The substitution process is the most impeccable one in the inventory model for deteriorating items considering their lifetime issues.In this developed model,we worked on the inventory system for substitutable deterior...The substitution process is the most impeccable one in the inventory model for deteriorating items considering their lifetime issues.In this developed model,we worked on the inventory system for substitutable deteriorating items(product 1 and product 2);and both products are similar.The demand of the product is considered to have three different types,including constant,price-dependent,and promotional effort-dependent demand,to show the uncertainty of demand for a product in real life,and it is a manufacturer-retailer supply chain,where the manufacturer gives the pre-payment option and also cash discount to the retailer.In the substitution phase,we considered three various cases according to the inventory level of products 1 and 2.Direct and indirect carbon emissions in production and transportation were also considered.Numerical examples were used to verify the developed model.Sensitivity analysis was carried out to verify the obtained optimal values.展开更多
This paper develops an economic production quantity(EPQ)model under the effect of inflation and time value of money.The rate of replenishment is considered to be a variable and the generalized unit production cost fun...This paper develops an economic production quantity(EPQ)model under the effect of inflation and time value of money.The rate of replenishment is considered to be a variable and the generalized unit production cost function is formulated by incorporating several factors,such as raw material,labour,replenishment rate,advertisements and other factors of the manufacturing system.The selling price of a unit is determined by a mark-up over the production cost.We have considered three types of continuous probabilistic deterioration function,and also considered that the holding cost of the item per unit time is assumed to be an increasing linear function of time spent in storage.In addition,shortages are allowed and partially backlogged.This model aids in minimizing the total inventory cost by finding the optimal cycle length and the optimal production quantity.The optimal solution of the model is illustrated with the help of numerical examples.展开更多
This paper develops an inventory model for deteriorating items with finite replenishment rate under a progressive payment scheme within the cycle time.In this model,the deterioration function follows a probability dis...This paper develops an inventory model for deteriorating items with finite replenishment rate under a progressive payment scheme within the cycle time.In this model,the deterioration function follows a probability distribution such as a(1)uniform distribution,(2)triangular distribution or(3)beta distribution.Here,the retailer is allowed a trade-credit offer by the supplier to buy more items.This model aids in minimizing the total inventory cost of the retailer by finding the optimal cycle length,the optimal time length of replenishment and the optimal order quantity.Some theorems have been framed to characterize the optimal solutions.The necessary and sufficient conditions of the existence and uniqueness of the optimal solutions are also provided.The optimal solution of the model is illustrated with the help of numerical examples,and numerical comparisons between the three models are also given.Finally,sensitivity analysis and graphical representations are given to demonstrate the model.展开更多
In this paper,economic order quantity(EOQ)inventory model is considered subject to promotional efforts.We adopt a demand function which is dependent on sales teams’initiatives in which shortages are allowed which are...In this paper,economic order quantity(EOQ)inventory model is considered subject to promotional efforts.We adopt a demand function which is dependent on sales teams’initiatives in which shortages are allowed which are completely backlogged under the condition of permissible delay in payments with timedependent holding cost.The main objective of this paper is to determine the optimal replenishment schedule and optimal order quantity to maximize the total profit.Expressions for various optimal indices are provided.First,we prove that a unique optimal replenishment schedule exists.Second,we present an effective iterative algorithm to obtain the optimal solution.Furthermore,we establish some useful theorems to characterize the optimal solution to determine the values of replenishment schedule and optimal order quantity.Third,we prove that the total profit is a concave function via differential calculus and present numerical examples using SCILAB 5.5.0 to illustrate the model.Finally,we extend the numerical example by performing a sensitivity analysis of the model parameters and discuss managerial insights.This study suggests to the management of firms to determine the optimal order quantity,optimal inventory cycle length and sales teams’initiatives/promotional effort in order to achieve their maximum profits.展开更多
In this paper,a two-warehouse economic order quantity(EOQ)model for noninstantaneously deteriorating items with stock-dependent demand under the effects of inflation and the time value of money is presented.Also in th...In this paper,a two-warehouse economic order quantity(EOQ)model for noninstantaneously deteriorating items with stock-dependent demand under the effects of inflation and the time value of money is presented.Also in this model,shortages are allowed and partially backlogged.The backlogging rate is dependent on the waiting time for the next replenishment.The objective of this model is to minimize the total inventory cost of the retailer by finding the optimal intervals and the optimal order quantity.An algorithm is designed to find the optimum solution of the proposed model.Numerical examples are given to demonstrate the results.Sensitivity analysis of the model with respect to several system parameters has been carried out and some managerial inferences are obtained.展开更多
