An Inventory Model of Production with Level Dependent Demand Allowing Few Defective Items

This paper considers a model regarding the products with finite life which allows defective items in reproduction and causes a small amount of decay. The market demand is assumed to be level dependent linear type. The model has also considered the constant production rate which stops after a desired level of inventories and that is the highest level of it. Due to the market demand, defective item and product’s decay, the inventory reduces to the zero level where again the production cycle starts. With a numerical search procedure, the proof of the proposed model has been shown. The objective of the proposed model is to find out the total optimum inventory cost, optimum ordering cost and optimum ordering cycle.

A Time Dependent Inventory Model for Exponential Demand Rate with Constant Production Where Shelf-Life of the Product Is Finite

In this paper a time dependent inventory model is developed on the basis of constant production rate and market demands which are exponentially decreasing. It advances in quest of total average optimum cost considering those products which have finite shelf-life. The model also considers the small amount of decay. Without having any sort of backlogs, production starts. Reaching at the desired level of inventories, it stops production. After that due to demands along with the deterioration of the items it initiates its depletion and after certain periods the inventory gets zero. The decay of the products is level dependent. The objective of this paper is to find out the optimum inventory cost and optimum time cycle. The model has also been justified with proving the convex property and by giving a numerical example.

A Production Inventory Model of Constant Production Rate and Demand of Level Dependent Linear Trend

The proposed model considers the products with finite shelf-life which causes a small amount of decay. The market demand is assumed to be level dependent and in a linear form. The model has also considered the constant production rate which stops attaining a desired level of inventories and that is the highest level of inventories. Production starts with a buffer stock and without any sort of backlogs. Due to the market demand and product’s decay, the inventory reduces to the level of buffer stock where again the production cycle starts. With a numerical search procedure the proof of the proposed model has been shown. The objective of the model is to obtain the total average optimum inventory cost and optimum ordering cycle.

An integrated fuzzy production inventory model for manufacturer–retailer coordination under simple carbon tax system

This paper develops twin models towards integrated production inventory planning for manufacturer–retailer ecosystem in a sustainable supply chain setup.Decision-making models are developed in fuzzy environment and under purview of carbon taxation system.Novel conception of Fermatean fuzzy numbers is introduced for handling parameters imprecision.The first model addresses planning problem without considering green investments,whereas the second one additionally identifies optimal green investments for each player of ecosystem.Models are formulated as nonlinear optimization problems with objective of maximizing profit.Comparison of results from both models enables decision-makers to figure out the profitability of green investment option.Numerical instance with data from the existing literature is solved using Mathematica 12.1.Computational results for studied case report profitability of green investments for supply chain partners and significant reduction in carbon emissions as well.Variation analysis demonstrates stability of the proposed model.Developed models equip small-scale retailer-manufacture tie-ups prevalent in developing economies for discussed decisions.

Analytics of an Imperfect Four-Layer Production Inventory Model Under Two-Level Credit Period Using Branch-and-Bound Technique

This paper explains an integrated production inventory supply chain model,which consists of a supplier,a manufacturer and a retailer under two-level credit period.One is manufacturer’s credit period offered by the supplier,and other is retailer’s credit period offered by the manufacturer.Here,the manufacturer replenishes raw materials from the supplier and produces non-deteriorating products in some cycles of equal length.It is noted that here four inventory structures have been considered to show the flow of the materials as either raw materials or finished products from supplier to retailer via manufacturer.Also in this model,manufacturer’s imperfect production has been considered.Here imperfect items are not repairable.The retailer receives good finished products from the manufacturer and sells these to his/her customers during some cycles of equal length in total time horizon.Our main objective is to find the optimal number of production and business cycles of the manufacturer such that the integrated system can get the maximum profit.The above discussed model is elaborated with the help of a numerical example,and a sensitivity analysis is done with respect to some parameters used in this model.

EPQ models with bivariate random imperfect proportions and learningdependent production and demand rates

In this paper,three production inventory models are constructed for an imperfect manufacturing system by considering a warm-up production run,shortages during the hybrid maintenance period,and the rework of imperfect items.The proportions of imperfect items produced during the warm-up and regular production runs are random and they are represented using a bivariate random variable.The shortage quantity is partially backordered and the supply of backorder quantity is planned simultaneously with regular demand satisfaction.The learning models are designed to accommodate the different learning capabilities of workers in unit production time during warm-up and regular production periods.The production and demand rates of these models are made dependent on the learning exponents.As the resulting models are highly nonlinear in the decision variable,they are optimized using a genetic algorithm.The models are illustrated using numerical examples and sensitivity studies are performed to find the influence of the key parameters.