INVENTORY THEORY INVENTORY PLANNING AND CONTROL SCIENTIFIC INVENTORY MANAGEMENT
INVENTORY (STOCKS OF MATERIALS) Because there is difference in the timing or rate of supply and demand What would happen if Supply>Demand? Demand>Supply?
INVENTORY IN INPUT-OUTPUT PROCESS Model 1 (k is constant): ΔV Δt = I k Model 2: ΔV Δt = I r (V See MS Excel file
INVENTORY IN INPUT-OUTPUT PROCESS ΔV Δt = I r (V Costs not yet included Satisfy Demand Minimize V What is the value of I? How much to order? When to order?
INVENTORY COSTS Cost of placing the order (affects when to order ) Price discount costs (affects how much to order ) Stock-out or shortage costs (e.g., cost of backlogging and cancellation of order; affects customer satisfaction) Working capital costs (this is due to the lag between paying the suppliers and receiving payment from customers; a type of opportunity cost and liquidity risk cost) Storage costs Obsolescence costs (e.g., salvage cost, discounted sale, etc.) Operating inefficiency costs (large inventory prevents seeing operational inefficiency)
THERE ARE DIFFERENT KINDS OF INVENTORY SYSTEMS
EOQ Economic Order Quantity Economic Lot-size
PRELIMINARIES Assumptions: One particular stock item in retail operation LEAD TIME between ordering and delivery = 0 Q items are supplied per order and they arrive in one batch instantaneously at reorder point Demand is deterministic, predictable and fixed (at a rate D items per period of time) When stocks are all depleted, new batch of Q items instantaneously arrives (a continuous review) Continuous review: an order is placed as soon as the stock level falls down to the prescribed level Periodic review: inventory is checked at discrete scheduled intervals even if inventory level dips below prescribed level before the review schedule Period here means a time of reference (e.g., 1 year, 1 month, 1 day, etc.). This DOES NOT pertain to the time interval between orders or deliveries.
Assumptions: One particular stock item in retail operation Q items are supplied per order and they arrive in one batch instantaneously at reorder point Demand is deterministic, predictable and fixed (at a rate D items per period of time) When stocks are all depleted, new batch of Q items instantaneously arrives (a continuous review) INVENTORY PROFILE (CHART)
Notes: Average inventory = Q/2 because two shaded areas are equal Time interval between deliveries = Q/D Frequency of deliveries per period = D/Q
WE CAN HAVE DIFFERENT INVENTORY PLANS
METHOD #1: EOQ MODEL ECONOMIC ORDER QUANTITY Most common approach in deciding how much and when to order a particular item (with replenishing) Finds the best balance between advantages and disadvantages of holding stock Total cost of stocking the item includes Holding Costs and Order Costs Holding Costs (per period) may include working capital costs, storage costs, insurance cost and obsolescence costs Order Costs may include administrative cost of placing the order, transportation cost of supplies and price discount costs
METHOD #1: EOQ MODEL ECONOMIC ORDER QUANTITY Holding Costs = holding cost per item x average inventory Holding costs = C 5 Q Order Costs = cost per order x number of orders per period + fixed administrative cost ØPrice discount cost not included Order costs = C ( D 2 Q + K
METHOD #1: EOQ MODEL ECONOMIC ORDER QUANTITY Total inventory costs C A = C 5 Q 2 + C ( D Q + K Q=200 is the EOQ
METHOD #1: EOQ MODEL ECONOMIC ORDER QUANTITY Total inventory costs C A Finding the EOQ (Q*) dc A dq = C 5 2 + C (D Q B = C 5 Q 2 + C ( D Q + K C 5 2 C (D Q B = 0 Q = 2C (D C 5
METHOD #1: EOQ MODEL ECONOMIC ORDER QUANTITY Remarks: When using the EOQ, the optimal inventory policy is Order quantity = Q* Time between orders = Q*/D Ø This is also the time interval between deliveries Order frequency = D/Q* per period Ø This is also the frequency of deliveries per period Q = 2C (D C 5
METHOD #1: EOQ MODEL SENSITIVITY OF EOQ Small errors (e.g., round-off error and estimation error) may still give nearoptimal solution
METHOD #1: EOQ MODEL EXAMPLE A building materials supplier obtains its bagged cement from a single supplier. Demand is reasonably constant throughout the year, and last year the company sold 2 million kg. of this product. It estimates the costs of placing an order at around PhP1,700 each time an order is placed, and calculates that the annual cost of holding inventory is 20 per cent of purchase cost. The company purchases the cement at PhP4,000 per 1,000 kg.. How much should the company order at a time? Also, compare computed EOQ with a more convenient order quantity.