Intelligent manufacturing design of a complex production-inventory system becomes a key issue for the organization of responsiveness to uncertainties.This paper addresses a two-echelon production-inventory model for a...Intelligent manufacturing design of a complex production-inventory system becomes a key issue for the organization of responsiveness to uncertainties.This paper addresses a two-echelon production-inventory model for a non-repairable product where the system consists of single manufacturer and single retailer.The manufacturer procures raw material(which also contains imperfect raw materials)from an outside supplier then proceeds to convert perfect-quality raw material as a finished product,and finally delivers to the retailer.In this study we assume that the demand is sensitive to promotional efforts/sales teams’initiatives and the production rate is uncertain but possible to describe with a triangular fuzzy number.Then we use the signed distance method to defuzzify the fuzzy joint total cost and an analytical method is employed to achieve the optimal solutions so that the total costs of both manufacturer and retailer are minimized.An efficient algorithm is developed to design an intelligent manufacturing strategy such as optimal production lot-size,backlogging and the initiatives of sales teams.A numerical example and sensitivity analysis are given to demonstrate the application of the proposed model.展开更多
In a fruit wholesale shop,a fruiterer needs to maintain huge inventory of different ranges of fruit items for customers because of uncertainty in consumer preferences and behaviour.But demand of them may differ and di...In a fruit wholesale shop,a fruiterer needs to maintain huge inventory of different ranges of fruit items for customers because of uncertainty in consumer preferences and behaviour.But demand of them may differ and different EOQ models for each item are required for optimal level of EOQ.This paper presents a single inventory model to assimilate these varieties.It is assumed that many fruit items bear constant rate of deterioration,some are with time proportional deterioration and some do not deteriorate.To control deterioration of the units in inventory,the advanced preservation technology is considered.The proposed single inventory model of this paper incorporates composite and heterogeneous features of multiple items and presents analysis for obtaining optimal level for output model parameters.展开更多
This paper analyses an inventory model for non-instantaneous deteriorating items under a two-warehouse system with the effect of inflation and time value of money.We propose the model from the seller’s prospective by...This paper analyses an inventory model for non-instantaneous deteriorating items under a two-warehouse system with the effect of inflation and time value of money.We propose the model from the seller’s prospective by incorporating the fact that granting the trade credit from the seller to its buyer not only increases sales and revenue but also opportunity cost and default risk.Moreover,in this model,shortages are allowed and partially backlogged.The backlogging rate is dependent on the waiting time for the next replenishment.The purpose of this study is to determine the optimal credit period and the optimal order quantity such that the total profit of the seller is maximised.Some numerical examples are presented for illustrating the proposed inventory model.Furthermore,sensitivity analysis of the optimal solutions with respect to major parameters is carried out and some managerial inferences are obtained.展开更多
On this paper,we proposed a generalize,incorporated deliver chain model for providers and outlets where delay in bills is obtainable through the suppliers and the shops for consistent deteriorating items.First,we prov...On this paper,we proposed a generalize,incorporated deliver chain model for providers and outlets where delay in bills is obtainable through the suppliers and the shops for consistent deteriorating items.First,we provide the mathematical formulations for the trouble beneath have a look at,and then endorse the solution process to derive the top-quality solution.right here shortages are not allowed.here we projected exponential call for for stores and the suppliers.An goal of this paper is to take a look at the stock modeling through fuzzy environment.right here we use triangular fuzzy range for purchasing the greatest answer.further an efficient algorithm is developed to decide most useful answer.Our technique is illustrated via a few numerical instance to showcase the utility and the overall performance of the proposed method.展开更多
The article presents a single-vendor and a single-buyer integrated production inventory system with inflation and the time value of money.The main focus is on the effect of ordering cost reduction dependent on lead ti...The article presents a single-vendor and a single-buyer integrated production inventory system with inflation and the time value of money.The main focus is on the effect of ordering cost reduction dependent on lead time and lead time reduction.Two integrated continuous review models are developed.For both cases,our objective is to minimise the total integrated system cost by simultaneously optimising the order quantity,safety factor,lead time and number of shipments.We take the transportation cost as a function of the shipment lot size and it is taken to be in an all unit-discount cost format.Thus we incorporate transportation cost explicitly into the model and develop optimal solution procedure for solving the proposed inventory system.An efficient algorithm for finding the optimal solution is developed and numerical examples are given to illustrate the model.展开更多
