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## Inventory Control Model

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**Inventory Control Model**Kusdhianto Setiawan Gadjah Mada University**Planning on what**Inventory to stock And how to acquire it Forecasting Parts/Product Demand Controlling Inventory Levels Feedback Measurements To revise plans and forecasts Inventory Planning & Control**Importance of Inventory Control**• The Decoupling Function….. Inventory as a buffer • Storing Resources…. Where JIT is not possible • Irregular Supply and Demand • Quantity Discount • Avoiding stockouts and shortages**Inventory Decision**• How much to order • When to order With respect to (constraint) inventory cost: • Cost of the items • Cost of ordering • Cost of carrying/holding • Cost of safey stock • Cost of stockouts**Economic Order Quantity (EOQ)**• Objective: Determining how much to order • Assumptions: • Demand is known and constant • Lead time, the time between the placement of the order and the receipt of the order, is known and constant • The receipt of inventory is instantaneous • Quantity discount are not possible • Variable costs: ordering cost and holding/carrying cost • If orders are placed at the right time, stockouts/shortages can be avoided completely**Order Quantity = Q = Maximum inventory level**Inventory Level 0 Time Minimum Inventory Level EOQ Continued….**Cost**Minimum Total Cost Carrying Cost Curve Optimal Order Quantity Ordering Cost Curve Order Quantity EOQ Continued….**Computing Average Inventory**Demand: Constant, 2 units/day Ending Inventory is assumed to be always zero Maximum level = 10 units Total of Daily average = 9 + 7 + 5 + 3 + 1 = 25 Number of days = 5 Average inventory level = 25/5 = 5 …… Q/2**Finding the EOQ**• Expression: Q = number of pieces per order Q* = optimal number of pieces per order D = annual demand in units for the inventory items C0 = ordering cost for each order Ch = holding cost per unit per year**Finding the EOQ**• Annual Ordering Cost = no. of order placed per year x order cost per order • Annual Holding or Carrying Cost = Average inventory level x carrying cost per unit per year = (Q/2) Ch • Optimal Order Quantity ordering cost = carrying cost (D/Q)Co = (Q/2)Ch 4.**Q***Slope = units/day = d Inventory Level (Units) Time (days) Lead Time = L Finding Reorder Point (ROP) • ROP = (demand/day) x (lead time for a new order in days) • ROP = d x L ROP (units)**EOQ Without The Instantaneous Receipt Assumption**Part of inventory cycle during which Production is taking place Inventory Level There is no production During this part of the inventory cycle Maximum Inventory time t Production Run Model**Annual Carrying Cost**• New terms: t = length of the production run (days) p = daily production rate • Annual inventory holding/carrying cost = average inventory level x carrying cost/unit/year = average inventory level x Ch • Average inventory level = ½ Maximum inventory level • Maximum inventory level = (total produced during the production run) - (total used during the production run) Q = pt t = Q/p Max Inv. Level = p(Q/p) – d(Q/p) = Q – (d/p)Q = Q(1-d/p) • Annual Inventory carrying cost = ½ (max. inv. Level) x Ch = ½ Q(1-d/p)Ch**Annual Setup/Ordering Cost**• Annual setup cost = (no. of setup/year) x (setup cost/setup) = (D/Qp)Cs where: D = annual demand in units Qp = Quantity produced in one batch Cs = setup cost per setup • Annual Ordering Cost = (D/Q)Co**Optimal Order Quantityfor Production Run Model**• Ordering Cost = Carrying Cost • (D/Q)Co = ½ ChQ(1-d/p) • Optimal Order Quantity Optimal Production Quantity, Q*p**Quantity Discount Model**Quantity Discount Schedule Total Cost = material cost + ordering cost + carrying cost = DC + (D/Q)Co + ½ QCh**Total Cost Curve**Total Cost TC for Disc. 1 TC for Disc. 3 TC for Disc. 2 Q* for Disc. 2 Order Quantity 0 1,000 2,000**Use of Safety Stock**• Safety stock: additional stock that is kept on hand • It is used only when demand is uncertain • Main purpose: to avoid stockouts when the demand is higher than expected • ROP = d x L (normal condition) • ROP = d x L + SS (demand is uncertain) • Because it is dealing with decision under risk, knowing the probability of demand is necessary.**Safety Stock with Known Stockout Costs**Case of ABCO • ROP = 50 units (= d x L) • Ch = $5 (per unit per year) • Cso = $40/unit (stockout cost) • Optimal number of orders per year is 6 • Objective: to find the reorder point, including safety stock, that will minimize total expected cost • Total expected cost is the sum of expected stockout cost plus expected additional carrying cost**Annual Expected Stockout Cost**• When the ROP < demand over lead time Total Cost = Stockout Cost = no. of units short x stockout cost/unit x no. of orders per year • When the ROP > demand over lead time Total Cost = total additional carrying cost = no. of surplus units x carrying cost**Safety Stock with Unknown Stockout Cost**• There are many situation when stockout cost are unknown or extremely difficult to determine, i.e: major stockout cost is the loss of goodwill, how to measure it? • Alternative approach: using service level • Service level = 1 – probability of a stockout or • Probability of a stockout = 1 – service level**Hinsdale Company Example**• Average demand = 350 units • Standard Deviation = 10 • Hinsdale wants to follow a policy that result in stockout occuring only 5% of the time. • How much safety stock should be maintained?**Safety Stock & Normal Distribution**σ=10 X = mean + safety stock SS = safety stock = X – μ Z = (X – μ) / σ = SS/ σ Z value for an area under the normal curve of 0.95 (=1-0.05) is 1,65 (see appendix A) SS = 1.65 (10) = 16.5 units or 17 units SS = Z σ SS μ=350 X=?