This work considers cooperative advertising in a manufacturer-retailer supply chain. While the manufacturer is the Stackelberg leader, the retailer is the follower. Using Sethi model it models the dynamic effect of the manufacturer and retailer's advertising efforts on sale. It uses optimal control technique and stochastic differential game theory to obtain the players' advertising strategies and the long-run value of the awareness share. Further, it models the relationship between the payoffs of both players and the awareness share. The work shows that with the provision of subsidy the retail advertising effort increases while the manufacturer's advertising effort reduces. It further shows that the total channel payoff is higher for subsidised retail advertising. However, the subsidy can only be possible if the rate of growth of the manufacturer's payoff is twice higher than that of the retailer.
It has been established that trade credit can be influenced by a lot of factors. However, no specific function has been used to neither represent these factors nor consider their effects. This paper considers a supplier-retailer Stackelberg game in which the supplier as the channel leader supplies credit goods to the retailer who in-turn sells to the consumers. It uses a credit function based on credit period, supplier’s price margin and product promotion effort to model the players’ payoffs. The work considers two game scenarios: a situation involving the provision of trade credit and a situation without trade credit. The work obtains a closed-form solution for the credit period for the credit provision scenario, and the promotion efforts and payoffs for both scenarios, and shows that credit period prolongation may not be in favour of the retailer, and that the retailer can attain a larger payoff than the supplier. It also shows that the retailer’s margin is very crucial for both channel scenarios, and observes that the players are better-off with trade credit.
This work deals with subsidy transfer from a manufacturer to a retailer through the distributor in cooperative advertising. While the retailer engages in local advertising, the manufacturer indirectly participates in retail advertising using advertising subsidy which is given to the distributor, who in turn transfers it to the retailer. The manufacturer is the Stackelberg game leader; the distributor is the first follower, while the retailer is the last follower. The work employs differential game in modelling the effect of subsidy on the individual and channel payoffs; and models the awareness share dynamics using Sethi's sales-advertising model. It obtains Stackelberg equilibriums characterising four-game scenario: no subsidy from neither the manufacturer nor the distributor; withholding of manufacturer's subsidy by the distributor; provision of subsidy by the distributor in the absence of the manufacturer's participation; and the participation of both the manufacturer and distributor in retail advertising. It shows that in the absence of subsidy from the manufacturer, the distributor should intervene by providing subsidy to the retailer. However, if this is impossible, he should avoid withholding the subsidy meant for retail advertising. The players' payoffs as well as the channel payoff are worst with non-participation of both the manufacturer and the distributor, and best with transfer of subsidy.
In this paper, we proposed the numerical method called the variational iteration orthogonal collocation method (VIOCM), for the approximate solution of the deadly Corona virus model using Mamadu-Njoseh polynomials as basis functions. The proposed method is an elegant mixture of the variational iteration method (VIM) and the orthogonal collocation method (OCM). It was observed that the proposed method converges rapidly to the exact solution even as N increases. This suggests that the use of orthogonal polynomials as trial functions for the SEIR model is indeed an effective approximant as it produces the analytic solution at just few iterations. Resulting numerical evidences were compared with the standard variational iteration method as available in literature. All computational frameworks were executed with MAPLE software.
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