Inventory Control Guide Page 22
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404.2 Lot size - reorder point model or
(Q, R) model
Let us try here to summarize the problem. The assumptions are the following.
Assumptions
1. Constant random demand: D
(item / time )
2. Lead time (Lt> 0)
3. Continuous review
Four different cost areas have to be considered. Here are the associated parameters.
Costs: Holding, Order, Item, Penalty
Random demand and positive lead time together induce the risk of shortage and therefore of
possible penalty costs.
Decision (lot size - reorder point)
Select Q and R = Lt × D + SS
The decision variables are the order lot size Q and the order point R. Since R is basically
defined as the demand during the lead time plus the safety stock, choosing R is equivalent to
choosing the safety stock SS.
General Objective
Minimize the costs / Optimize the service
These are the two general goals which are pursued. The notion of "good service" requires
however further specifications. Here are two classical ways.
Objective 1
Minimize the total costs and
Guarantee a maximum stockout frequency (f)
This means that the safety stock will be chosen in order to guarantee that the frequency of
stocking out does not exceed some given value (e.g., once a year).
Objective 2
Minimize the total costs and
Guarantee a minimum fill rate ( β β β β )
The fill rate(β) is the average percentage of the sales which are directly satisfied from the
shelves. The goal here is thus to select the safety stock which guarantee that, for example, 95
percent of the units ordered can be immediately served from the stock.
Objective 3
Minimize the total costs (assuming penalty costs)
Here we assume that each demand unit that is backordered induces a penalty cost (which is
independent of the time the unit is backordered). Knowing this cost, we can choose the best
safety stock SS and the best lost size Q by a pure economical analysis.
Prod 2100-2110
Inventory Control
21
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