In the following excercise a problem concerning Safety  Stock is considered. Safety stocks are determined for several items with a fixed budget.


Several models are used: Cycle Service Level, Fill Rate, Time between Stockouts etc. Afterwards variable Lead Times are considered and their impact on Inventory Performance are evaluated. Finally the fact that stock are committed is introduced and implications in safety stocks are discussed.  For further informations see Silver et alii, Inventory Management and Production Planning and Scheduling, 1998.

 Let us consider the following items that follow a Fixed Quantity, Continuos Review (s,Q) Inventory Policy:


Table 1 - Excercise Data 
Items i Demand Di [items/year] Standard Deviations σ[items/year] Value v €/unit Lead Times [weeks]
1  1200   360   2   2
2  3000   1300  1.5   2
3  2500   300   1.8  2
4  3800   500  1  2
5  600   300  6  4
6  400   50   3  8

A, the order setup cost is 120 €/order, the carrying cost r is 0.25 €/€/year and the total maximum value of safety stocks is 1000 €.  

Find the reorder point si , the Expected Total Stocksout Occasion per Year (ETSOPY), the Expected Total Shortage in Value per Year (ETSVPY), in the following cases: 

  1. The same safety stock factor k for all the items;
  2. The same Cycle Service Level P1 for all the items;
  3. The same costs for the items in shortage B2 [% of item values/item];
  4. The same Time Between Stock Outs; 
  5. the same Fill Rate, P2, complete backlog;
  6. The same costs for item in shortage for unit of time B3 [% of item vales/items-unit of time];
  7. The same costs for stock out incidents B1;
  8. Minimum Expected Total Stockout Occasions per Year ETSOPY;
  9. Minimum Expected Total Shortage in Value per Year ETSVPY;

10. Considering then only the results in case 2, (same P1) determine the  variation in P1 if Lead Time is not fixed but probabilistic. The average value of LT is the same as the one in Table 1, while standard deviation is 1 week for each item.

11. Considering now only case 2 (same P1) and only item 1. We can suppose that when an order is received inventory are immediatly committed, but items are physically picked from the warehouse one day after. So there is a distinction in between stocks are committed and when they are effettively used. What are the Safety Stocks reduction for item 1 if we include this day items waits between commitment and effective use?