This article includes policies regarding optimal dynamic pricing and ordering for items with synchronized deterioration of quality and physical quantity. Qualitative deterioration is an instantaneous process while physical deterioration-a non-instantaneous process. In view of the dynamic nature of the problem, selling price is assumed to be a time-dependent function of the initial price and discount rate. Initially with no physical deterioration, the product is sold at initial price value in the time period, successively in order to enhance customer's demand, price is exponentially discounted. For boosting the dynamic essence of the proposed model, the customer's demand is expressed as a quadratic function of time, price and changes in price over time, which is appropriate for the products for which demand increases initially and after sometime, it starts to decrease. Along with determining initial price, discount rate and optimal ordering cycle, the model also maximizes the total profit of the system. Numerical results with sensitivity analysis on the decision variables outputs managerial insights.
An attempt is made to formulate optimal ordering policies for the retailer when the supplier offers progressive credit periods to settle the account. We define progressive credit periods as follows: If the retailer settles the outstanding amount by M, the supplier does not charge any interest. If the retailer pays after M but before N(M < N), then the supplier charges the retailer on the un-paid balance at the rate Ic 1 . If the retailer settles the account after N, then he will have to pay an interest rate of Ic 2 ( Ic 2 > Ic 1 ). The objective function to be optimized is considered as present value of all future cash-out-flows. An algorithm is given to find the flow of optimal ordering policy. Analytic proofs are discussed to study the effect of various parameters on an objective function.
In this cut-throat competitive business world, cash-on-delivery is no longer a practice. Consequently, the retailer offers numerous short-term or long-term credit limits to the customer. The middle-layered player passes the offer of delay payment to the end users. In addition, most of the items have a fixed lifetime and deteriorate continuously, which cannot be sold after its expired dates. However, preservation technology investment can reduce deterioration rate of items in retailer's inventory system. In this paper, an inventory model is formulated when retailer offers partial credit, which he received from the supplier when demand is decreasing with time and price. The profit function is constructed using inflation rate and risk involved due to offer of credit period in generating revenue. The decision policies are analysed for the decision maker. Numerical examples are used to demonstrate the theoretical derivations. Sensitivity analysis is carried out for the advantageous scenario depending upon the lengths of the credit periods.
A mathematical model on cleanliness drive in India is analysed for active cleaners and passive cleaners. Cleanliness and endemic equilibrium points are found. Local and global stability of these equilibrium points are discussed using Routh-Hurwitz criteria and Lyapunov function respectively. Impact of media (as a control) is studied on passive cleaners to become active. Numerical simulation of the model is carried out which indicates that with the help of media transfer rate to active cleaners from passive cleaners is higher.
The drive for vaccinations is playing crucial role to manage the ongoing pandemic. These vaccinations have various strategies. Especially in India, two doses of each vaccine are given. Every dose holds the reinforcement into the human body. These doses subsequently cannot hold the immunity. In this term, the booster dose of vaccination is desired. In this paper, the effectiveness of these two doses and one booster dose is calculated on advancement of COVID-19 through a system of non-linear differential equations. This system has divided population into two parts, that is exposed individuals and unexposed individual. The improvement of the doses on these individuals is calculated through the threshold. The stability of the model along with the simulation is considered to brace the ongoing situation.
This study analyses measles transmission vertically with vaccination failure and delay of vaccination. The effect of infected newborns as a time delay is analysed. Time delay is considered as a loss of maternal immunity amongst newborns. The system of non-linear differential equations for the proposed problem is formulated. The next generation matrix method is used to find the reproduction number, and to obtain the stability of the infection free as well as the endemic equilibrium. Effect of time delay in vaccination has been studied for disease-free equilibrium. The local and global stability of the system is analysed. Sensitivity of the key parameters is measured using numerical simulation and observed that it supports the analytical results.
In this article, a production inventory model with dynamic production rate and production time dependent selling price has been presented. We consider the product with constant deterioration rate which is a very realistic approach. It is also considered that the production rate is a decreasing function of the inverse efficiency of the system. Here, time dependent quadratic demand is deliberated which is suitable for the products whose demand increases initially and subsequently it starts to decrease. Industries like fashion and electronics most probably deals with this type of demand. The main objective is to maximise the total profit with respect to inverse efficiency and total production period. The model is supported with numerical example. Sensitivity analysis is done to derive insights for decision-maker. Graphical results, in two and three dimensions, are exhibited for optimality of the model with supervisory decisions.
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