EOQ with trade promotion

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Russian: Оптимальный размер заказа и стимулирование торговли

Suppliers provide incentives to buyers to acquire more of a product by offering trade promotions. A trade promotion is analogous to a consumer promotion with the former offered in a channel of distribution by one firm to another and the latter in a channel where a retailer offers a promotion to a consumer. As with a consumer promotion, a trade promotion specifies terms of the discount in terms of price (e.g., a 5% reduction per case ordered), location (e.g., Spain), duration (2 weeks starting from September 1), and productsuch as a specific set of SKUs. There are a number of reasons why manufactueres utilize trade promotions including: (1) manufacturer forecast error which results in excessive inventory; (2) pushing inventory onto the next level of the channel; (3) response to competitor actions; and (4) through retail tie-ins, inducing retailers to offer more product support at the retail level. The basic EOQ model can be modified to account for a temporary trade promotion:[1]

\! \mbox{EOQ}^{\mbox {dis}}=\frac{dis\cdot D}{(v-dis)h}+\frac{v\cdot EOQ}{v-dis}


  • EOQ = economic order quantity
  • D = demand
  • K = fixed order cost
  • dis = the discount, expressed in relevant monetary units
  • v = value of unit of inventory, expressed in relevant monetary units
  • \,\!\mbox{EOQ}^{\mbox{dis}} = EOQ after taking taking into account the trade promotion
  • c = inventory carrying cost rate
  • h = inventory carrying cost rate per unit per relevant time period
  • If D is expressed annually, then h = c × v


Suppose a manufacturer sells a product to a retail with a standard price (v) of €5. The retailer's inventory carrying cost rate is .20 (c) and fixed cost to place an order (K) is €10. Annual demand for the product (D) equals 5,000 units. The manufacturer offers a 10% discount of €0.50. How much should the retailer order to take advantage of the discount?

The first step is to evaluate the EOQ.

\mbox {EOQ} =\sqrt{\frac{2KD}{h} } =\sqrt{\frac{2\cdot 10\cdot 5000}{.20\cdot 5} } =316 \mbox {units}


\! \mbox{EOQ}^{\mbox {dis}}=\frac{dis\cdot D}{(v-dis)h}+\frac{v\cdot EOQ}{v-dis}=\frac{.50\cdot 5000}{(10-.50).20}+\frac{10\cdot 316}{10-.50}=1,648

\,\!\mbox{Forward buy}=\mbox {EOQ}^{\mbox{dis}} - \mbox {EOQ}=1,48-316=1,332

Additional Comments

In summary, the retailer should purchase 1,648 units, which represents a forward buy of 1,332 units. The is an increase of more than 500% in the order quantity. We previusly mentioned the positive aspects of trade promotions, including ability to foster a push orientation. However, a significant increase in order quantities of this sort contributes to the bullwhip effect. In other words, trade promotions artifically increase variance in the quantity ordered. If the business does not properly plan for spikes in demand, then stockouts may be increased further toward sources of supply. Furthermore, trade promotions are antithetical to the EDLP philosophy, which seeks to minimize variance in demand and throughput by increasing price consistency across time periods. The disruptive nature of trade promotions on operational smoothness has led some Fortune 500 companies to "ban" end-of-period cumulative discounts for similar reasons.

A regional trade promotion exists when a discount is offered in one region, but not in another. These types of trade promotions have the potential to result in gamesmanship by buyers. For example, a buyer may transship product from the eastern United States where a trade promotion exists to the mid west where the promotion does not exist (given that the cost of shipping and handling is less than the value of the discount). The buyer then sells the product at full price in the mid west. This practice inflates demand in one region while deflating in another. From the buyer's perspective, profits are increased. From the seller's persepctive the buyer has not added value to the product in the process.


  1. Chopra, S. and P. Mendl (2007), Supply Chain Management: Strategy, Planning, and Operation, Upper Saddle River, New Jersey: Pearson
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