Ud Understanding di inventory issues

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1 Lecture 10: Inventory Management Ud Understanding di inventory issues Definition of inventory Types of inventory Functions of inventory Costs of holding inventory Introduction to inventory management Economic order quantity (EOQ) model Readings: Chapter 17 What is Inventory? Supplier Customer Materials that has been purchased from a supplier, may have been partially or completely converted, but not yet sold to the customer. Usually, we name inventory by its location in a supply chain and by its function in an organization. 1 Types of Inventory Functions of Inventory (1) Replacement parts, tools, and supplies Theoretical/Pipeline Inventory: To meet anticipated demand, a minimum amount of WIP is needed hours hours hours Raw materials and purchased parts Inventory by Location Work-in-process Finished goods Goods-intransit to warehouses or customers Without the production capacity limit A Perfect Production Line One unit of work-in-process at any given time, output rate =? Two units of work-in-process at any given time, output rate =? Ten units of work-in-process at any given time, output rate =? 3 4

2 Functions of Inventory () Cycle or Batch Inventory Fixed costs associated with batches Quantity discounts Trade promotions To take advantage of order cycles Economies of scale Seasonal and Safety Inventories Uncertainty Information uncertainty Supply/demand uncertainty Protect against stock-outsouts due to uncertainty 5 Functions of Inventory (3) Decoupling Inventories Buffers between operations to decouple components of the production-distribution system A Production Line Strategic t Inventories Level production Availability Speculation (to hedge against price increases) Natural disasters and wars 6 Costs of Holding Inventory Holding (carrying) costs - physically having items in storage. Costs include interest, insurance, taxes, depreciation, obsolescence, warehousing and etc. Ordering costs - costs of ordering and receiving inventory. Costs include paperwork, transportation and etc. Shortage costs - stock-out costs. Costs include opportunity of not making a sale, loss of customer goodwill, late charges and etc. Inventory in an Economy There are more than $ trillion in US at a given time: 1/3 held by retailers; 1/4 of which in auto industry; 1/5 by wholesalers; the remainder by manufacturers Inventory cost at 5% - 35% of the value is more than $350 billion per year For each dollar of GNP in manufacturing and trade, about $0.4 worth of inventory was held 7 8

3 Inventory Management in a Firm Statements of Kmart and Wal-Mart Inventory accounts about 34% of current assets, 90% of working capital of a typical US company Inventory management is NOT warehouse management. Inventory management can be crucial in corporate strategy. Interaction between inventory management and other functional areas, such as procurement, production, transportation, quality, maintenance, marketing, IT system, finance, etc Decisions in Inventory Management What are the important decisions to be made in inventory management? Two major decisions: How much should we order? When should we order? What factors may influence the decisions on the above problems? Models in Inventory Management The quantitative inventory management models range from simple to very complicated ones. However, there are two simple models that capture the essential tradeoffs in inventory theory. EOQ (Economic Ordering Quantity) model Newsvendor model 11 1

4 Independent and Dependent Demands B(4) A C() D() E(1) D(3) F() Independent Demand (Focus of Inventory Theory) Dependent Demand (Use MRP, MRP II or ERP) Inventory Control with Constant Demand Miss Emily had been working at ASAT for a few years since graduating from XJTU SBM. Recently, she became the material manager. In the meeting with the manager of division (MD), she was told to cut down the high inventory cost that the company was experiencing while still maintaining a high material availability. Miss Emily immediately started her investigation of the problem and found the cost related to inventory was indeed very high. For example, she estimated that the annual inventory cost for a molding material used for IC packaging production is 33,410, which is more than 7.4% of the total purchasing cost for this material ( 450,000). Why was the inventory cost so high? How could she reduce it? Miss Emily decided to start from the molding material to find a way to cut down the inventory cost. Could she accomplish the task given to her by the MD? Data and the Problem Miss Emily found the following information: the IC packaging production was using an average of 9,000 kg molding material per year. The material department was ordering 5,000 kg each time at the price of 50/kg and a fixed ordering and shipping cost of 1,00/order. The average inventory holding cost was 1.5/kg/year. She further estimated that the total material ordering cost and holding cost were,160 and 31,50 per year, respectively. What could ldbe wrong with the ordering practice at the material department according to the above figures? How did Miss Emily estimate t the ordering and holding costs? What should be done to address the problem? Economies of Scale in Inventory Ordering One of the oldest economics principle Setup/ordering cost and economies of scale: Fixed ordering and shipping cost = 1,00; Annual demand = 9,000 /year; Number of orders per year 9,000/Q. Q 1,000,000 3,000 4,000 5,000. 1,00 10,800 5,400 3,600,700,160 The annual ordering cost 1, The per unit ordering cost 15 16