Lead time is an essential factor in any supply chain and inventory management system.In stochastic inventory models,lead time is often viewed as a prescribed constant or a random variable that is not subject to contro...Lead time is an essential factor in any supply chain and inventory management system.In stochastic inventory models,lead time is often viewed as a prescribed constant or a random variable that is not subject to control.In many practical situations,lead times can be controlled by paying additional investment.Using this viewpoint,notion of the crashing cost into stochastic inventory model,in which lead time can be controlled by additional investment.Many researchers have developed various analytical inventory models we have considered the piecewise linear function.So in this proposed model,we derive the mathematical model which is developed by incorporating three types of lead time crashing cost functions(i)exponential function,(ii)polynomial function and(iii)negative exponential function.An integrated inventory model is recognized to find the optimal solutions of order quantity,lead time,total cost for buyer,total cost for vendor and the total number of deliveries from the single-vendor to the single-buyer in one production run.A solution process is suggested for solving the proposed model and numerical examples to illustrate the feature of the proposed model,and examined the effect of the key parameters on the optimal solution and managerial implications are discussed.Numerical examples show that this model offers significant improvements over existing models.A computer code using the software Matlab is developed to derive the optimal solution.The main contribution of this paper is developing a mathematical model and an effective solution procedure to find the optimal solution.Finally,a graphical representation of the computational algorithm is represented by a flowchart in each model.展开更多
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 ...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.展开更多
This paper develops an economic production quantity(EPQ)model for a singlemanufacturer multi-retailer(SMMR)production and reworking system with green and environmental sensitive customer demand.The minimum cost of the...This paper develops an economic production quantity(EPQ)model for a singlemanufacturer multi-retailer(SMMR)production and reworking system with green and environmental sensitive customer demand.The minimum cost of the manufacturer has obtained under carbon emissions(CE)policies and discrete ordering cost reduction.The model is used to optimize the total number of shipments,greening investment level,environmental measure,and lot size for productions and rework.This research work determines that the manufacturer’s and retailer’s profits will be increased after considering the environmental and green dependent demand of customers.Further,the development of green and environmental demand is proposed to minimize the CE and maximize the demand for the customers.In the existing literature,no discrete investment is developed for reducing the cost of ordering for the retailer/buyer.However,in this paper,we have introduced it.We provide numerical examples to explain the models and determine the significance of model parameters.展开更多
This article considers the two-level supply chain model incorporating an imperfect production process under a variable lead time.The cost of producing a unit item is calculated as a function of the production rate.In ...This article considers the two-level supply chain model incorporating an imperfect production process under a variable lead time.The cost of producing a unit item is calculated as a function of the production rate.In addition,two alternative production functions(linear and quadratic functions)are used to relate process quality and production rate.Lead time demand follows two different distributions,based on which two mathematical formulations are described in this paper.In the first model,the lead time demand follows a normal distribution.In the second model,the lead time demand doesn’t follow any particular distribution,but the mean and the standard deviation are known.The lead time length is minimized by incorporating the lead time crashing cost.This research aims to analyze the optimized total cost of the supply chain under two different distributions.展开更多
This paper considers an inventory model with non-instantaneous deteriorating item in which demand rate is a function of selling price and time,taking account of time value of money.This paper aids the retailer in maxi...This paper considers an inventory model with non-instantaneous deteriorating item in which demand rate is a function of selling price and time,taking account of time value of money.This paper aids the retailer in maximising the total profit by determining optimal replenishment policies.Shortages are allowed which are partially backlogged.This model also takes into cognizance the fact that in business activities nowadays customers are given delay in payments.Under these assumptions,a mathematical model is formulated over a finite planning horizon and then some useful theoretical results have been framed to characterise the optimal solutions.The necessary and sufficient conditions for the existence and the uniqueness of the optimal solutions are also derived.An algorithm is designed to find the optimum solutions of the proposed model.Numerical examples are included to illustrate the algorithmic procedure and the effects of key parameters are studied to analyse the behaviour of the model.展开更多
文摘The substitution process is the most impeccable one in the inventory model for deteriorating items considering their lifetime issues.In this developed model,we worked on the inventory system for substitutable deteriorating items(product 1 and product 2);and both products are similar.The demand of the product is considered to have three different types,including constant,price-dependent,and promotional effort-dependent demand,to show the uncertainty of demand for a product in real life,and it is a manufacturer-retailer supply chain,where the manufacturer gives the pre-payment option and also cash discount to the retailer.In the substitution phase,we considered three various cases according to the inventory level of products 1 and 2.Direct and indirect carbon emissions in production and transportation were also considered.Numerical examples were used to verify the developed model.Sensitivity analysis was carried out to verify the obtained optimal values.
