K.K. Aggarwal

Inventory and pricing strategies for deteriorating items with limited capacity and time-proportional backlogging rate

In the present study, a two-warehouse deterministic inventory model for deteriorating items with price-sensitive demand is developed. A rented warehouse (RW) is used to store the excess units over the fixed capacity of the own warehouse (OW). In addition, shortages are allowed in the OW and it is assumed that the backlogging demand rate is dependent on the duration of the stock-out. The objective is to find the optimal inventory and pricing strategies maximising the total average profit over the infinite planning horizon. For any given selling price, we first prove that the optimal replenishment schedule not only exists but is unique. Next, we show that the total average profit is a concave function of price when the replenishment schedule is given. The optimal selling price and replenishment schedule is also calculated for the proposed model. Finally, the results have been validated with the help of a numerical example.

Economic order quantity model under fuzzy sense when demand follows innovation diffusion process having dynamic potential market size

The conventional inventory models are associated with different kind of uncertainties and these uncertainties make the model unrealistic. The fuzzy set theory plays a pivotal role to address this problem. In this paper, a mathematical model has been developed for obtaining the economic order quantity (EOQ) in which the demand of the product is assumed to follow an innovation diffusion process as proposed by Fourt and Woodlock (1960). The potential market size is considered to be dynamic. To make the model more realistic an attempt has been made to solve the model in the light of fuzzy set theory under the trapezoidal membership function. The total cost formula has been derived by applying the median rule of defuzzification and the graded mean integration representation approach of defuzzification. The effectiveness of this model is illustrated with a numerical example and sensitivity analysis of the optimal solution with respect to different parameters of the system is performed.

Economic order quantity model with innovation diffusion criterion having dynamic potential market size

Introduction of a new product in the market forces the inventory managers to consider the effects of marketing policies especially for innovation effects at the earlier stage of the product life cycle to make the economic order quantity (EOQ) model more realistic. Traditional EOQ models generally do not consider the effect of marketing parameters. In this paper, a time dependent innovation driven demand model has been introduced in the basic EOQ model to calculate the different optimal policies. This model assumes that potential market size is dynamic over time. The proposed model acknowledges relationship between the innovation coefficient and the optimal policies. The effectiveness of this model is illustrated with a numerical example and sensitivity analysis of the optimal solution with respect to different parameters of the system is performed.

A model to jointly determine inventory and credit policies in an inventory system with date-terms credit linked demand

In order to increase sales over and above cash sales, firms generally give trade credit to their customers. Trade credit policy through its influence on demand becomes a determinant of inventory policy which is intended to meet that demand. Therefore, inventory and trade credit policies are interrelated which should be determined simultaneously in a systems perspective. However, inventory policy is generally determined independent of the credit policy. This paper develops a mathematical model for simultaneously determining inventory and credit policies when demand rate consists of: 1 cash demand rate 2 credit demand rate depending upon date-terms credit period. Discounted cash flow approach has been used to establish the model. The objective of the model is to maximise the present value of firm’ s net profit per unit time by jointly determining the optimal date-terms credit period and replenishment time. Numerical example and sensitivity analysis are presented to illustrate the effectiveness of proposed model and results are discussed. The model suggests that at high values of inventory carrying cost and accounts receivable carrying cost the firm should invest less in accounts receivables by following a tight credit policy.

An inventory decision model for new products when demand depends on dynamic advertising expenditure

The new product acceptance theory which is well recognised in the marketing literature plays a pivotal role in determining the procurement schedule of the products which are newly introduced in the market for the models developed in the inventory management field. The diffusion of new products are made mainly through the advertisements in different media and the word-of-mouth which are popularly known as external and internal influences respectively. The external influences in the form of advertising greatly influence the innovators, that is, those persons who are to purchase the product as new one. This paper develops an inventory model where demand of the product is assumed to be dynamic over time and influenced by level of advertising expenditure in an innovation diffusion environment based on Horsky and Simon (1983). The paper derives the profit functions for different situations and conditions and jointly optimises the level of initial advertising expenditure with the cycle length. A simple solution procedure in the form of algorithm has been developed to obtain the optimal solution. The numerical example followed by comprehensive sensitivity analysis with respect to different parameters has been performed to know the behaviour and effectiveness of the model.

