This paper presents the possible effects of a temporary price discount offered
by a supplier on a retailer’s replenishment policy for deteriorating items with
linear time dependent demand rate. The optimal ordered quantity of a special
order policy for a selected case is obtained by maximizing the total cost saving
between special and regular orders for the duration of the depletion time. An
algorithm is given to find the optical solution. Numerical examples are used to
illustrate the theoretical results. Truncated Taylor’s series is used for finding
closed form optimal solution.