Power-of-two policies for single-warehouse multi-retailer inventory systems with order frequency discounts

– All-unit order frequency discount • 94%-effective policy for a variable base period – Incremental order frequency discount • 94%-effective policy for a fixed base period • 98%-effective policy for a variable base period Introduction • A supply chain is a network of facilities that procure raw materials, transform them into intermediate goods and then final products, and deliver the products to customers through a distribution system. • Multiechelon inventory systems are used to manage the inventories of a supply chain, which spans procurement, manufacturing, and distribution. • Key objectives of a supply chain are to minimize the cost associated with the entire multiechelon inventory system as well as to win the competitive battle in bringing the product to the customers as promptly as possible. • Assumptions: – The assumptions of the basic EOQ model hold at installation 2, where d = constant demand rate, Q 2 = order quantity provided by installation 1 when the inventory level drops to zero. – At installation 1, Q 1 = order quantity provided by supplier placed in time to replenish the inventory at installation 1when the inventory level is zero. – Relevant costs at installations 1 and 2: K i = setup cost, h (i) = unit holding cost, i = 1 , 2. – Units increase in value from installation 1 to installation 2. So, h (1) < h (2). – Lead times are assumed to be zero (or constant). Time Inventory level at Installation 1 Inventory level at Installation 2 4 Q 1 2 Q 2-2 0 2 4 6 8 Time 2 4 6 8 10 10 12 2 Synchronized inventory levels (Q 1 = 3 Q 2) Time Echelon inventory (system inventory), item 1 Inventory level at Installation 1 Inventory level at Installation 2 – Orders placed only when inventory is zero. • Stationary – Constant order intervals and order quantities. • Define h 1 = h (1) : echelon unit holding cost for installation 1, h 2 = h (2) – h (1) : echelon unit holding cost for installation 2.