1st International Scientific and Expert Conference TEAM 2009 (Technics, Education, Agriculture & Management) Lot sizing of spare parts M. Bošnjakovića,*, M. Cobovića a University of Applied Sciences in Slavonski Brod, Dr. Mile Budaka 1, HR-35000 Slavonski Brod, Croatia *Corresponding author. E-mail address: firstname.lastname@example.org Introduction Least Period Cost Model (LPC) Whenever the demand is positive model find the order size that To achive ability and reliability of machines, it is necessary to will cover the next "n" periods, where "n" is set to minimize the stock a certain amount of spare parts. However, ordering and average cost per unit time. inventory holding costs are affecting performance. It is therefore necessary to find the optimal order size that will minimize total Part-Period Balancing Model (PPB) costs. To find the optimal ordering plan, there are different This model was introduced 1968 and is basically the same as the mathematical models, but the question is which of them give the Least Total Cost. The basic idea is that the requirements for the best result in the issue of procurement of spare parts. successive periods can be added to the same lot so long as the In general, for solving this problem we can use static and cumulative holding cost does not exceed the ordering cost. Figure 2. Lot-for-lot lot sizes dynamic programming inventory models. Inventory models Input dana Spare parts demand often tends to be "lumpy," that is, Static models Dynamic models discontinuous and no uniform, with periods of zero demand. According this assumption appropriate test data are used in Economic Order Quantity Wagner-Within evaluation of certain inventory models. Period Order Quantity Least Period Cost Table 1. The spare part demand Period 1 2 3 4 5 6 7 8 9 10 11 12 Total Lot for Lot Least Unit Cost Demand 22 62 0 35 124 68 25 0 120 70 44 30 600 Part-Period Balancing In this test ordering (setup) cost per order is 30,00 € and holding cost per unit and period is 0,2 €. Figure 1. Inventory models Figure 3. Economic Order Quantity lot sizes Static models Results Economic Order Quantity (EOQ) The figures 2. to 9. show the calculation results of the ordering This is mathematical model that determines the amount of goods plan for particular model. Calculation is done according to given to order to meet demand while minimizing inventory costs. procedures. It is necessary to know the following values for the optimization: All values in the figures are given in Euros (€). D - Annual demand in units of the spare part Cn - Fixed cost per order h - Holding cost per unit per year 2 D Cn Conclusion Optimal lot size is determined by the equation: Q* = In general, dynamic models give better result than static models h for approximately 20%. The results of dynamic methods depend Period Order Quantity (POQ) on the value and mutual respect of input data, and especially Period Order Quantity is an EOQ based technique. The EOQ about the relationship between the ordering and holding cost. quantity is divided by the average demand during one period to However, as it is evidently from the example and additional obtain the number of periods whose requirements are to be analysis, the best result in determining the optimal lot size of Figure 4. Period order quantity lot sizes covered by the lot size (rounded to the nearest positive integer). spare parts gives Wagner-Whitin method. Lot-For-Lot Model (LFL) Spare parts are ordered precisely when needed. Each period is ordered a lot to satisfy only that period’s demand. Literature cited 1) HM. Wagner, Comments on “Dynamic version of the economic lot-size model”. Management Science, Vol. 50, No 12, December 2004, pp. 1775- Dynamic models 1777 Dynamic lot-sizing models are used within the demand which 2) R. Kleber, K. Inderfurth, A Heuristic Approach for Integrating Product vary during a period of time. Recovery into Post PLC Spare Parts Procurement. Springer Berlin Heidelberg, 2009., ISBN 978-3-642-00141-3, pp. 209-214 Wagner-Whitin algorithm 3) E. Silver, H. Meal, A heuristic for selecting lot size requirements for the This model evaluates multiple alternatives that consider period case of a deterministic time varying demand rate and discrete demand, holding and setup costs to produce an optimal lot size opportunities for replenishment. Production and Inventory Management that varies for each period as required. Journal, Vol. 14, No 2 1973., pp. 64–74 Least Unit Cost Model (LUC) Figure 5. Least unit cost lot sizes Whenever the demand is positive model find the order size that For further information will cover the next "n" periods, where "n" is set to minimize the Please contact : email@example.com average ordering and holding cost per unit. Tel: +385 35492634 Figure 6. Part-period balancing lot sizes Figure 7. Least period cost lot sizes Figure 8. Wagner-Within lot sizes Figure 9. Comparison of the total cost Slavonski Brod, Hotel Savus, December 10 & 11, 2009.