INVENTORY MANAGEMENT Sub: Resource Management (Subject Code: 1721402) GUIDED BY: Prof. J. J. BHAVSAR Associate professor and PG – Coordinator, M.E. Construction Engineering & Management, Civil Engineering Department, Prof. JAYESH R. PITRODA Assist. Prof. & Research Scholar, Civil Engineering Department M.E. CIVIL (CEM) B.V.M. Engineering College - V. V. Nagar Ashish Makwana 1 Date: 7/5/’13 INTRODUCTION TYPES OF INVENTORY INVENTORY DECISIONS INVENTORY COSTS INVENTORY MANAGEMENT SYSTEMS 2 INVENTORY MANAGEMENT Vital to the successful functioning of manufacturing & retailing organizations Consist of • raw materials • work-in-progress • spare parts • finished goods Not necessary that an organization has all these inventory classes Different departments within the same organization adopt different attitudes towards inventory 3 In an inventory control situation, there are three basic questions to be answered. They are: • How much to order? • When should the order be placed? • How much safetystock should be kept? 4 INVENTORY COSTS Purchase Cost Ordering Cost Carrying Cost Stock out Cost 5 Two inventory management systems :- 1. Fixed order quantity system or The reorder point system • The re-order level is determined. • An order for a predetermined number of units is placed. 2. Periodic review system • The inventories are replenished at fixed intervals of time. • In this system the time after which the supplies are ordered is fixed but not the quantity to be ordered. 6 FIXED ORDER QUANTITY SYSTEM Assumptions: The demand for the item is certain, continuous and constant over time. The lead time, that is the time between placing an order and its delivery, is known and fixed. Thus, when the lead time is zero, the delivery of item is instantaneous. Within the range of the quantities to be ordered, per unit holding cost and the ordering cost (per order) are constant and thus independent of the quantity ordered. 7 The inventory is replenished immediately as the stock level reaches exactly equal to zero. Consequently, there are no stock overages or shortages. With this set of assumption, the inventory level would vary over time as depicted in Figure 1. 8 Figure 1 Inventory Profile of Classical EOQ Model 9 Lower rates are quoted if the orders are of a big size. There may be one or more than one price break that may be offered. In this case, the quantity ordered has to be determined carefully taking into consideration the price levels for the different quantity ranges. 10 Under the conditions of price break(s), the item cost, being a function of the order quantity, is the incremental cost and must be included in the cost model. As such, the cost model would include the ordering, the holding and the purchasing cost of the items. Thus, 𝑻 𝑸 = 𝑫 𝑨 𝒒 + 𝑸 𝒉+ 𝟐 𝒄𝒊𝑫 11 In which To understand how the optimal order quantity can be determined – A TV tubes example This cost model is clearly a step function and not continuous like the one given earlier. D = 2000 units per annum -- A = Rs.150 per order -- h = Rs.2.40 per unit per annum -- ORDER QUANTITY UNIT PRICE Q/q = 500 units  c1 - Rs.10 per tube Q/q = 800 units  c2 - Rs.9.80 per tube 12 EOQ = 500 (units already established) •𝑇 𝑄 = 2000 500 × 150 + • 𝑇 𝑄 = 𝑹𝒔. 𝟐𝟏, 𝟐𝟎𝟎 500 2 × 2.40 + 10 × 2000 Suppose now that the supplier informs that if the order size is at least 800 units •𝑇 𝑄 = 2000 800 × 150 + • 𝑇 𝑄 = 𝑹𝒔. 𝟐𝟎, 𝟗𝟑𝟓 800 2 × 2.40 + 9.80 × 2000 13 Figure 2 Cost Curve for the Price-Break Model 14 Consider situations in which the goods are received for inventory at a constant rate over time. This is particularly relevant for situations when the item in question is being produced internally rather than being procured from external suppliers. When the production begins, a constant number of units are supposed to be added to the inventory each day till the time the production run is completed. Simultaneously, the items would be demanded at a constant rate, as stipulated earlier. Obviously, the rate at which they are produced has to be higher than the rate of their depletion, for only then can we think of the inventory buildup. 