Inventory Control. Inventory. Inventories in a manufacturing plant. Why inventory? Reasons for holding Raw Materials. Reasons for holding WIP

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1 Inventory Control Inventory the oldest result of the scientific management efforts inventory plays a key role in the logistical behavior of virtually all manufacturing systems the classical inventory results are central to more modern techniques such as MRP, JIT, TBC (time based competition), etc. $ 1.25 trillion ($1,250,000,000,000) in 1st quarter of 1995, USA == 20 to 25 % of total annual GNP Why inventory? Inventories in a manufacturing plant economies of scale uncertainties transportation smoothing logistics technological restrictions quantity discounts raw materials components, subassemblies or materials that are purchased from outside work in process (WIP) all unfinished parts or products that have been released to a production line finished goods inventory (FGI) finished product that has not been sold spare parts components used to maintain or repair production equipment Reasons for holding Raw Materials Reasons for holding WIP batching quantity discounts limited capacity of the plant s purchasing function economies of scale in deliveries randomness schedule problems quality problems obsolescence changes in demand changes in design queueing a job is waiting for a resource processing a job is being worked on by a resource waiting for batch a job has to wait for other jobs to arrive in order to form a batch moving a job is being transported between resources waiting to match when components wait for their counterparts to arrive for an assembly 1

2 Reasons for holding FGI Reasons for holding Spare Parts customer responsiveness make-to-stock policy batch production output will sometime not match customer orders forecast errors production variability seasonality built-ahead inventory service purchasing lead times production lead times batch replenishment economies of scale Functional classifications of inventories The A-B-C classification Cycle inventories Due to batch processing Congestion stocks Due to items competing for limited capacity Safety stock To allow for uncertainty of demand and supply Anticipation inventory In advance of an expected peak in sales Pipeline (or WIP) inventory Decoupling stocks To permit the separation of decision making at different echelons (locations) SKU (stock-keeping unit) An item of stock that is completely specified as to function, style, size, color and usually location. Class A The first 5-10 percent of the SKUs account for about 50 percent or more of the total annual dollar usage Class B More than 50 percent of total SKUs account for most of the remaining 50 percent of the total annual dollar usage Class C The relatively numerous remaining SKUs that make up only a minor part of total dollar usage The Economic Order Quantity Model The EOQ Model Assumptions Ford W. Harris (1913), How Many Parts to Make at once example of a metal-working shop that produced copper connectors setup cost as the sum total of the labor and material cost to ready the shop to produce a product Dilemma large lots reduce setup costs small lots reduce inventory Production is instantaneous. Delivery is immediate. Demand is deterministic. Demand is constant over time. A production run incurs a constant setup cost. Products can be analyzed singly. 2

3 The Notation EOQ D = Demand rate (in units per year). v = Unit variable cost, not counting setup or inventory costs (in dollars per unit). A = Constant setup (ordering) cost to produce (purchase) a lot (in dollars). r = the carrying charge (in $/$/unit time), or h = vr where h is the holding cost. Q = Lot size (in units); this is the decision variable. TRC(Q) = the total relevant costs per unit time. also referred to as the economic lot size AD Q Qvr 2 TCR ( Q) = + + Q*= 2AD vr Dv The Key Insights Inventory Systems There is a tradeoff between lot size and inventory. Holding and setup costs are fairly insensitive to lot size. Demand constant vs. variable known v. unknown Lead time Review time Excess demand backordered lost Inventory Costs Holding cost Holding cost Order cost Penalty cost Cost of physical space Taxes and insurance Breakage, spoilage, deterioration, obsolescence Opportunity cost of alternative investment 3

4 Order cost Penalty cost cost of procuring x items fixed + proportional components cost when demand exceeds supply per unit of excess demand Economic Production Lot (EPL) Model Assumptions Quantity Discount Models No Instantaneous production. but a finite, constant and deterministic production rate Immediate delivery. Deterministic demand. Constant demand. Known constant setup costs. Single product or separable products. All units discount model Incremental discount model Carload discount model All Units Discount Model Incremental Discount Model A solution technique Determine the largest realizable EOQ value. Compute the EOQ for the lowest price first, and continue with the next higher price. Stop when the first EOQ value is realizable (i.e., within the correct interval). Compare the value of the average annual cost at the largest realizable EOQ and at all of the price breakpoints that are greater than the largest realizable EOQ. The optimal Q is the point at which the average annual cost is a minimum. A solution technique Determine an algebraic expression for C(Q) corresponding to each price interval. Use that to determine an algebraic expression for C(Q)/Q. Substitute the expressions derived for C(Q)/Q into the defining equation for G(Q). Compute the minimum value of Q corresponding to each price interval separately. Determine which minima computed in the previous step are realizable (i.e., fall into the correct interval). Compare the values of the average annual costs at the realizable EOQ values and pick the lowest. 4

5 Carload Discount Model Gentle Electric Company (GEC) A carload consists of M units. The supplier charges a constant c per unit up until you have paid for the cost of a full carload, at which point there is no charge for the remaining units in that carload. Once the first carload is full, you again pay c per unit until the second carload is full, and so forth. Situation (i) purchase at $500 per unit (ii) quantity discount (iii) transportation cost 5