Waste management and reworking are very crucial issues in the cleaner production system. The adap... more Waste management and reworking are very crucial issues in the cleaner production system. The adaptation of preservation mechanism in inventory control is also a key aspect from an economic and environmental point of view. In the current study, an inventory model for a cleaner production system is modelled considering all these practical issues and inflation. Deterioration process takes place in the production system. In the model, market demand is viewed sales team efforts and selling price dependent. Here, rate of production along with the unit production cost are taken as variables. An investment in preservation technology is made with the goal to lower the percentage of defective products. Further, partial backordering is considered. In order to demonstrate the model, numerical example is provided. A Hessian matrix is used to establish the concavity of the objective function. A theoretical result is provided to obtain the concavity of the objective function. Sensitivity analysis ...
Supply chain management aims to integrate environmental thinking with efficient energy consumptio... more Supply chain management aims to integrate environmental thinking with efficient energy consumption into supply chain management. It includes a flexible manufacturing process, more product delivery to customers, optimum energy consumption, and reduced waste. The manufacturing process can be made more flexible through volume agility. In this scenario, production cannot be constant, and with the concept of volume agility, production is taken as a decision variable under the effect of optimum energy consumption. Considering a two-echelon supply chain, we consider a producer and supplier with two-level-trade-credit policies (TLTCP) with the optimum consumption. To reduce the integrated total inventory cost, we believe that demand is a function of the credit period and selling price. The cost function is analyzed, either with the credit period dependent demand rate or with the selling price dependent demand rate through the numerical examples under energy costs. Energy and carbon emission...
This research paper builds a manufacturer-retailer integrated inventory model to compute jointly ... more This research paper builds a manufacturer-retailer integrated inventory model to compute jointly the optimal values for the order quantity, the lead time, the reorder point and the number of shipments taking into consideration the effect of learning-forgetting phenomenon on the setup cost. The fabrication process of manufacturer is not perfect and certain level of product quality can attain with an additional cost. Service level constraint is incorporated into the inventory model to evade the backorder which gives negative impact to company reputation. The lead time is reduced with the help of crashing cost. The proposed inventory model is illustrated with the help of an example. From this example, it is detected that centralized decision is better than decentralized one. It is also observed from the analysis that players have to compromise with their profit if they decide to increment the service level and quality of the product. Due to the effect of learning-forgetting on the setu...
International Journal of Applied and Computational Mathematics, 2021
The primary concern of every business manager of supply chain system is to obtain economical sust... more The primary concern of every business manager of supply chain system is to obtain economical sustainability. To achieve this goal they adopt different polices such as multi-stage manufacturing process, promotional strategies, learning effect, screening process etc. In the present study, a supply chain model consisting one retailer and one manufacturer is examined regarding the financial viability. An imperfect multi-stage manufacturing process is considered here with a probabilistic deteriorating item. The screening process under the effect of learning is performed in each stage of production and further the imperfect products are reworked in the same stage. Promotional efforts are initiated by the retailer to boost up demand. Shortages are allowed at the retailer end with partially backlogging. All the cost parameters are imprecise parameters due to the presence of uncertainty in the market. The presence of impreciseness in cost parameters is handled by applying the fuzzy set theory. To defuzzify the objective function of the system, the centroid method is used. Aim of this work is to minimize the average inventory cost so that order quantity and backorder quantity are optimal. Objective function in the developed model is nonlinear optimization problem which is solved with the help of calculus based classical optimization technique. Further, convexity of the objective function is explored with the help of graphs and Hessian matrix. Results indicate that average inventory cost decreases by 5% as the supply chain system shifted to three-stage manufacturing process to five-stage manufacturing process. Further, analysis shows that incorporating impreciseness in costs capture the real picture of business. Sustainability of the proposed model is explored with the help of numerical example and sensitive analysis. Form sensitivity analysis, positive impact of screening rate and promotional efforts are observed on the average cost of the system. Analysis also reflects that inventory cost of the system is high due to high backlogging rate.
This paper investigates an Economic Order Quantity (EOQ) model with backorder by taking imprecise... more This paper investigates an Economic Order Quantity (EOQ) model with backorder by taking imprecise demand rate with dependence upon the frequency of advertisement. The formulated model also incorporates learning effects on percentage of defective items present in each lot. Due to imprecision in demand, the obtained profit function is fuzzy. To determine the optimal values, we determine the equivalent crisp profit function by applying the signed distance method. Optimal order quantity and backorder level are obtained by using algebraic method in place of differential calculus. A numerical example is used to study the behavior of the model with respect to different inventory parameters. All calculations are performed with MATLAB 7.4.
