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The proposed IT2FMOVMI model intends to concurrently minimize total cost and warehouse space for the single vendor-retailer, multi-item and a consolidated vendor store. Regarding demand and order quantities with the deterministic and type-1 fuzzy numbers, we have also formulated the classic/crisp MOVMI model and type-1 fuzzy MOVMI (T1FMOVMI) model. The suggested solution technique can solve both crisp MOVMI and T1FMOVMI problems. By finding the optimal ordered quantities and backorder levels, the Pareto-fronts are constructed to form the solution sets for the three models.

A multi-objective vendor managed inventory (MOVMI) is the most recognized marketing and delivery technique for the service provider and the retail in the supply chain in Industry 4.0. Due to the evolving market conditions, the characteristics of the individual product, the delivery period and the manufacturing costs, the demand rate and order quantity of the MOVMI device are highly unpredictable. In such a scenario, a MOVMI system with a deterministic demand rate and order quantity cannot be designed to estimate the highly unforeseen cost of the problem. This paper introduces a novel interval type-2 fuzzy multi-objective vendor managed inventory (IT2FMOVMI) system, which uses interval type-2 fuzzy numbers (IT2FNs) to represent demand rate and order quantities. As the model is an NP-hard, the well-known meta-heuristic algorithm named NSGA-II (Non-dominated sorted genetic algorithm-II) with EKM (Enhanced Karnink-Mendel) algorithm based solution method has been established.

The experimental simulations for the five test problems that demonstrated distinct conditions are considered from the real-datasets of SAPCO company. Experimental study concludes that T1FMOVMI and crisp MOVMI schemes are outclassed by IT2FMOVMI model, offering more accurate Pareto-Fronts and efficiency measurement values.

Using fuzzy sets theory, a significant amount of work has been already done in past decades from various points of views to model the MOVMI. However, this is the very first attempt to introduce type-2 fuzzy modelling for the problem to address the realistic implementation of the imprecise parameters.

Good management strives to align and corporate processes for more attention being paid to supply chain management. Firms realize that greater co-operation and improved coordination can help to manage the entire supply chain more efficiently. The imperfect quality item is one of the most important issues that affect the expected profit of green supply chain. The imprecise cost with screening process of poor quality items posed in supply chain is the subject of this study.

The present study explores production model for imperfect items having uncertain cost parameters with three-layer supply chain encompassing supplier, manufacturer and retailer. The model is considering the impact of business tactics such as order size, production rate, production cost and appropriate times in various sectors on collaborative marketing systems. Due to imprecise cost parameters, the pentagonal fuzzy numbers are set to fuzzify the total cost and defuzzifition by using graded mean integration.

This study offers an explicit condition in uncertain environment to manage the imperfect quality item to increase the potential profit of the supply chain. The influence of changes in parameter values on the optimal inventory policy under fuzziness is provided managerial insights.

This model makes a significant contribution to fuzzy inference. The results of the study provide a trading strategy for the industry to avoid losses. The prescribed study can be suitable for the industries like sculpture, jewelry, pottery, etc.

Most of the literature published regarding the performance of lot‐sizing algorithms has been in a deterministic environment. The first objective of this article is to propose a way to incorporate fuzzy sets theory into lotsizing algorithms for the case of uncertain demand in a fuzzy master production schedule. Triangular fuzzy numbers are used to represent uncertainty in the master production schedule. It is shown that the fuzzy sets theory approach provides a better representation of fuzzy demand and more information to aid the determination of lot size. The second objective is to evaluate three lot sizing methods: part‐period balancing, Silver‐Meal, and Wagner‐Whitin. The performance of each lot‐sizing algorithm was calculated over nine examples. The results indicate that the part‐period balancing algorithm may be a better overall choice to determine lot sizes.

In this paper, we propose a scenario based global supply chain planning (GSCP) process considering demand uncertainty originated from various global supply chain risks. To generate the global supply chain plan, we first formulate a GSCP model. Then, we need to generate several scenarios which can represent various demand uncertainties. Lastly, a planning procedure for considering those defined scenarios is applied. Unlike the past related researches, we adopt the fuzzy set theory to represent the demand scenarios. Also, a scenario voting process is added to calculate a probability (possibility) of each scenario. An illustrative example based on a real world case is presented to show the feasibility of the proposed planning process.

The purpose of this paper is to develop a multi-item economic production quantity (EPQ) strategy under grey environment and space constraint. Since the “demand” cannot be predicted with certainty, it is assumed that data behave under grey environment and compare the proposed inventory model with other studies using crisp or fuzzy environments.

This paper is to optimise the cycle time and total cost of the multi-item EPQ inventory model. For this purpose, the Lagrangian coefficient is used to solve the constrained optimisation problem. The grey relational analysis approach and grey data are applied in developing the EPQ inventory model.

The results are compared with the analysis using crisp and fuzzy data. Sensitivity analysis is done to illustrate the effect of parameter variations on the optimal solution. The results of the study demonstrate that crisp data outperform the other two data in all scales problems in terms of cycle time and cost; grey data perform better in all scales problems than fuzzy data.

The contribution of this research is the use of grey data in developing the EPQ inventory model with space constraint.

A plethora of studies focused on the cause and solutions for the bullwhip effect, and consequently many have successfully experimented to dampen the effect. However, the feasibility of such studies and the actual contribution for supply chain performance are yet up for debate. This paper aims to fill this gap by providing a holistic system-based perspective and proposes a fuzzy logic decision-making implementation for a single-product, three-echelon and multi-period supply chain system to mitigate such effect.

This study uses system dynamics (SD) as the central modeling method for which Vensim® is used as a tool for hybrid simulation. Further, the authors used MATLAB for undertaking fuzzy logic modeling and constructing a fuzzy inference system that is later on incorporated into SD model for interaction with the main supply chain structure.