基金The research work is supported by DST INSPIRE Fellowship,Ministry of Science and Technology,Government of India under the grant no.DST/INSPIRE Fellowship/2011/413B dated 15 January 2014,and UGC–SAPDepartment of Mathematics,Gandhigram Rural Institute–Deemed University,Gandhigram–624302,Tamilnadu,India.
文摘This paper develops an economic production quantity(EPQ)model under the effect of inflation and time value of money.The rate of replenishment is considered to be a variable and the generalized unit production cost function is formulated by incorporating several factors,such as raw material,labour,replenishment rate,advertisements and other factors of the manufacturing system.The selling price of a unit is determined by a mark-up over the production cost.We have considered three types of continuous probabilistic deterioration function,and also considered that the holding cost of the item per unit time is assumed to be an increasing linear function of time spent in storage.In addition,shortages are allowed and partially backlogged.This model aids in minimizing the total inventory cost by finding the optimal cycle length and the optimal production quantity.The optimal solution of the model is illustrated with the help of numerical examples.
基金This research work is supported by DST INSPIRE,Ministry of Science and Technology,Government of India under the grant no.DST/INSPIRE Fellowship/2011/413B dated 02.12.2014.
文摘This paper develops an inventory model for deteriorating items with finite replenishment rate under a progressive payment scheme within the cycle time.In this model,the deterioration function follows a probability distribution such as a(1)uniform distribution,(2)triangular distribution or(3)beta distribution.Here,the retailer is allowed a trade-credit offer by the supplier to buy more items.This model aids in minimizing the total inventory cost of the retailer by finding the optimal cycle length,the optimal time length of replenishment and the optimal order quantity.Some theorems have been framed to characterize the optimal solutions.The necessary and sufficient conditions of the existence and uniqueness of the optimal solutions are also provided.The optimal solution of the model is illustrated with the help of numerical examples,and numerical comparisons between the three models are also given.Finally,sensitivity analysis and graphical representations are given to demonstrate the model.
文摘In this paper,economic order quantity(EOQ)inventory model is considered subject to promotional efforts.We adopt a demand function which is dependent on sales teams’initiatives in which shortages are allowed which are completely backlogged under the condition of permissible delay in payments with timedependent holding cost.The main objective of this paper is to determine the optimal replenishment schedule and optimal order quantity to maximize the total profit.Expressions for various optimal indices are provided.First,we prove that a unique optimal replenishment schedule exists.Second,we present an effective iterative algorithm to obtain the optimal solution.Furthermore,we establish some useful theorems to characterize the optimal solution to determine the values of replenishment schedule and optimal order quantity.Third,we prove that the total profit is a concave function via differential calculus and present numerical examples using SCILAB 5.5.0 to illustrate the model.Finally,we extend the numerical example by performing a sensitivity analysis of the model parameters and discuss managerial insights.This study suggests to the management of firms to determine the optimal order quantity,optimal inventory cycle length and sales teams’initiatives/promotional effort in order to achieve their maximum profits.
基金The first author’s research work is supported by DST INSPIRE,Ministry of Science and Technology,Government of India under grant no.DST/INSPIRE Fellowship/2011/413B dated 2 December 2014.
文摘In this paper,a two-warehouse economic order quantity(EOQ)model for noninstantaneously deteriorating items with stock-dependent demand under the effects of inflation and the time value of money is presented.Also in this model,shortages are allowed and partially backlogged.The backlogging rate is dependent on the waiting time for the next replenishment.The objective of this model is to minimize the total inventory cost of the retailer by finding the optimal intervals and the optimal order quantity.An algorithm is designed to find the optimum solution of the proposed model.Numerical examples are given to demonstrate the results.Sensitivity analysis of the model with respect to several system parameters has been carried out and some managerial inferences are obtained.