ABSTRACT Trade credit plays an important role in financing many industries. In the classical inve... more ABSTRACT Trade credit plays an important role in financing many industries. In the classical inventory model it is assumed that the buyer must pay for the items as soon as the items are received. In this problem, it is considered that the retailer can pay the supplier either at the end of the credit period or later pay interest on the unpaid amount for the overdue period. Here, the retailer's inventory model for the optimal cycle time and payment time for a retailer is developed. The effects of the inflation rate, deterioration rate and delay in payment have been discussed. The whole study is performed in a fuzzy environment by taking the opportunity cost, interest earned and interest paid rate as a triangular fuzzy number. Fuzzy profit functions, which involve fuzzy arithmetic operation, are defined using the function principle. We use the signed distance method to defuzzify the fuzzy profit function. Moreover, numerical and sensitivity analysis is performed to validate the proposed model.
Abstract Carbon emission plays a vital role in global warming. In addition to this, wastages due ... more Abstract Carbon emission plays a vital role in global warming. In addition to this, wastages due to the deterioration have a hazardous impact on the ecosystem. The responsible managers' primary concern is to form a sustainable supply chain. Further, supply chain managers select some appropriate combinations when dealing with items that possess cross-price elasticity of demand to make a profitable system. The present model aims to make a sustainable supply chain to reduce waste by obtaining the optimal values of production rate, batch size, several shipments, and preservation investment such that the total profit of the system is maximum. In the present study, a supply chain model with two manufacturers and one common retailer is developed. The proposed supply chain deals with products having negative or positive cross-price elasticity of demand. The carbon emission is also considered, which is associated with different operational activities of inventory such as preparation of setup of manufacturers, transportation of products, waste management, and holding stock at manufacturers and the retailer's end. The objective function in the present study is a mixed-integer nonlinear optimization problem. A solution methodology based on differential calculus is adopted. The result shows that products of low negative or high positive cross-price elasticity are a profitable combination. Additionally, a 20% reduction in wastage quantity is observed due to the investment in preservation technology. This result indicates that preservation technology positively impacts the environment and the finance associated with the inventory system. The proposed integrated system's sustainability is illustrated with numerical examples, sensitivity analysis, and pictorial representation. In addition to this, several valuable managerial insights based on the study are provided.
Abstract: Multi-item inventory model for deteriorating items with stock dependent
demand under tw... more Abstract: Multi-item inventory model for deteriorating items with stock dependent demand under two-warehouse system is developed in fuzzy environment (purchase cost, investment amount and storehouse capacity are imprecise ) under inflation and time value of money. For display and storage, the retailers hire one warehouse of finite capacity at market place, treated as their own warehouse (OW), and another warehouse of imprecise capacity which may be required at some place distant from the market, treated as a rented warehouse (RW). Joint replenishment and simultaneous transfer of items from one warehouse to another is proposed using basic period (BP) policy. As some parameters are fuzzy in nature, objective (average profit) functions as well as some constraints are imprecise in nature, too. The model is formulated so to optimize the possibility/necessity measure of the fuzzy goal of the objective functions, and the constraints satisfy some pre-defined necessity. A genetic algorithm (GA) is used to solve the model, which is illustrated on a numerical example.
It is a natural phenomenon that the performance of a system engaged in a
repetitive process impro... more It is a natural phenomenon that the performance of a system engaged in a repetitive process improves with time. In literature, this phenomenon is referred to as the ‘learning effect’. The present paper analyzes the impact of learning on optimal solution of inventory problem. The aim of this paper is to develop an inventory model to deal the fuzziness aspect of demand and effect of learning on holding cost, ordering cost and number of defective items present in each lot. In this model, it is assumed that the received items are not of perfect quality and after100% screening, imperfect items are withdrawn from inventory and sold at discounted price. Due to acquaintance with the system and handling methodology, holding cost and ordering cost are gradually decreases from one shipment to another. These concepts are best fitted in industry such as automotive and stabilizer industry. In these industries, number of defective items, holding cost and ordering cost reduces from one shipment to another due to learning effect. Extension principle is used to fuzzify the profit expression. Unique optimal lot size is obtained by calculus method. Finally, the feasibility of model and the effect of learning on optimal solution are shown through numerical example. Sensitivity analysis is also carried out with respect to different inventory parameters.