METHOD #1: EOQ MODEL WITH QUANTITY DISCOUNTS Order Costs = cost per order x number of orders per period + fixed administrative cost Cost per order = C (,L C (,B C (,R if Q < q L ifq L Q < q B ifq q R Order costs F = C (,F D Q + K, i = 1,2,, m
METHOD #1: EOQ MODEL ECONOMIC ORDER QUANTITY Q F = 2C (,FD C 5 Total inventory costs C A,F i = 1,2,, m Compare the computed C t,i s. Choose the Q i * that gives minimum total inventory costs. = C 5 Q F 2 + C (,F D Q F + K
EBQ Economic Batch Quantity Economic Manufacturing Quantity Production Order Quantity
METHOD #2: EBQ MODEL ECONOMIC BATCH QUANTITY In EOQ, order (Q items) arrives at one point in time, i.e., one lot or one batch). In EBQ, we have similar assumptions as EOQ except that order (Q items) arrives in more than one batch, i.e., we do gradual replacement.
METHOD #2: EBQ MODEL ECONOMIC BATCH QUANTITY Batches arrive (% of Q items) for some period of time at rate P, and at the same time demand is removing stocks in the inventory at a rate D.
METHOD #2: EBQ MODEL ECONOMIC BATCH QUANTITY If P>D, inventory is increasing. If P<D, such as when all Q items already arrived, inventory decreases.
METHOD #2: EBQ MODEL ECONOMIC BATCH QUANTITY Maximum stock level = M Slope inventory build-up = P D (derivation: use rates) Slope inventory build-up = M Q/P (derivation: use slope)
METHOD #2: EBQ MODEL ECONOMIC BATCH QUANTITY Slope inventory build-up = P D Slope inventory build-up = M Q/P MP = P D Q P D Q M = P Average inventory: M P D Q = 2 2P
METHOD #2: EBQ MODEL ECONOMIC BATCH QUANTITY Like in EOQ: Total inventory costs = holding costs + order costs Total inventory costs C A = C 5 M 2 + C ( D Q + K Total inventory costs C A = C 5 P D Q 2P + C ( D Q + K
METHOD #2: EBQ MODEL ECONOMIC BATCH QUANTITY Total inventory costs C A = C 5 P D Q 2P + C ( D Q + K Finding the EBQ (Q*) dc A dq = C 5 C 5 P D 2P P D 2P C ( C ( D Q B D Q B = 0 Note: P>D Q 2C ( D = C 5 1 D/P
METHOD #2: EBQ MODEL EXAMPLE The manager of a bottle-filling plant which bottles soft drinks needs to decide how long a run of each type of drink to process. Demand for each type of drink is reasonably constant at 80,000 per month (a month has 160 production hours). The bottling lines fill at a rate of 3,000 bottles per hour, but take an hour to clean and reset between different drinks. The cost (of labor and lost production capacity) of each of these changeovers has been calculated at PhP7,000 per hour. Stock holding costs are counted at PhP7 per bottle per month.
METHOD #2: EBQ MODEL EXAMPLE The staff who operate the lines have devised a method of reducing the changeover time from 1 hour to 30 minutes. How would that change the EBQ?
PROBLEMS WITH EOQ AND EBQ: The model and solution are as good as the assumptions! The assumptions are over-simplistic. Factors in inventory management are generally NOT deterministic and fixed linear instantaneous accurately known zero-lead-time For products that deteriorates or go out of fashion, a periodic review is more likely to be used.
PROBLEMS WITH EOQ AND EBQ: EOQ and EBQ methods are usually descriptive and not prescriptive. However, sometimes they can be good approximates of reality. From the perspective of Japanese-inspired lean and Just-In- Time (JIT) philosophies: EOQ and EBQ methods are reactive approaches. They fail to ask the right question: How can I change the operation in some way to reduce the overall level of inventory? Inventory costs minimization is not the only objective for inventory management.