Some seasonal products have limited sales season, and the demand of such products over the sales season is of increasing-steady-decreasing type. Customers are highly sensitive to the prices of the products. In such situation, adjustment of unit selling price is needed to accelerate inventory depletion rate and for determining order quantity for the sales season. In this paper, we focus on the issue by jointly determining optimal unit selling prices and optimal lot size over the sales season. Unlike the conventional inventory models with pricing strategy, which were restricted to prespecified pricing cycle lengths, that is, fixed number of price changes over the time horizon, we allow the number of price changes to be a decision variable. The mathematical model is developed and existence of optimal solution is verified. A solution procedure is developed to determine optimal prices, optimal number of pricing cycles, and optimal lot size. The model is illustrated by a numerical example. Sensitivity analysis of the model is also carried out. 1. Introduction Items like fashion apparel, hi-tech product parts, periodicals, Christmas accessories, and so forth, have limited sales season and become outdated at end of season. Demand of such products is sensitive to time as well as price. Initially after introduction of the product, demand increases up to a point of time then it becomes steady. Finally towards end the of the season, it decreases. Ramp-type time-dependent demand pattern is very close to the demand pattern in such situations. The inventory model with ramp-type demand rate was first proposed by Hill [1]. Since then many researchers and practitioners have given considerable attention to analyze ramp-type demand. Mandal and Pal [2] have extended the inventory model with ramp-type demand for exponentially deteriorating items by allowing shortages. Wu and Ouyang [3] have developed an inventory model by considering two different replenishment policies: shortage followed by inventory and inventory followed by shortage. Wu [4] has further proposed an inventory model for deteriorating items with ramp-type demand, Weibull distribution deteriorating rate, and waiting time-dependent partial backlogging rate. Giri et al. [5] have extended ramp-type demand inventory model with more general Weibull distribution deterioration rate. Manna and Chaudhuri [6] have developed a production inventory model with ramp-type two time periods classified demand pattern where the finite production rate depends on demand. Deng et al. [7] have pointed out the questionable results
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