This paper investigates an Economic Order Quantity
(EOQ) model with backorder by taking imprecis... more This paper investigates an Economic Order Quantity (EOQ) model with backorder by taking imprecise demand rate with dependence upon the frequency of advertisement. The formulated model also incorporates learning effects on percentage of defective items present in each lot. Due to imprecision in demand, the obtained profit function is fuzzy. To determine the optimal values, we determine the equivalent crisp profit function by applying the signed distance method. Optimal order quantity and backorder level are obtained by using algebraic method in place of differential calculus. A numerical example is used to study the behavior of the model with respect to different inventory parameters. All calculations are performed with MATLAB 7.4. Keywords: learning curve, advertisement, signed distance, triangular fuzzy number, backorder, inventory model.
Aquilaria agallocha Roxb. family, Thymelaeaceae, is an evergreen plant of South-East Asia, common... more Aquilaria agallocha Roxb. family, Thymelaeaceae, is an evergreen plant of South-East Asia, commonly described as aloe wood or agarwood. Traditionally, the bark, root and heartwood are used for their medicinal properties as a folk medicine for hundreds of years. Chemical analyses revealed that the bulk of the oil is constituted by agarospirol (12.5%), jinkoh-eremol (11.8%) and hinesol (8.9%) as major contributor. In the present work, a QSAR model for anti-inflammatory activity of 10-epi-γ-Eudesmol, jinkoh-eremol, agarospirol and other compounds has been developed by multiple linear regression method. The r2 and rCV2 of a model were 0.89 and 0.81 respectively. In silico molecular docking study suggests that compound 10-epi-γ-Eudesmol, jinkoh-eremol and agarospirol are preferentially more active than other identified compounds with strong binding affinity to major anti-inflammatory and immunomodulatory receptors. The oil displayed a significant and dose dependent reduction of 12-O-tetr...
Waste management and reworking are very crucial issues in the cleaner production system. The adap... more Waste management and reworking are very crucial issues in the cleaner production system. The adaptation of preservation mechanism in inventory control is also a key aspect from an economic and environmental point of view. In the current study, an inventory model for a cleaner production system is modelled considering all these practical issues and inflation. Deterioration process takes place in the production system. In the model, market demand is viewed sales team efforts and selling price dependent. Here, rate of production along with the unit production cost are taken as variables. An investment in preservation technology is made with the goal to lower the percentage of defective products. Further, partial backordering is considered. In order to demonstrate the model, numerical example is provided. A Hessian matrix is used to establish the concavity of the objective function. A theoretical result is provided to obtain the concavity of the objective function. Sensitivity analysis ...
Supply chain management aims to integrate environmental thinking with efficient energy consumptio... more Supply chain management aims to integrate environmental thinking with efficient energy consumption into supply chain management. It includes a flexible manufacturing process, more product delivery to customers, optimum energy consumption, and reduced waste. The manufacturing process can be made more flexible through volume agility. In this scenario, production cannot be constant, and with the concept of volume agility, production is taken as a decision variable under the effect of optimum energy consumption. Considering a two-echelon supply chain, we consider a producer and supplier with two-level-trade-credit policies (TLTCP) with the optimum consumption. To reduce the integrated total inventory cost, we believe that demand is a function of the credit period and selling price. The cost function is analyzed, either with the credit period dependent demand rate or with the selling price dependent demand rate through the numerical examples under energy costs. Energy and carbon emission...
This research paper builds a manufacturer-retailer integrated inventory model to compute jointly ... more This research paper builds a manufacturer-retailer integrated inventory model to compute jointly the optimal values for the order quantity, the lead time, the reorder point and the number of shipments taking into consideration the effect of learning-forgetting phenomenon on the setup cost. The fabrication process of manufacturer is not perfect and certain level of product quality can attain with an additional cost. Service level constraint is incorporated into the inventory model to evade the backorder which gives negative impact to company reputation. The lead time is reduced with the help of crashing cost. The proposed inventory model is illustrated with the help of an example. From this example, it is detected that centralized decision is better than decentralized one. It is also observed from the analysis that players have to compromise with their profit if they decide to increment the service level and quality of the product. Due to the effect of learning-forgetting on the setu...