This research illustrated the usefulness of fuzzy estimations based on experts’ linguistically and logically defined parameters instead of relying merely on the traditional demand forecasting based on time series. Despite the increased complexity of the calculations and structure of the fuzzy model, the bullwhip effect has been considerably decreased resulting in an improved supply chain performance.

This dynamic modeling approach is not only useful in supply chain management but also the model developed for this study can be integrated into a corporate financial planning model. Further, this model enables optimization for an automated system in a company, where decision-makers can adjust the fuzzy variables according to various situations and inventory policies.

This study presents a systemic approach to deal with uncertainty and vagueness in dynamic models, which might be a major cause in generating the bullwhip effect. For this purpose, the combination between fuzzy set theory and system dynamics is a significant step forward.

The awareness for protecting the environment has resulted in remanufacturing and recycling policies in manufacturing industries. Carbon emission is one of the most important elements affecting the environment. Carbon emission due to production and transportation creates complicated situations for the manufacturing firms by affecting the manufacturer's carbon quota. The ecological consequences posed in a reverse logistic model are the subject of this study.

The present study explores the fuzzy model of economic production for both remanufacturing and recycling with uncertain cost parameters under the cap-and-trade rule to control the carbon emission due to different modes of transportation. Due to imprecise cost parameters, the hexagonal fuzzy numbers are set to fuzzify the overall cost, which leads to correct decisions in a more confident way. The result is defuzzified by using graded mean integration.

This study offers an explicit condition to control the carbon emission of the manufacturer and reduce the optimum cost. The findings indicate that the collection of used goods that can be remanufactured must be increased. The model is validated numerically. Sensitivity analysis explores the various aspects of different parameters on net cost to accomplish the fuzzy production model.

Under fuzzy inference, the research offers a relevant contribution in the field of recycling with controlling carbon emission by using the cap-and-trade policy. This study provides a trading strategy for a manufacturer's decision to avoid losses.

The purpose of this paper is to study the impact of learning effect and demand uncertainty on aggregate production planning (APP), provide practitioners with some important managerial implications for improving production planning and productivity.

Motivated by the background of one labour-intensive manufacturing firm – a mosquito expellant factory – an APP model considering workforce learning effect and demand uncertainty is established. Numerical example and comparison with other two models without considering learning and uncertainty of demand are conducted.

The result shows that taking into account the uncertain demand and learning effect can reduce total production cost and increase flexibility of APP.

Managerial implications are provided for practitioners with four propositions on improving workforce learning effect, i.e. emphasizing employee training, combing individual and organizational learning and reduction of forgetting effect.

This paper has practice value in improving APP in labor-intensive manufacturing.

The purpose of this paper is to deal with profit maximization problem of two-layer supply chain (SC) under fuzzy stochastic demand having finite mean and unknown variance. Buyback policy is employed from the retailer to supplier. The profit of the supplier solely depends on the order size of the retailers. However, the loss of shortage items is related to loss of profit and goodwill dependent. The authors develop the profit function separately for both the retailer and supplier, first, for a decentralized system and, second, joining them, the authors get a centralized system (CS) of decision making, in which one is giving more profit to both of them. The problem is solved analytically first, then the authors fuzzify the model and solve by fuzzy Hausdorff distance method.

The analytical models are formed for both centralized and decentralized systems under non-cooperative and cooperative environment with suitable constraints. A significant assumption on density function, namely Cauchy-type density function, is introduced for demand rate because of its wider range of the retailers’ satisfactions. Fuzzy Hausdorff metric is incorporated within the fuzzy components of the fuzzy sets itself. Using this method, the authors find out closure values of both centralized and decentralized policies, which is an essential part of any cooperative and non-cooperative two-layer SC models. Moreover, the authors take care of the profit values with corresponding ambiguities for both the systems explicitly.

It is found that the centralize policy of SC could only be able to maximize the profit of both the retailers and suppliers. All analytical results are illustrated numerically along with sensitivity analysis and side by side comparative studies between Hausdorff and Euclidean distance measure are done exclusively.

The main focus of attention of the proposed model is given to usefulness of Hausdorff distance. Unlike other distances, Hausdorff distance can take special care on the similarity measures of different fuzzy sets. Researchers have been engaged to use Hausdorff distance on the different fuzzy sets but, in this study, the authors have used it within the components of a same fuzzy set to gain more closure values than other methods.

The use of this Hausdorff distance approach is totally new as per literature survey suggested yet. However, the Cauchy-type density function has not been introduced anywhere in SC management problems by modern researchers still now. In crisp model, the sensitivity on goodwill measures really provides a special attention also.

In the paper, the authors study the simultaneous influence of incentive compatibility and individual rationality (IR) on a multi-echelon supply chain (SC) under uncertainty. The authors study the impact of contract sequence on coordination strategies of a serial three-echelon SC consisting of a supplier, a manufacturer and a retailer in an uncertain environment.

The authors develop a game-theoretic framework of a serial decentralized three-echelon SC. Under a decentralized setting, the supplier and the manufacturer can choose from two contract types namely, wholesale price (WP) and linear two-part tariff (LTT) and it leads to four different cases of contract sequence.

The study show that SC coordination is possible when both the supplier and the manufacturer choose LTT contract. This study not only identifies the influence of contract sequence on profit distribution among SC agents, but also establishes cut-off policies for all SC agents for each contract sequence. This study also examine the influence of chosen contract sequence on optimal profit distribution among SC agents.

Three-echelon SC coordination under uncertain environment depends upon the contract sequence chosen by SC agents.

This study results will be helpful to managers of various SCs to take operational decisions under uncertain situations.

The main contribution of this study is that it explores the possibility of coordination by supply contracts for three-echelon SC in a fuzzy environment.