Inventory Control Model Kusdhianto Setiawan Gadjah Mada University

Inventory Planning & Control 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

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

Inventory Cost Factors Ordering Cost Factors Carrying Cost Factor Developing & Sending Purchase Order (PO) Cost of Capital Processing & inspecting incoming iventory Taxes Bill Paying Insurance Inventory Inquiries Spoilage Utilities, phone bills, etc for the purchasing dept. Theft Salaries & wages for purchasing dept. employees Obselescence Supplies e.g: paper, toner printer, billing form, etc. for the purchasing dept. Salaries & wages for warehouse employees Utilities & building cost for the warehouse Supplies such as forms & papers for the warehouse.

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

EOQ Continued…. Order Quantity = Q = Maximum inventory level Minimum Inventory Level Time

EOQ Continued…. Cost Minimum Total Cost Carrying Cost Curve Ordering Cost Curve Optimal Order Quantity Order Quantity

Computing Average Inventory Day Inventory Level Beginning Ending Average 1 (order received) 10 8 9 2 6 7 3 4 5 1 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.

Finding Reorder Point (ROP) ROP = (demand/day) x (lead time for a new order in days) ROP = d x L Inventory Level (Units) Q* Slope = units/day = d Lead Time = L Time (days) ROP (units)

EOQ Without The Instantaneous Receipt Assumption Inventory Level Part of inventory cycle during which Production is taking place 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 Quantity for 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 Discount Number Discount Quantity Discount (%) Discount Cost ($) 1 0-999 5.00 (normal cost) 2 1,000 – 1,999 4 4.80 3 2,000 – over 5 4.75 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 Q* for Disc. 2 Order Quantity 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

Probability of Demand for ABCO Number of Units Probability 30 0.2 40 50 (ROP) 0.3 60 70 0.1 Total 1.0

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

ABCO’s Stockout Costs Probability 0.20 0.30 0.10 State of Nature Alternative 30 40 50 60 70 EMV 2,400 4,800 7,200 9,600 4,320 2,410 100 990 150 305 200 110

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=?