Types of Inventories (manufacturing firms) (retail stores) Raw materials & purchased parts Partially completed goods called work in progress Finished-goods inventories or merchandise (manufacturing firms) (retail stores)

Types of Inventories (Cont’d) Replacement parts, tools, & supplies Goods-in-transit to warehouses or customers

Functions of Inventory To meet anticipated demand To smooth production requirements To decouple operations To protect against stock-outs To take advantage of quantity discounts To help hedge against price increases To permit operations

Objective of Inventory Control To achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds Level of customer service Costs of ordering and carrying inventory

Key Inventory Terms Lead time: time interval between ordering and receiving the order Holding (carrying) costs: cost to carry an item in inventory for a length of time, usually a year Ordering costs: costs of ordering and receiving inventory

Economic Order Quantity Models

Costs Associated with Inventory Control Three categories of costs associated with inventory: Purchasing costs Ordering costs Carrying costs

Purchasing Costs Purchasing costs are the costs of goods acquired from suppliers including incoming freight or transportation costs. These costs usually make up the largest single cost category of inventory. Discounts for different purchase-order sizes and supplier credit terms affect purchasing costs.

Ordering Costs Ordering costs are the costs of preparing, issuing, and paying purchase orders, plus receiving and inspecting the items included in the orders. Purchase approval and special processing costs are related to the number of purchase orders processed. MGT 504 by Dr. Bin Jiang

Purchasing Process Needs Identification Purchasing requisition Reorder point system Statement of work/scope of work 2. Description by: Market grade/industry standard Brand Specification Performance characteristics 3. Supplier Selection/Contracting Competitive bidding Selecting Negotiating Contracting 4. Ordering Purchase orders EDI 5. Follow-up and Expediting 6. Receipt and Inspection 7. Settlement and Payment 8. Records Maintenance Order Cycle MGT 504 by Dr. Bin Jiang

Carrying Costs Carrying costs arise when an organization holds an inventory of goods for sale. These costs include the opportunity cost of the investment tied up in inventory and the costs associated with storage such as space rental, insurance, obsolescence, and spoilage. MGT 504 by Dr. Bin Jiang

Economic-Order-Quantity Decision Model The economic-order-quantity (EOQ) is a decision model that calculates the optimal quantity of inventory to order under a restrictive set of assumptions. The simplest version of this model incorporates only ordering costs and carrying costs into the calculations. MGT 504 by Dr. Bin Jiang

Simplest EOQ Model The simplest EOQ model minimizes the relevant ordering costs and carrying costs. Relevant total costs = Relevant ordering costs + Relevant carrying costs MGT 504 by Dr. Bin Jiang

The Simplest EOQ Assumptions Demand is known Lead time is known & constant No quantity discounts are available Ordering (or setup) costs are constant All demand is satisfied (no shortages) The order quantity arrives in a single shipment MGT 504 by Dr. Bin Jiang

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 MGT 504 by Dr. Bin Jiang

Costs Holding Cost: Setup Costs: A per lot Cost Function: MGT 504 by Dr. Bin Jiang

EOQ Model How Much to Order? Annual Cost Total Cost Curve Holding Cost Curve Order (Setup) Cost Curve Order Quantity Optimal Order Quantity (Q*) MGT 504 by Dr. Bin Jiang

Economic Order Quantity EOQ Square Root Formula MGT 504 by Dr. Bin Jiang

Minimum Total Cost The total cost curve reaches its minimum where the carrying and ordering costs are equal. MGT 504 by Dr. Bin Jiang

The Key Insight of EOQ There is a tradeoff between lot size and inventory costs. Large lot size = high inventory and infrequent orders. Small lot size = frequent orders lower average inventory MGT 504 by Dr. Bin Jiang

Total Inventory Cost (TC) Example: A computer company has annual demand of 10,000. They want to determine EOQ for circuit boards which have an annual holding cost (H) of $6 per unit, and an ordering cost (S) of $75. They want to calculate TC and the reorder point (R) if the purchasing lead time is 5 days. EOQ (Q) Reorder Point (R) Total Inventory Cost (TC) MGT 504 by Dr. Bin Jiang

