Quantity discount

Quantity discounts refer to the practice of offering lower prices for large volume purchases. There are two types of quantity discoimts offered by vendors as follows  

Both types of quantity discount models result in nonlinear cost functions. However, they can be modeled as linear functions with the help of binary variables. We shall discuss the IP formulations of the quantity discount models next. 

The mathematical representation of the cost function /(X), where X is the quantity purchased, is as follows  

The cost function /(X) is nonlinear in X since the slope changes depending on the value of X. However, we can linearize it using three binary variables, 8i, 82, and 83, one for each price range as follows  

The mixed integer linear programming (MILP) formulation will be as 

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Educational facilities, companies, and organizations interested in multiple copies or licensing of this book should contact the publisher for quantity discount information. Training manuals, CD-ROMs, and portions of this book also maybe available individually or may be tailored for specific needs. 

Quantity discounts Quantity discounts traditionally have been offered as an incentive for purchasing large quantities of single products or a special grouping of specific products offered by a manufacturer (West, 2003). For example, a wholesaler may sell one bottle... 

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