# scientific poster - LOT SIZING by mladbos

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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

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