Quantitative Techniques for Decision Making in Construction

7.INVENTORY MODELLING II

7.1 Inventor y Modelling Involvin g Stockout Cost We have seen in Chapter 6 that under normal circumstances, when inventory is delivered at the instant when an order is placed, the inventory level can be represented graphically as shown in Fig. 7.1. Inventory value ($) EOQ •• Tim e Fig. 7.1 Th e simple inventor y model . Order s ar e placed a t the instan t inventory fall s to zero. I t is then immediatel y replaced . QUANTITATIVE TECHNIQUE FOR DECISION MAKING IN CONSTRUCTION However, ne w stoc k ma y arrive late r tha n scheduled , an d ther e ma y b e unexpected excessive demand on stock. Such situations lead to what is known as stockout, which is when the inventory on hand cannot cover needs. This shortage of stock is represented by the shaded portion of the graph unde r zero inventory in Fig. 7.2. Inventory value ($) •Tim e Fig. 7.2 Th e inventory model with stockout. Stockout is represented by the shaded portion of the graph. Notice that the new inventory level after stockout does not rise to the original inventory level, because unfilled order s (bac k orders) o f stock have to be filled. Stockout is expensive because operations have to temporarily cease and the firm may suffer a loss in reputation. Stockout cost is usually expressed as an average cost per item out-of-stock pe r day, taking all the above costs into account. We can see that the average inventory, however, will be less than half th e maximum inventor y when ther e is stockout in a firm. Thi s mean s les s carrying cost . INVENTORY MODELLING11 Incorporating the Stockout Cost in the Inventory Mode l In earlier sections, we saw that the total inventory cost is given by the sum of the ordering cost and the carrying cost only. However, if carrying cost is very high, it may be desirable to create a stockout situation deliberately . This can reduce the high carrying cost so that the total inventory cost can be further reduced . In such a case, the stockout create s a back order . Tha t is, the custome r does not withdraw the order during the time that the required item is out of stock because th e firm will fill the order immediately th e inventory ite m arrives. For such a model, the total inventory cost is the sum of the stockout cost , the carrying cost and the ordering cost. In this section, we will see how to obtain the minimum total inventory cost for such a problem. Let us consider the inventory of a firm with stockout and back orders. Suppose that the inventory is represented by the graph in Fig. 7.3. y • Tim e (days) Fig. 7.3 Inventor y with stockou t and bac k order s Let u = usage rate (items per day) y = batch order quality x = apparent initial stock (after fillin g back orders) t1 = days when there is stock t2 = days when there is stockout s = stockout cost (dollars per item per day) h = carrying cost (dollars per item per day) QUANTITATIVE TECHNIQUE FOR DECISION MAKINGIN CONSTRUCTION Stockout Cost The shaded area in Fig 7.3 represents the number of 'item-days' that items are out of stock. When this is multiplied by the stockout cost per item per day, the total stockout cost is determined. Total stockout cos t for an inventory cycl e (th e period of items between two arrival of new stocks) is given by the shaded area in Fig. 7.2 multiplied by the stockout cost and is given by: 1 2 - ? ( y - *)t2 s Now, the total number of days in an inventory cycle is tx + t2 Therefore, the average stockout cost per day is given by: \{y -x)t 2s tl+t2 xt Since t = — (usin g similar triangles), 1 y - x 1 (y _ x)t S Stockout cost per day = — — + U y - x2 (y - x)2 s 2y Carrying Cost The carrying cost can be obtained in a similar manner as follows. Carrying cost for an inventory cycle = ( i xt Y)h Carrying cost per day = -—l — tl+ t 2 = £ - - — (sinc e t, = —2-) xt ^ + t l y-x y-x 2 x2 h 2y INVENTORY MODELLING1 1...