International Journal of Applied and Computational Mathematics, 2021
The primary concern of every business manager of supply chain system is to obtain economical sust... more The primary concern of every business manager of supply chain system is to obtain economical sustainability. To achieve this goal they adopt different polices such as multi-stage manufacturing process, promotional strategies, learning effect, screening process etc. In the present study, a supply chain model consisting one retailer and one manufacturer is examined regarding the financial viability. An imperfect multi-stage manufacturing process is considered here with a probabilistic deteriorating item. The screening process under the effect of learning is performed in each stage of production and further the imperfect products are reworked in the same stage. Promotional efforts are initiated by the retailer to boost up demand. Shortages are allowed at the retailer end with partially backlogging. All the cost parameters are imprecise parameters due to the presence of uncertainty in the market. The presence of impreciseness in cost parameters is handled by applying the fuzzy set theory. To defuzzify the objective function of the system, the centroid method is used. Aim of this work is to minimize the average inventory cost so that order quantity and backorder quantity are optimal. Objective function in the developed model is nonlinear optimization problem which is solved with the help of calculus based classical optimization technique. Further, convexity of the objective function is explored with the help of graphs and Hessian matrix. Results indicate that average inventory cost decreases by 5% as the supply chain system shifted to three-stage manufacturing process to five-stage manufacturing process. Further, analysis shows that incorporating impreciseness in costs capture the real picture of business. Sustainability of the proposed model is explored with the help of numerical example and sensitive analysis. Form sensitivity analysis, positive impact of screening rate and promotional efforts are observed on the average cost of the system. Analysis also reflects that inventory cost of the system is high due to high backlogging rate.
This paper investigates an Economic Order Quantity (EOQ) model with backorder by taking imprecise... more This paper investigates an Economic Order Quantity (EOQ) model with backorder by taking imprecise demand rate with dependence upon the frequency of advertisement. The formulated model also incorporates learning effects on percentage of defective items present in each lot. Due to imprecision in demand, the obtained profit function is fuzzy. To determine the optimal values, we determine the equivalent crisp profit function by applying the signed distance method. Optimal order quantity and backorder level are obtained by using algebraic method in place of differential calculus. A numerical example is used to study the behavior of the model with respect to different inventory parameters. All calculations are performed with MATLAB 7.4.
ABSTRACT Trade credit plays an important role in financing many industries. In the classical inve... more ABSTRACT Trade credit plays an important role in financing many industries. In the classical inventory model it is assumed that the buyer must pay for the items as soon as the items are received. In this problem, it is considered that the retailer can pay the supplier either at the end of the credit period or later pay interest on the unpaid amount for the overdue period. Here, the retailer's inventory model for the optimal cycle time and payment time for a retailer is developed. The effects of the inflation rate, deterioration rate and delay in payment have been discussed. The whole study is performed in a fuzzy environment by taking the opportunity cost, interest earned and interest paid rate as a triangular fuzzy number. Fuzzy profit functions, which involve fuzzy arithmetic operation, are defined using the function principle. We use the signed distance method to defuzzify the fuzzy profit function. Moreover, numerical and sensitivity analysis is performed to validate the proposed model.
Abstract Carbon emission plays a vital role in global warming. In addition to this, wastages due ... more Abstract Carbon emission plays a vital role in global warming. In addition to this, wastages due to the deterioration have a hazardous impact on the ecosystem. The responsible managers' primary concern is to form a sustainable supply chain. Further, supply chain managers select some appropriate combinations when dealing with items that possess cross-price elasticity of demand to make a profitable system. The present model aims to make a sustainable supply chain to reduce waste by obtaining the optimal values of production rate, batch size, several shipments, and preservation investment such that the total profit of the system is maximum. In the present study, a supply chain model with two manufacturers and one common retailer is developed. The proposed supply chain deals with products having negative or positive cross-price elasticity of demand. The carbon emission is also considered, which is associated with different operational activities of inventory such as preparation of setup of manufacturers, transportation of products, waste management, and holding stock at manufacturers and the retailer's end. The objective function in the present study is a mixed-integer nonlinear optimization problem. A solution methodology based on differential calculus is adopted. The result shows that products of low negative or high positive cross-price elasticity are a profitable combination. Additionally, a 20% reduction in wastage quantity is observed due to the investment in preservation technology. This result indicates that preservation technology positively impacts the environment and the finance associated with the inventory system. The proposed integrated system's sustainability is illustrated with numerical examples, sensitivity analysis, and pictorial representation. In addition to this, several valuable managerial insights based on the study are provided.
