scientific poster - LOT SIZING by mladbos


Scientific poster for lot sizing

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									                                              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:

                                                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)
                                                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
                                                Optimal lot size is determined by the equation:             Q* =                               In general, dynamic models give better result than static models
                                                                                                                                               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 :
                                                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.

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