基金The second author’s research work is supported by DST INSPIRE,Ministry of Science and Technology,Government of India under the grant no.DST/INSPIRE Fellowship/2011/413B dated 15.01.2014.
文摘Intelligent manufacturing design of a complex production-inventory system becomes a key issue for the organization of responsiveness to uncertainties.This paper addresses a two-echelon production-inventory model for a non-repairable product where the system consists of single manufacturer and single retailer.The manufacturer procures raw material(which also contains imperfect raw materials)from an outside supplier then proceeds to convert perfect-quality raw material as a finished product,and finally delivers to the retailer.In this study we assume that the demand is sensitive to promotional efforts/sales teams’initiatives and the production rate is uncertain but possible to describe with a triangular fuzzy number.Then we use the signed distance method to defuzzify the fuzzy joint total cost and an analytical method is employed to achieve the optimal solutions so that the total costs of both manufacturer and retailer are minimized.An efficient algorithm is developed to design an intelligent manufacturing strategy such as optimal production lot-size,backlogging and the initiatives of sales teams.A numerical example and sensitivity analysis are given to demonstrate the application of the proposed model.
文摘In a fruit wholesale shop,a fruiterer needs to maintain huge inventory of different ranges of fruit items for customers because of uncertainty in consumer preferences and behaviour.But demand of them may differ and different EOQ models for each item are required for optimal level of EOQ.This paper presents a single inventory model to assimilate these varieties.It is assumed that many fruit items bear constant rate of deterioration,some are with time proportional deterioration and some do not deteriorate.To control deterioration of the units in inventory,the advanced preservation technology is considered.The proposed single inventory model of this paper incorporates composite and heterogeneous features of multiple items and presents analysis for obtaining optimal level for output model parameters.
基金supported by DST INSPIRE Fellowship,Ministry of Science and Technology,Government of India under the grant number DST/INSPIRE Fellowship/2011/413B dated 02.12.2014.
文摘This paper analyses an inventory model for non-instantaneous deteriorating items under a two-warehouse system with the effect of inflation and time value of money.We propose the model from the seller’s prospective by incorporating the fact that granting the trade credit from the seller to its buyer not only increases sales and revenue but also opportunity cost and default risk.Moreover,in this model,shortages are allowed and partially backlogged.The backlogging rate is dependent on the waiting time for the next replenishment.The purpose of this study is to determine the optimal credit period and the optimal order quantity such that the total profit of the seller is maximised.Some numerical examples are presented for illustrating the proposed inventory model.Furthermore,sensitivity analysis of the optimal solutions with respect to major parameters is carried out and some managerial inferences are obtained.
基金National Board for Higher Mathematics,Government of India under the scheme of NBHM research project[grant number 2/48(9)/2013/NBHM(R.P)/R&D II/Dated16.01.2014].
文摘On this paper,we proposed a generalize,incorporated deliver chain model for providers and outlets where delay in bills is obtainable through the suppliers and the shops for consistent deteriorating items.First,we provide the mathematical formulations for the trouble beneath have a look at,and then endorse the solution process to derive the top-quality solution.right here shortages are not allowed.here we projected exponential call for for stores and the suppliers.An goal of this paper is to take a look at the stock modeling through fuzzy environment.right here we use triangular fuzzy range for purchasing the greatest answer.further an efficient algorithm is developed to decide most useful answer.Our technique is illustrated via a few numerical instance to showcase the utility and the overall performance of the proposed method.
基金supported by DST-INSPIRE Fellowship,Ministry of Science and Technology,Government of India under the grant no.DST/INSPIRE Fellowship/2014/IF170071 and UGC-SAPDepartment of Mathematics,The Gandhigram Rural Institute-Deemed to be University,Gandhigram-624302,Tamil Nadu,India.
文摘The article presents a single-vendor and a single-buyer integrated production inventory system with inflation and the time value of money.The main focus is on the effect of ordering cost reduction dependent on lead time and lead time reduction.Two integrated continuous review models are developed.For both cases,our objective is to minimise the total integrated system cost by simultaneously optimising the order quantity,safety factor,lead time and number of shipments.We take the transportation cost as a function of the shipment lot size and it is taken to be in an all unit-discount cost format.Thus we incorporate transportation cost explicitly into the model and develop optimal solution procedure for solving the proposed inventory system.An efficient algorithm for finding the optimal solution is developed and numerical examples are given to illustrate the model.
