Inventory Management Chapter 13

MIS 373: Basic Operations Management Inventory Costs Purchase cost The amount paid to buy the inventory Holding (carrying) costs Cost to carry an item in inventory for a length of time, usually a year Interest, insurance, taxes (in some states), depreciation, obsolescence, deterioration, spoilage, pilferage, breakage, tracking, picking, and warehousing costs (heat, light, rent, workers, equipment, security). Ordering costs Costs of ordering and receiving inventory determining how much is needed, preparing invoices, inspecting goods upon arrival for quality and quantity, and moving the goods to temporary storage. Shortage costs Costs resulting when demand exceeds the supply of inventory; often unrealized profit per unit MIS 373: Basic Operations Management

Profile of Inventory Level Over Time The Inventory Cycle Profile of Inventory Level Over Time Quantity on hand Q Receive order Place Lead time Reorder point Usage rate Time MIS 373: Basic Operations Management

MIS 373: Basic Operations Management Total Annual Cost Total Cost = Annual Holding Cost + Annual Ordering Cost (TC) where Q = order quantity in units H = holding (carrying) cost per unit, usually per year D = demand, usually in units per year S = ordering cost per order = Q H + D S 2 Average number of units in inventory Number of orders MIS 373: Basic Operations Management

MIS 373: Basic Operations Management Deriving EOQ Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q. The total cost curve reaches its minimum where the carrying and ordering costs are equal. 𝑇 𝐶 ′ = 𝐻 2 + −1 𝐷𝑆 𝑄 2 =0 → 𝐷𝑆 𝑄 2 = 𝐻 2 → 𝐷𝑆 𝑄 = 𝐻𝑄 2 𝑄 ∗ = 2𝐷𝑆 𝐻 = 2 𝑎𝑛𝑛𝑢𝑎𝑙 𝑑𝑒𝑚𝑎𝑛𝑑 𝑜𝑟𝑑𝑒𝑟 𝑐𝑜𝑠𝑡 𝑎𝑛𝑛𝑢𝑎𝑙 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 ℎ𝑜𝑙𝑑𝑖𝑛𝑔 𝑐𝑜𝑠𝑡 MIS 373: Basic Operations Management

EPQ: Inventory Cycle Q Qp Imax 13-6 Time Production and usage Usage only Cumulative production Amount on hand Time 13-6 Instructor Slides

Time Cycle time Run time The time between setups of consecutive runs The production phase of the cycle

EPQ – Total Cost 13-8 Instructor Slides

EPQ Optimal Batch size a.k.a Economic Produciton Quantity (EPQ) 13-9 Instructor Slides

Quantity Discount Model Price reduction for larger orders offered to customers to induce them to buy in large quantities 13-10 Instructor Slides

MIS 373: Basic Operations Management Reorder-Point ROP = (Demand per day) * (Lead time for a new order in days) = d * L where d = (Demand per year) / (Number of working days in a year) Example: Demand = 12,000 iPads per year 300 working day year Lead time for orders is 3 working days In other words, the manager should place the order when only 120 units left in the inventory. d = 12,000 / 300 = 40 units ROP = d * L = 40 units per day * 3 days of leading time = 120 units MIS 373: Basic Operations Management