Economic order quantity model under fuzzy sense with demand follows Bass’s innovation diffusion process

The economic order quantity (EOQ) model is usually not paid attention to make the model more realistic. The realistic EOQ model can bring a significant change while evaluating the profit and loss of any organisation. In this paper a mathematical model has been developed for obtaining the EOQ in which the demand of the product is assumed to follow an innovative imitative behaviour as proposed by Bass (1969). The theory of innovation-diffusion has been incorporated in this model. To make the model more realistic an attempt has been made to solve the model in light of fuzzy set theory under the trapezoidal membership function. The coefficient of innovation, the coefficient of imitation and the inventory carrying cost is assumed to be fuzzy numbers with trapezoidal membership function. By the median rule of defuzzification, total cost formula has been derived in the fuzzy sense in order to obtain the optimal order quantity. The effectiveness of this model is illustrated with a numerical example and sensitivity analysis of the optimal solution with respect to different parameters of the system is performed.

Two-warehouse inventory model for deteriorating items when demand is price sensitive

The main objective of this article is to develop a two-warehouse inventory model for deteriorating items when demand is price sensitive. It is assumed that the units are transported under a bulk release pattern from Rented Warehouse to Own Warehouse and the deterioration rates of the items are different in the two warehouses. Further, the model jointly optimises the order quantity and selling price. Depending upon the optimal order quantity, decision is made whether to rent other warehouse. The optimal shipment policy is also provided if indeed the other warehouse is needed. The results have been validated with the help of a numerical example. Sensitivity analysis on the demand parameters is also performed.

Economic Order Quantity Model with Innovation Diffusion Criterion under Influence of Price-Dependent Potential Market Size

In last few decades various models developed under inventory control section whether of probabilistic or deterministic nature did not consider the effect of marketing parameters. The marketing parameters especially associated with innovation diffusion theory make the inventory models more realistic. In this paper, an inventory model has been proposed based on the explicit assumptions of interaction of marketing parameters to the optimal inventory replenishment policy. A time-dependent innovation driven demand has been incorporated in the basic economic order quantity (EOQ) model to know the realistic features of the model. This model assumes that potential market size is dynamic over time and is dependent on the price of the product. The model is illustrated with a numerical example and to know the effectiveness of the model a sensitivity analysis of the optimal solution with respect to different parameters has been performed.

Optimal Replenishment Policy for an Inventory Model with Demand Follows Innovation Diffusion Process under Permissible Delay in Payments

In this paper a mathematical model has been developed for obtaining the Economic Order Quantity (EOQ) in which the interaction of EOQ with marketing parameters such as external and internal influences under the condition of permissible delay in payments have been considered. The model assumes that the demand is a function of time follows from the adoption behaviour of Basss diffusion model [5]. The two different cases of permissible delay in payments have been discussed to know the condition of economic ordering policies in a different situation of credit period offered. The integrated effect of both the factors that is permissible delay in payments as well as the marketing parameters on the economic ordering policies of the products has been considered. A solution procedure is developed to find the optimal order quantity and replenishment time, which minimizes the total cost of an inventory system. A numerical example followed by sensitivity analysis of the optimal solution with respect to different parameters of the system has been performed to illustrate the effectiveness of the model.

Optimal Inventory and Credit Policies under Two Levels of Trade Credit Financing in an Inventory System with Date-Terms Credit Linked Demand

Credit policy through its influence on demand indirectly affects the inventory policy which is designed to meet that demand; therefore inventory policy is interrelated with the credit policy. Consequently, they must be coordinated and should be determined simultaneously in a systems perspective. In this paper, a mathematical model is developed in a discounted cash flow (DCF) framework to jointly determine inventory and credit policies under two levels of trade credit financing in the presence of stimulating as well as disintegrating effect of credit period on demand. The objective of the model is to maximize the present value of firms net profit per unit time by jointly optimizing the date-terms credit period and replenishment interval. Numerical example and sensitivity analysis are presented to illustrate the effectiveness of the proposed model and results are discussed.