A decision model of optimal production reliability and warranty length in an imperfect production system

A decision model to maximize the total profit of manufacturers in an imperfect production system is constructed.In this model the production reliability and the warranty length are jointly used as decision variables for the case that products are sold with a warranty i.e. the demand is dependent on the warranty length and sale price.Also all the non-conforming quality defective items in the production process are refurbished to conform to quality ones at a cost. The existence and uniqueness of the optimal values of production reliability and the warranty length are proved by using the Euler-Lagrange method in analyzing the model.A numerical example is also provided to illustrate the effectiveness of the decision model.The sensitivity analysis of the key parameters of the optimal solution and objective value is presented in addition.

A supply chain model for imperfect production system with stochastic lead time demand

This study deals an integrated manufacturer-buyer supply chain system for imperfect production under stochastic lead time demand.Here,defective rate has been followed as a function of production rate.Also,the produced units have been inspected in order to screen the defective units but screening rate is less than the production rate and greater than the demand rate.Buyer purchases the products from the manufacturer.Also,we assume that shortage during the lead time is permitted and demand during the shortage period is fully backordered.The objective is to derive the optimal production rate,ordering quantity and to maximize joint total profit.Basically,two different models for different probability distribution functions of stochastic lead time demand have been developed.Some numerical examples are provided to show the applicability of the proposed models comparing the optimum average profits.Finally,sensitive analysis,conclusion and future researches are presented.

Optimal batch shipment policy for an imperfect production system under price-,advertisementand green-sensitive demand

In this paper,we consider an imperfect production-inventory system which consists of a single manufacturer and a single retailer.The manufacturer delivers the order quantity to the retailer in some unequal-sized batches.To separate the defective items,the retailer performs an error-free screening process after receiving each delivery from the manufacturer.Shortage in retailer’s inventory is allowed and completely backlogged.The customer demand is influenced by the retail price,advertisement frequency and greening level of the product.The centralized model and the decentralized model based on a Stackelberg gaming approach are developed to determine optimal pricing,advertising and inventory decisions.A cost-sharing contract between the manufacturer and the retailer is implemented,which enhances the environmental performance,advertisement frequency and profitability of the supply chain significantly.The proposed model is illustrated with a numerical example.Sensitivity analysis for some key parameters is carried out and several managerial insights are also highlighted.

Ordering Cost Depletion in Inventory Policy with Imperfect Products and Backorder Rebate

This study presents an inventory model for imperfect products with depletion in ordering costs and constant lead time where the price discount in the backorder is permitted.The imperfect products are refused or modified or if they reached to the customer,returned and thus some extra costs are experienced.Lately some of the researchers explicitly present on the significant association between size of lot and quality imperfection.In practical situations,the unsatisfied demands increase the period of lead time and decrease the backorders.To control customers'problems and losses,the supplier provides a price discount in backorders during shortages.Also,an order’s policies may result in including some imperfect products in arrival lots.A discount on price may be offered by the supplier on the out-of-stock products to manage the backorder problems.The study aims to develop a model with imperfect products by permitting the price discount in backorders,and the cost of ordering is considered a decision variable.First,it is assumed that the demand for lead time is followed by a normal distribution and then stops it and assumed that the first two moments of demand for lead time are known.Further,the minimax distribution method is used to solve this model,and a separate algorithm is designed.In this study,two models are discussed with and without a normally distributed rate of demand.The current study verified with the help of some numerical examples over various model parameters.

Multi-item EPQ model with learning effect on imperfect production over fuzzy-random planning horizon

Uncertainty is certain in the world of uncertainty.This study revisits an economic production quantity(EPQ)model with shortages for stock-dependent demand of the items with reworking and disposing of the imperfect ones over a random planning horizon under the joint effect of inflation and time value of money,where the expected time length is imprecise in nature.Transmission of learning effect has been incorporated to reduce the defective production.The total expected profit over the random planning horizon is maximized subject to the imprecise space constraint.The possibility,necessity and credibility measures have been introduced to defuzzify the model.The simulation-based genetic algorithm is used to make decision for the above EPQ model in different measures of uncertainty.The model is illustrated through an example.Sensitivity analysis shows the impacts of different parameters on the objective function in the model.

An inventory model under development cost-dependent imperfect production and reliability-dependent demand

This paper considers a model that deals with an imperfect production process where both perfect and imperfect quality items are produced.Here,demand depends on selling price and reliability of the product.Each manufacturing company expects to produce perfect quality items.But due to the long-run process,several kinds of problem such as labor,machinery,and technology arise.As a result,the manufacturing system becomes out-of-control state and consequently produces both perfect and imperfect quality items.Perfect items are ready to sell but imperfect items are reworked at a cost to become perfect.Reworking cost,reliability of the product and reliability parameter of the manufacturing system can be improved by introducing the development cost and also by improving the quality of the raw material of the production system.Under such circumstances,a profit function has been developed to find the optimum values of reliability parameter of the manufacturing system,reliability of the product and duration of production such that a manufacturer gets a maximum profit.Finally,the model has been illustrated with some numerical examples exploring the sensitivity analysis with respect to some parameters.

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.