2TpFN into a crisp equivalent form. Multi-choice and probabilistic random variables are transformed into an equivalent value using Stochastic Programming (SP) approach and the binary variable, respectively. It is assumed that the supply and demand parameter follows various types of probabilistic distributions like Weibull, Extreme value, Cauchy and Pareto, Normal distribution, respectively. The unknown parameters of probabilistic distributions estimated using the maximum likelihood estimation method at the defined probability level. The best fit of the probability distributions is determined using the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), respectively. Using the Fuzzy Goal Programming (FGP) method, the final problem is solved for the optimal decision. A case study is intended to provide the effectiveness of the proposed work.

In a multivariate stratified sample survey, we assumed p-characteristics which are to be measured on each unit of the population and the population is further subdivided into L subpopulations. For estimating the p-population means of all characteristics, which are not known in advance usually, a random sample is taken out from the population with the help of simple random sampling. In a multivariate stratified sample survey, the optimum allocation of one character is not considered as optimum for others. Then a solution is needed to work out an allocation that may be optimum for all characteristics in some sense, called as compromise allocation in sampling literature. The estimation of p-population means in the presence of non-response, for a fixed cost, is discussed. The formulated integer non-linear programming problem is converted into a binary goal programming problem. The problem's solution is obtained by using the concept of flexible fuzzy goal programming.