15 (Refer Fig. 3) Here the total quantity Q is produced over a period, tp which is defined by the production rate p. Since the inventory does not pile up in one shot but rather continuously over a time period and is also consumed simultaneously, the average inventory level would be determined not only by the lot size Q, but also be affected-by the production rate p and depletion (demand) rate d. 16 Figure 3 Inventory Profile – Build-up Model 17 In general inventory situations, a shortage is considered undesirable and is avoided, if possible. This is because shortages may and are likely to, mean loss of customer goodwill, reduction in future orders, unfavourable change in the market share, and so on. While in some situations the customers shift to other sources for their requirements, and so may be lost forever, in some others the customers may not withdraw the orders and wait until the next shipment arrives. This latter situation is called the back-ordering situation. We shall now develop an inventory model under the assumption that back-ordering is possible. 18 The EOQ model assumes that the inventory is replenished precisely when the inventory level tall, off to zero. There is no question of shortages and therefore, the cost of shortage is not considered in that model. With the assumption of back-ordering, shortages may in fact be deliberately planned to occur. It may be advisable on economic considerations, specially when the value of the item in question is very high with consequent high holding cost. Basically, then, it is a question of setting off the cost of shortages against the saving in the holding cost. 19 Figure 4 Inventory Profile – Planned Shortages Model 20 S below the zero level indicates negative inventory i.e. the number of units backordered. As soon as the lot of Q items is received, the customers whose orders are pending would be supplied their requirements immediately and as such the maximum inventory level would be Q-S. The inventory cycle T would be divided in two phases: t1 - the time when inventory is on hand and orders filled as and when they occur and t2-when there is a stockout and all the orders are placed on backorder. In developing the cost function, we would consider the cost of shortages in addition to the holding and the ordering costs. 21 Cost of shortages or the backordering cost is incurred in terms of the labour and special delivery expenses and the loss of customer goodwill (which may be taken to be a function of the time a customer has to wait). Thus, Total (variable) cost = ordering cost + holding cost + shortage cost Ordering cost : If the cost of placing an order be A and the total demand be D, we have, Annual ordering cost = 𝐷 𝑄 𝐴 22 Holding cost: t1 is the period in a given inventory cycle when positive inventory is held. Since the maximum inventory, M is Q-S, the average inventory level equals (𝑄 −𝑆) . 2 Shortage cost: We shall now develop expressions for the average number of shortage and the shortage cost with the help of which we shall determine the annual shortage cost. 23 Since S represents the maximum level of shortages, the average level of shortages, during the period when there 𝑠 is a shortage (t2) shall be . 2 If we let b represent the backorder cost, that is to say, the shortage cost per unit of shortage per year, we have. Shortage cost in a given cycle T= 𝑺 𝒃 t2 𝟐 24 In the periodic review system, the stock is replenished after reviewing the stock level at regular time intervals. It is unlike the fixed order quantity system where replenishment is triggered by the stock level reaching the reorder point. In this system, the stock is reviewed after a fixed interval of time and an order is placed for a quantity sufficient to replenish inventory to a predetermined level, referred to as target inventory (TI) level. 25 After the re-order lead time, the shipment arrives and goes into inventory. While the review period is the same, the quantities ordered may be, and generally are, different in each period, being calculated as follows: Q = TI — inventory on hand — previous ordcis not yet received OS any) 26 The safety stock is an important constituent of the re-order point. In the fixed order quantity inventory system under consideration, the re-order level would be determined as the expected demand of the item during lead time plus the safety stock. If the demand varies about the mean daily demand equal to d with the expected lead time equal to L days and we set the reorder level R at L 𝑑 units, then we should expect a shortage to occur in about half the lead time periods. 27 To reduce this 50% probability of being out of stock, the safety stock SS would be required to be kept. Thus, Re-order level, 𝑹 = 𝑳𝒅 + 𝑺𝑺 28 Figure 5.1 SS to meet a high demand 29 Figure 5.2 SS to meet a delayed deliver 30 31