A Coordinated Planning Model with Price-Dependent Demand
This paper presents a coordinated planning model of price-dependent demand for a single-manufacturer and a single-retailer. The demand is assumed to be normally distributed, with its mean being price dependent. The manufacturer and retailer coordinate with each other to jointly and simultaneously determine the retail selling price and the retailer order quantity to maximize the joint expected total profit. This model is then compared to a 'returns' policy model where manufacturer buys back unsold items from the retailers. It is shown that the optimal total profit is higher for coordinated planning model than that for the returns policy model, in which the retail price is set by the retailer. A compensation or profit sharing scheme is then suggested and it is shown that the coordinated model with profit sharing yields a 'win-win' situation. Numerical results are presented to illustrate the profit patterns for both linear and nonlinear demand functions. The coordinated planning model, in addition, has a lower optimal price than for a returns policy model, which would result in higher sales, thus expanding the markets for the whole supply chain.
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