Abstract: Multi-item inventory model for deteriorating items with stock dependent
demand under tw... more Abstract: Multi-item inventory model for deteriorating items with stock dependent demand under two-warehouse system is developed in fuzzy environment (purchase cost, investment amount and storehouse capacity are imprecise ) under inflation and time value of money. For display and storage, the retailers hire one warehouse of finite capacity at market place, treated as their own warehouse (OW), and another warehouse of imprecise capacity which may be required at some place distant from the market, treated as a rented warehouse (RW). Joint replenishment and simultaneous transfer of items from one warehouse to another is proposed using basic period (BP) policy. As some parameters are fuzzy in nature, objective (average profit) functions as well as some constraints are imprecise in nature, too. The model is formulated so to optimize the possibility/necessity measure of the fuzzy goal of the objective functions, and the constraints satisfy some pre-defined necessity. A genetic algorithm (GA) is used to solve the model, which is illustrated on a numerical example.
It is a natural phenomenon that the performance of a system engaged in a
repetitive process impro... more It is a natural phenomenon that the performance of a system engaged in a repetitive process improves with time. In literature, this phenomenon is referred to as the ‘learning effect’. The present paper analyzes the impact of learning on optimal solution of inventory problem. The aim of this paper is to develop an inventory model to deal the fuzziness aspect of demand and effect of learning on holding cost, ordering cost and number of defective items present in each lot. In this model, it is assumed that the received items are not of perfect quality and after100% screening, imperfect items are withdrawn from inventory and sold at discounted price. Due to acquaintance with the system and handling methodology, holding cost and ordering cost are gradually decreases from one shipment to another. These concepts are best fitted in industry such as automotive and stabilizer industry. In these industries, number of defective items, holding cost and ordering cost reduces from one shipment to another due to learning effect. Extension principle is used to fuzzify the profit expression. Unique optimal lot size is obtained by calculus method. Finally, the feasibility of model and the effect of learning on optimal solution are shown through numerical example. Sensitivity analysis is also carried out with respect to different inventory parameters.
This paper investigates an Economic Order Quantity
(EOQ) model with backorder by taking imprecis... more This paper investigates an Economic Order Quantity (EOQ) model with backorder by taking imprecise demand rate with dependence upon the frequency of advertisement. The formulated model also incorporates learning effects on percentage of defective items present in each lot. Due to imprecision in demand, the obtained profit function is fuzzy. To determine the optimal values, we determine the equivalent crisp profit function by applying the signed distance method. Optimal order quantity and backorder level are obtained by using algebraic method in place of differential calculus. A numerical example is used to study the behavior of the model with respect to different inventory parameters. All calculations are performed with MATLAB 7.4. Keywords: learning curve, advertisement, signed distance, triangular fuzzy number, backorder, inventory model.
Aquilaria agallocha Roxb. family, Thymelaeaceae, is an evergreen plant of South-East Asia, common... more Aquilaria agallocha Roxb. family, Thymelaeaceae, is an evergreen plant of South-East Asia, commonly described as aloe wood or agarwood. Traditionally, the bark, root and heartwood are used for their medicinal properties as a folk medicine for hundreds of years. Chemical analyses revealed that the bulk of the oil is constituted by agarospirol (12.5%), jinkoh-eremol (11.8%) and hinesol (8.9%) as major contributor. In the present work, a QSAR model for anti-inflammatory activity of 10-epi-γ-Eudesmol, jinkoh-eremol, agarospirol and other compounds has been developed by multiple linear regression method. The r2 and rCV2 of a model were 0.89 and 0.81 respectively. In silico molecular docking study suggests that compound 10-epi-γ-Eudesmol, jinkoh-eremol and agarospirol are preferentially more active than other identified compounds with strong binding affinity to major anti-inflammatory and immunomodulatory receptors. The oil displayed a significant and dose dependent reduction of 12-O-tetr...