5 Q Q/ Q/3 Q/6 0 The Effect of how much Let Q be the quantity Miss Emily would order each time average inventory level = Q/ Average inventory Level Alternative Solutions Solution 1: Q = 800 No. of orders per year ordering cost = 1,00 x (9,000/800) = 13,500 holding cost = 1.5 x (800/) = 5,000 inventory cost = 18,500 Solution : Q = 1,350 ordering cost = hldi holding cost = inventory cost = Average inventory level l Solution 3: Q = 5,000 (what ASAT was doing) ordering cost = holding cost = inventory cost = Economic Order Quantity (EOQ) Model The Inventory Cycles Assumptions Products can be analyzed singly Production is instantaneous and delivery is immediate (Infinite capacity) A production run incurs a constant setup cost Demand rate is deterministic and constant over time Shortages are not permitted. Two major decisions: How much (Q) and when should we order? What are affected by decision Q? Number of orders, hence ordering cost Average inventory level, hence holding cost Q Usage rate Average inventory = Q/ Place and Receive order We do not need to consider when to order. Why? Time 19 0

6 The Inventory Cost Assume an annual demand rate of D Total cost = Material cost + Order cost + Holding cost = Material cost + Inventory cost = cd + G(Q) Inventory cost = G(Q) = h(q/) +K(D/Q) Inventory Cost Curves D=9,000, K=1,00,, h= G(Q) Holding cost - c: unit cost (dollars per unit) - Q is the lot size, order quantity -K is the setup cost per setup -his the annual unit holding cost (h can be in % of c) ) Ordering cost Q* The Calculus of the EOQ Inventory cost function: G(Q) = h(q/) +K(D/Q) First order condition dg h / KD / Q dq dg * / / * h KD Q 0 Q dq * Q KD / h The Economic Order Quantity KD EOQ Q * (1) h G G(Q) Q dg/dq =0 3 Q The Optimal Inventory Cost h(q * /) = KDh / K(D/Q ( * ) = KDh / Observation: The minimum is achieved at the quantity where Od Ordering cost = holding hldi cost. The Optimal Inventory Cost G(Q*) = (hq*/)= hq* = G( Q*) KhD () h KD h 4

7 Miss Emily s EOQ Solution K= 1 1,00, D=9 9,000 kg/year, h = 1.5 EOQ = {()(1,00)(9,000)/(1.5)} 1/ =1, ,315 The optimal inventory cost G(1,315) = {()(1,00)(1.5)(9,000)} 1/ = 16,43 Exercise The Park & Smencer retail shop has observed a stable demand for its line of Karmani sweater on the order of 100 per week. The retail shop incurs a fixed cost of $00 every time it places an order to the warehouse for stock replenishment. The marginal cost of a sweater is $400, and the shop s cost of capital is approximately 5%. What order size would you recommend? warehouse retailer 5 6 Solution D = 5*100 shirts/ year, K = $ 00 / order c = $ 400 / unit, r = Cost of capital = 5%, Holding cost h = r x c = $100 per unit per year Optimal order quantity = Number of orders per year = D/Q = Time between orders = Q/D = Annual order cost = (D/Q)K = Average inventory I = Q/ = Annual holding cost = (Q/)h = Average cycle time T = I/D = Inventory turns = D/I = 1/T = The Square Root Law Suppose there are m identical installations which are governed by the EOQ model. If we can aggregate them into one installation, what happens? 7 8

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