Optimal Ordering and Trade Credit Policy for EOQ Model

Trade credit is the most prevailing economic phenomena used by the suppliers for encouraging the retailers to increase their ordering quantity. In this article, an attempt is made to derive a mathematical model to find optimal credit policy and hence ordering quantity to minimize the cost. Even though, credit period is offered by the supplier, both parties (supplier and retailer) sit together to agree upon the permissible credit for settlement of the accounts by the retailer. A numerical example is given to support the analytical arguments.Trade Credit, Optimal ordering quantity, Lot-size

Optimal Inventory Policies for Weibull Deterioration under Trade Credit in Declining Market

The aim of this study is to develop mathematical model for Weibull deterioration of items in inventory in declining market when the supplier offers his retailers a credit period to settle the accounts against the dues. The computational steps are explored for a retailer to determine the optimal purchase units which minimize the total inventory cost per time unit. The numerical examples are given to demonstrate the retailer’s optimal decision. A sensitivity analysis is carried out to study the variations in the optimal solution.Weibull deterioration, trade credit, declining market

Modelling and Analysis of HIV/AIDS Menace using Differential Equations

Mathematical models play important role in understanding the population dynamics of HIV/AIDS. In this study, a mathematical model is formulated for a community which has the structure of two classes with different levels of sexual activity one is high activity group that include commercial sex workers and their male customers; and the other is low activity group. These two groups are further divided into two sub-groups as HIV infected and unaware, and HIV infected and aware after screening. It is assumed that people in low activity group when become aware, do not spread infection any more by means of either not participating in sexual activity at all or by taking some preventive measures. The model is analysed using stability theory of differential equations, numerical simulation and sensitivity analysis

Vendor-buyer ordering policy when demand is trapezoidal

A joint vendor-buyer strategy is analyzed which is beneficial to both the players in the supply chain. The demand is assumed to be trapezoidal. It is established numerically that the joint venture decreases the total cost of the supply chain when compared with the independent decision of the buyer. To entice the buyer to order more units, a permissible credit period is offered by the vendor to the buyer. A negotiation factor is incorporated to share the cost savings

Optimal Pricing Policies For Deteriorating items With Preservation Technology And Price Sensitive Demand

This paper considers the problem of determining the price, cycle time and preservation technology cost strategies for deteriorating items. It is assumed that preservation technology investment and demand rate do follow the function of selling price. The objective is to maximize the total profit per unit time with determining the optimal selling price, length of replenishment cycle and preservation technology investment. We will be proving that the optimal cycle length and selling price are unique with respect to given preservation cost. Also, total profit per unit time will be a concave function as it will reach its optimum value for optimum value of selling price, cycle length and preservation technology cost. Numerical examples are also presented to demonstrate the solution process

Mathematical model for the dispersion of toxicity through commuters

In the proposed paper, we consider three types of vehicle. One is those vehicles which are used for personal purposes called private vehicles. Second is for public transportation named as public vehicles. Third one is used for other activities known as cargo vehicles. These vehicles can be either polluted or non-polluted according to their fuel category. They produce toxic air pollutants which makes environment toxic. To compare the dispersion of toxicity through these vehicles, a mathematical model is formulated. In this model, dynamical system is developed with the help of non-linear differential equations. Threshold for each vehicle category is acquired and compared. Threshold and backward bifurcation govern the stability of the model. Simulation is prepared to brace the output.The authors have been supported by the ”DST-FIST file # MSI-097” for technical support to the department.Publisher's Versio

FEASIBILTY ANALYSIS OF WALKING OF PASSIVE DYNAMIC BIPED ROBOT

  Passive dynamic walking is an essential development for the biped robots. So the focus of our work is a systematic analysis of the passive walk of a planar biped robot on an inclined slope. The dynamics of passive biped robot is only caused of gravity. The biped robot with two point masses at kneeless legs and a third point mass at the hip-joint is kinematically equivalent to a double pendulum. In this paper, we represent a general method for developing the equations of motion and impact equations for the study of multi-body systems, as in bipedal models. The solution of this system depends on the initial conditions. But it is difficult to find the proper initial conditions for which the system has solutions, in other words, the initial conditions for which the robot can walk. In this paper, we describe the cell mapping method which able to compute the feasible initial conditions for which the biped robot can move forward on the inclined ramp. The results of this method described the region of feasible initial conditions is small and bounded. Moreover, the results of cell mapping method give the fixed of Poincare map which explains the symmetric gait cycle of the robot and describe the orientation of legs of robot

Optimal Ordering policy in demand declining market under inflation when supplier credits linked to order quantity

In this research paper, a lot–size model is proposed when supplier offers the retailer a credit period to settle the account if the retailer orders a large quantity. The proposed study is meant for demand declining market. Here, the retailer needs to arrive at a static decision when demand of a product is decreasing and on the other side the supplier offer the credit period if the retailer orders for more than pre – specified quantity. Shortages are not allowed and the effect of inflation is incorporated. The objective to minimize the total cost in demand declining market under inflation when the supplier offers a credit period to the retailer if the ordered quantity is greater than or equal to pre – specified quantity. An easy – to – use flow chart is given to find the optimal replenishment time and the order quantity. The mathematical formulation is supported by a numerical example. The sensitivity analysis of parameters on the optimal solution is carried out

A Lot-Size Model for Deteriorating Items under Conditions of a One-Time Only Extended Credit Period

Now-a-days, the offer of credit period to the customer for settling the account for the units purchased by the supplier is considered to be the most beneficial policy. In this article, an attempt is made to formulate the mathematical model for a customer to determine optimal special cycle time when the supplier offers the special extended credit period for one time only during a special period. A decision policy for a retailer is developed to find optimal special cycle time. The theoretical results and effects of various parameters are studied by appropriate dataset