Abstract
One of the most important responsibilities of a supply chain manager is to decide “how much” (or “many”) of inventory items to order and how to transport them. This paper presents four mixed-integer linear programming models to help supply chain managers make these decisions for multiple products subject to multiple constraints when suppliers offer quantity discounts and shippers offer freight discounts. Each model deals with one of the possible combinations of all-units, incremental quantity discounts, all-weight and incremental freight discounts. The models are based on a piecewise linear approximation of the number of orders function. They allow any number of linear constraints and determine if independent or common (fixed) cycle ordering has a lower total cost. Results of computational experiments on an example problem are also presented.
Highlights
Chain management has been receiving an everincreasing attention from both academicians and business managers for the past several decades
The main reason for this attention seems to be the realization that a well coordinated supply chain will lead to lower costs, and greater profits, for its members compared to the costs incurred by members of a supply chain that is not coordinated
According to 2013 Annual State of Logistics Report [1] of Council of Supply Chain Management Professionals (CSCMP), the average investment in all business inventories reached to almost $2.3 trillion in 2012, which was equivalent to 8.5 percent of the Gross Domestic Product (GDP) of the same year
Summary
Chain management has been receiving an everincreasing attention from both academicians and business managers for the past several decades. According to 2013 Annual State of Logistics Report [1] of Council of Supply Chain Management Professionals (CSCMP), the average investment in all business inventories (agriculture, mining, construction, services, manufacturing, wholesale, and retail trade) reached to almost $2.3 trillion in 2012, which was equivalent to 8.5 percent of the Gross Domestic Product (GDP) of the same year. In this total there are inventory carrying costs and transportation (all modes) costs, $434 billion and $897 billion, respectively. Two appendices provide relevant mathematical background that forms the foundation for the four models
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