Example A large bakery buys flour in 25-pound bags. The bakery uses an average of 4,860 bags a year. Preparing an order and receiving a shipment of flour involves a cost of $10 per order. Annual carrying costs are $75 per bag. Determine the economic order quantity. What is the average number of bags on hand? How many orders per year will there be? Compute the total cost of ordering and carrying flour. If ordering costs were to increase by 10% per order, how much would that affect the minimum total annual cost? If holding costs were to increase by 10%, how much would that affect the minimum total annual cost? If holding costs were to increase by 10%, but ordering cost were to decrease 10%, how much would that affect the minimum total annual cost? MGT 504 by Dr. Bin Jiang

Production Order Quantity Model Assumptions: Demand is known Lead time is known & constant No quantity discounts are available Ordering (or setup) costs are constant All demand is satisfied (no shortages) The order quantity arrives in a single shipment MGT 504 by Dr. Bin Jiang

Production Order Quantity Model Used when units are produced and sold simultaneously Inventory level Time Part of inventory cycle during which production (and usage) is taking place Demand part of cycle with no production Maximum inventory t MGT 504 by Dr. Bin Jiang

Production Order Quantity Model Q = Number of pieces per order p = Daily production rate H = Holding cost per unit per year d = Daily demand/usage rate t = Length of the production run in days = (Average inventory level) x Annual inventory holding cost Holding cost per unit per year = (Maximum inventory level)/2 Average inventory level = – Maximum inventory level Total produced during the production run Total used during the production run = pt – dt MGT 504 by Dr. Bin Jiang

Production Order Quantity Model Q = Number of pieces per order p = Daily production rate H = Holding cost per unit per year d = Daily demand/usage rate t = Length of the production run in days = – Maximum inventory level Total produced during the production run Total used during the production run = pt – dt Q = total produced = pt ; thus t = Q/p Maximum inventory level = p – d = Q 1 – Q p d Holding cost = (H) = 1 – H d p Q 2 Maximum inventory level MGT 504 by Dr. Bin Jiang

Production Order Quantity Model Q = Number of pieces per order p = Daily production rate H = Holding cost per unit per year d = Daily demand/usage rate D = Annual demand Setup cost = (D/Q)S Holding cost = (1/2)HQ[1 - (d/p)] (D/Q)S = (1/2)HQ[1 - (d/p)] Q2 = 2DS H[1 - (d/p)] Q* = 2DS H[1 - (d/p)] p MGT 504 by Dr. Bin Jiang

Quantity Discount Model Assumptions: Demand is known Lead time is known & constant No quantity discounts are available Ordering (or setup) costs are constant All demand is satisfied (no shortages) The order quantity arrives in a single shipment MGT 504 by Dr. Bin Jiang

Quantity Discount Model Reduced prices are often available when larger quantities are purchased Trade-off is between reduced product cost and increased holding cost Total cost = Setup cost + Holding cost + Product cost MGT 504 by Dr. Bin Jiang

Quantity Discount Model A typical quantity discount schedule Discount Number Discount Quantity Discount (%) Discount Price (P) 1 0 to 999 no discount $5.00 2 1,000 to 1,999 4 $4.80 3 2,000 and over 5 $4.75 Total Annual Demand is 5000 MGT 504 by Dr. Bin Jiang

Quantity Discount Model Steps in analyzing a quantity discount For each discount, calculate Q* If Q* for a discount doesn’t qualify, choose the smallest possible order size to get the discount Compute the total cost for each Q* or adjusted value from Step 2 Select the Q* that gives the lowest total cost MGT 504 by Dr. Bin Jiang

Quantity Discount Model Total cost $ Order quantity 1,000 2,000 Total cost curve for discount 2 Total cost curve for discount 1 Total cost curve for discount 3 Q* for discount 2 is below the allowable range at point a and must be adjusted upward to 1,000 units at point b a b 1st price break 2nd price break MGT 504 by Dr. Bin Jiang

Quantity Discount Example 2DS IP Calculate Q* for every discount Q1* = = 700 units/order 2(5,000)(49) (.2)(5.00) Q2* = = 714 units/order 2(5,000)(49) (.2)(4.80) Q3* = = 718 units/order 2(5,000)(49) (.2)(4.75) MGT 504 by Dr. Bin Jiang

Quantity Discount Example 2DS IP Calculate Q* for every discount Q1* = = 700 units/order 2(5,000)(49) (.2)(5.00) Q2* = = 714 units/order 2(5,000)(49) (.2)(4.80) 1,000 — adjusted Q3* = = 718 units/order 2(5,000)(49) (.2)(4.75) 2,000 — adjusted MGT 504 by Dr. Bin Jiang