基金DST INSPIRE Fellowship,Ministry of Science and Technology,Government of India under the grant no.DST/INSPIRE Fellowship/2011/413A dated 09.09.2016 and UGC-SAPDepartment of Mathematics,The Gandhigram Rural Institute-Deemed University,Gandhigram-624302,Tamil Nadu,India.
文摘Lead time is an essential factor in any supply chain and inventory management system.In stochastic inventory models,lead time is often viewed as a prescribed constant or a random variable that is not subject to control.In many practical situations,lead times can be controlled by paying additional investment.Using this viewpoint,notion of the crashing cost into stochastic inventory model,in which lead time can be controlled by additional investment.Many researchers have developed various analytical inventory models we have considered the piecewise linear function.So in this proposed model,we derive the mathematical model which is developed by incorporating three types of lead time crashing cost functions(i)exponential function,(ii)polynomial function and(iii)negative exponential function.An integrated inventory model is recognized to find the optimal solutions of order quantity,lead time,total cost for buyer,total cost for vendor and the total number of deliveries from the single-vendor to the single-buyer in one production run.A solution process is suggested for solving the proposed model and numerical examples to illustrate the feature of the proposed model,and examined the effect of the key parameters on the optimal solution and managerial implications are discussed.Numerical examples show that this model offers significant improvements over existing models.A computer code using the software Matlab is developed to derive the optimal solution.The main contribution of this paper is developing a mathematical model and an effective solution procedure to find the optimal solution.Finally,a graphical representation of the computational algorithm is represented by a flowchart in each model.
基金This work was supported by University Grants Commission–Special Assistance Program(DSA I)[grant number F.510/7/DSA-I/2015(SAP-I)],Government of India,New Delhi.
文摘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.
基金supported by University Grants Commission–Special Assistance Program(DSA I)[grant number F.510/7/DSA-I/2015(SAP-I)],Government of India,New Delhi.
文摘This paper develops an economic production quantity(EPQ)model for a singlemanufacturer multi-retailer(SMMR)production and reworking system with green and environmental sensitive customer demand.The minimum cost of the manufacturer has obtained under carbon emissions(CE)policies and discrete ordering cost reduction.The model is used to optimize the total number of shipments,greening investment level,environmental measure,and lot size for productions and rework.This research work determines that the manufacturer’s and retailer’s profits will be increased after considering the environmental and green dependent demand of customers.Further,the development of green and environmental demand is proposed to minimize the CE and maximize the demand for the customers.In the existing literature,no discrete investment is developed for reducing the cost of ordering for the retailer/buyer.However,in this paper,we have introduced it.We provide numerical examples to explain the models and determine the significance of model parameters.
文摘This article considers the two-level supply chain model incorporating an imperfect production process under a variable lead time.The cost of producing a unit item is calculated as a function of the production rate.In addition,two alternative production functions(linear and quadratic functions)are used to relate process quality and production rate.Lead time demand follows two different distributions,based on which two mathematical formulations are described in this paper.In the first model,the lead time demand follows a normal distribution.In the second model,the lead time demand doesn’t follow any particular distribution,but the mean and the standard deviation are known.The lead time length is minimized by incorporating the lead time crashing cost.This research aims to analyze the optimized total cost of the supply chain under two different distributions.
文摘This paper considers an inventory model with non-instantaneous deteriorating item in which demand rate is a function of selling price and time,taking account of time value of money.This paper aids the retailer in maximising the total profit by determining optimal replenishment policies.Shortages are allowed which are partially backlogged.This model also takes into cognizance the fact that in business activities nowadays customers are given delay in payments.Under these assumptions,a mathematical model is formulated over a finite planning horizon and then some useful theoretical results have been framed to characterise the optimal solutions.The necessary and sufficient conditions for the existence and the uniqueness of the optimal solutions are also derived.An algorithm is designed to find the optimum solutions of the proposed model.Numerical examples are included to illustrate the algorithmic procedure and the effects of key parameters are studied to analyse the behaviour of the model.