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demand under two-warehouse system is developed in fuzzy environment (purchase cost,
investment amount and storehouse capacity are imprecise ) under inflation and time
value of money. For display and storage, the retailers hire one warehouse of finite
capacity at market place, treated as their own warehouse (OW), and another warehouse
of imprecise capacity which may be required at some place distant from the market,
treated as a rented warehouse (RW). Joint replenishment and simultaneous transfer of
items from one warehouse to another is proposed using basic period (BP) policy. As
some parameters are fuzzy in nature, objective (average profit) functions as well as some
constraints are imprecise in nature, too. The model is formulated so to optimize the
possibility/necessity measure of the fuzzy goal of the objective functions, and the
constraints satisfy some pre-defined necessity. A genetic algorithm (GA) is used to solve
the model, which is illustrated on a numerical example.
repetitive process improves with time. In literature, this phenomenon is
referred to as the ‘learning effect’. The present paper analyzes the impact of
learning on optimal solution of inventory problem. The aim of this paper is to
develop an inventory model to deal the fuzziness aspect of demand and effect
of learning on holding cost, ordering cost and number of defective items
present in each lot. In this model, it is assumed that the received items are not
of perfect quality and after100% screening, imperfect items are withdrawn
from inventory and sold at discounted price. Due to acquaintance with the
system and handling methodology, holding cost and ordering cost are
gradually decreases from one shipment to another. These concepts are best
fitted in industry such as automotive and stabilizer industry. In these
industries, number of defective items, holding cost and ordering cost reduces
from one shipment to another due to learning effect. Extension principle is
used to fuzzify the profit expression. Unique optimal lot size is obtained by
calculus method. Finally, the feasibility of model and the effect of learning on
optimal solution are shown through numerical example. Sensitivity analysis is
also carried out with respect to different inventory parameters.
(EOQ) model with backorder by taking imprecise demand rate with
dependence upon the frequency of advertisement. The formulated
model also incorporates learning effects on percentage of defective
items present in each lot. Due to imprecision in demand, the obtained
profit function is fuzzy. To determine the optimal values, we
determine the equivalent crisp profit function by applying the signed
distance method. Optimal order quantity and backorder level are
obtained by using algebraic method in place of differential calculus.
A numerical example is used to study the behavior of the model
with respect to different inventory parameters. All calculations are
performed with MATLAB 7.4.
Keywords: learning curve, advertisement, signed distance, triangular
fuzzy number, backorder, inventory model.
demand under two-warehouse system is developed in fuzzy environment (purchase cost,
investment amount and storehouse capacity are imprecise ) under inflation and time
value of money. For display and storage, the retailers hire one warehouse of finite
capacity at market place, treated as their own warehouse (OW), and another warehouse
of imprecise capacity which may be required at some place distant from the market,
treated as a rented warehouse (RW). Joint replenishment and simultaneous transfer of
items from one warehouse to another is proposed using basic period (BP) policy. As
some parameters are fuzzy in nature, objective (average profit) functions as well as some
constraints are imprecise in nature, too. The model is formulated so to optimize the
possibility/necessity measure of the fuzzy goal of the objective functions, and the
constraints satisfy some pre-defined necessity. A genetic algorithm (GA) is used to solve
the model, which is illustrated on a numerical example.
repetitive process improves with time. In literature, this phenomenon is
referred to as the ‘learning effect’. The present paper analyzes the impact of
learning on optimal solution of inventory problem. The aim of this paper is to
develop an inventory model to deal the fuzziness aspect of demand and effect
of learning on holding cost, ordering cost and number of defective items
present in each lot. In this model, it is assumed that the received items are not
of perfect quality and after100% screening, imperfect items are withdrawn
from inventory and sold at discounted price. Due to acquaintance with the
system and handling methodology, holding cost and ordering cost are
gradually decreases from one shipment to another. These concepts are best
fitted in industry such as automotive and stabilizer industry. In these
industries, number of defective items, holding cost and ordering cost reduces
from one shipment to another due to learning effect. Extension principle is
used to fuzzify the profit expression. Unique optimal lot size is obtained by
calculus method. Finally, the feasibility of model and the effect of learning on
optimal solution are shown through numerical example. Sensitivity analysis is
also carried out with respect to different inventory parameters.
(EOQ) model with backorder by taking imprecise demand rate with
dependence upon the frequency of advertisement. The formulated
model also incorporates learning effects on percentage of defective
items present in each lot. Due to imprecision in demand, the obtained
profit function is fuzzy. To determine the optimal values, we
determine the equivalent crisp profit function by applying the signed
distance method. Optimal order quantity and backorder level are
obtained by using algebraic method in place of differential calculus.
A numerical example is used to study the behavior of the model
with respect to different inventory parameters. All calculations are
performed with MATLAB 7.4.
Keywords: learning curve, advertisement, signed distance, triangular
fuzzy number, backorder, inventory model.