identified and remediated some technical errors with the total inventory holding cost used in scenario (2) by Sarker and
Kindi [2]. This has corrected the base model but increased the total cost as calculated by Sarker and Kindi. Scenario (3), (4) and (5) are special case and extension to scenarios.
The principle of special discounts, special orders and forward buying has been extensively studied in marketing, inventory and microeconomic literatures. One of the initial models was developed by Aucamp [3] who evaluated the trade-offs involved in decisions under discount period scenarios. It provided insights about situation in which it will be profitable to consider discount price to place a special orders. The decision based on the model proves that it is profitable to order more quantity for the discount period only and only if, the ratio of special order quantity to EOQ optimum order quantity is higher than the square-root of the ratio of normal price and the discount price. This model is further developed by Tersine to take advantage of the situations where the buyer deterministically knows the discount period to cover multiple order cycles consecutively
[4]. This was one of the initial papers that developed on the idea of proactively deciding on order policy with the knowledge of length of discount period [4]. Srinivasan,
Pakkala, and Arcelus further developed on the idea by introducing some stochastic elements to the termination date of the discount periods [5].
Sarker and Kindi [1] in their paper have evaluated the different situations that arise due to interaction between the
EOQ model replenishment period and discount period, broadly either the replenishment point coincide with the discount period or not. Several papers have shown that highest savings are assumed under discount situation where replenishment period coincide with the discount period [1] [6].
Aull-Hyde has even suggested that a policy with planned backlog can also be considered if the buyer is aware of a discount in the immidiate future [6]. On the similar lines
Barron Smith and Goyal has extended the model presented by
Sarker and Kindi to include back orders [7]. Wen-Kai and
Honf-Fwe has extended the discount model to accommodate defective items received as part of special order [8]. But largely the literature has not considered the decision models that influence the normal EOQ cycles before the discount

Abstract— This paper examines a buyer response to a vendor’s trade promotion, when the discount is guaranteed at a specific time that is known with some uncertainty before the beginning of the planning period. The issue in hand is to develop optimum policy that reduces the total cost of inventory to minimum. The model developed in the paper reduces the decision to just two policies; adjusting the order quantity for either all the pre-discount standard EOQ cycles or modify the order quantity for just one EOQ cycle immediately before the discount. The decision is substantially simplified to a range of value for decision variable (m) that dictates which policy will be optimum.
Keywords—Discount;
Policy;Sale Period

I.

Pricing,

Forward

buying;Ordering

INTRODUCTION

Most of the products undergo temporary price discounts for different reasons; to facilitate quick inventory turnovers, cope with increased supply due to surge in production or simply offer off-season pricing. For certain products these discounts are regular and are predictable. This paper is an effort to use inherent predictable nature of discount for these goods to plan ahead and maximize the profit by reducing the total cost including the ordering cost, inventory holding cost and purchasing cost.
Sarker and Kindi in their paper ‘Optimal ordering policies in response to a discount offer’ dealt with an inventory model that determines the optimal ordering policies from the buyer perspective, when offered a