Quantity Discount Example Discount Number Unit Price Order Quantity Annual Purchase Cost Annual Ordering Cost Annual Holding Cost Total 1 $5.00 700 $25,000 $350 $25,700 2 $4.80 1,000 $24,000 $245 $480 $24,725 3 $4.75 2,000 $23,750 $122.50 $950 $24,822.50 Choose the price and quantity that gives the lowest total cost Buy 1,000 units at $4.80 per unit MGT 504 by Dr. Bin Jiang

Safety Stock Model Demand is known Lead time is known & constant Assumptions: Demand is known Lead time is known & constant No quantity discounts are available Ordering (or setup) costs are constant All demand is satisfied (no shortages) The order quantity arrives in a single shipment MGT 504 by Dr. Bin Jiang

Safety Stock Model In the simplest EOQ model, ROP = dL In the safety stock model, ROP = (safety stock) Q+SS SS MGT 504 by Dr. Bin Jiang

Safety Stock Model SS is decided by the following five factors: The variability of demand; The variability of lead time; The average demand; The average lead time; The desired service level. MGT 504 by Dr. Bin Jiang

Safety Stock: Two Uncertainties MGT 504 by Dr. Bin Jiang

Safety Stock Model z-Value Associated Service Level 0.84 80% 1.28 90% 1.65 95% 2.33 99% MGT 504 by Dr. Bin Jiang

Safety Stock Model Example A retailer sells, on average, 16 Panasonic microwave ovens a day ( ), with a standard deviation in daily demand of 3 ( ). If a retailer reorders suppliers directly from its supplier, they will take, on average, nine days to arrive ( ), with a standard deviation in lead time of 2 ( ). The retailer has decided to maintain a 95% service level. How many safety stock should the retailer hold? What is the retailer’s reorder point? MGT 504 by Dr. Bin Jiang

Safety Stock Model Example MGT 504 by Dr. Bin Jiang

Warehouse Effect in Supply Chain Risk Pooling and Inventory Impact Consider a distribution supply chain consisting of a set of n downstream retailers linked to a common source warehouse. Suppose the supplier lead time is L and every retailer faced a demand with a mean of µ and a variance of σ2 Supplier Lead time: L Warehouse Retailer 1 Retailer 2 …………. …………. …………. Retailer n Customer µ, σ2 Customer µ, σ2 Customer µ, σ2 MGT 504 by Dr. Bin Jiang

Warehouse Effect in Supply Chain Risk Pooling and Inventory Impact   MGT 504 by Dr. Bin Jiang

Net Requirements Plan MGT 504 by Dr. Bin Jiang

Lot-Sizing Techniques Lot-for-lot techniques order just what is required for production based on net requirements May not always be feasible If setup costs are high, costs may be high as well Economic order quantity (EOQ) EOQ expects a known constant demand and MRP systems often deal with unknown and variable demand MGT 504 by Dr. Bin Jiang

Lot-for-Lot Example 1 2 3 4 5 6 7 8 9 10 Gross requirements 35 30 40 55 Scheduled receipts Projected on hand Net requirements Planned order receipts Planned order releases MGT 504 by Dr. Bin Jiang

Lot-for-Lot Example No on-hand inventory is carried through the system Total holding cost = $0 There are seven setups for this item in this plan Total setup cost = 7 x $100 = $700 1 2 3 4 5 6 7 8 9 10 Gross requirements 35 30 40 55 Scheduled receipts Projected on hand Net requirements Planned order receipts Planned order releases MGT 504 by Dr. Bin Jiang

EOQ Lot Size Example Holding cost = $1/week; Setup cost = $100; 2 3 4 5 6 7 8 9 10 Gross requirements 35 30 40 55 Scheduled receipts Projected on hand Net requirements 16 Planned order receipts 73 Planned order releases Holding cost = $1/week; Setup cost = $100; Average weekly gross requirements = 27; EOQ = 73 units MGT 504 by Dr. Bin Jiang

EOQ Lot Size Example Annual demand = 1,404 Total cost = setup cost + holding cost Total cost = (1,404/73) x $100 + (73/2) x ($1 x 52 weeks) Total cost = $3,798 Cost for 10 weeks = $3,798 x (10 weeks/52 weeks) = $730 1 2 3 4 5 6 7 8 9 10 Gross requirements 35 30 40 55 Scheduled receipts Projected on hand Net requirements 16 Planned order receipts 73 Planned order releases Holding cost = $1/week; Setup cost = $100; Average weekly gross requirements = 27; EOQ = 73 units MGT 504 by Dr. Bin Jiang