<Dd> z i (t) ≥ 0 (\ displaystyle z_ (i) (t) \ geq 0) t = 0,..., T - 1, i = 1,..., J </Dd> <Dl> <Dd> m i n ∑ i ∑ t = 0 T − 1 (k i (t) δ (z i (t)) + c i (t) z i (t)) + ∑ i ∑ t = 1 T h i ′ (t) x i ′ (t) (\ displaystyle min \ sum _ (i) \ sum _ (t = 0) ^ (T - 1) \ left (k_ (i) (t) \ delta (z_ (i) (t)) + c_ (i) (t) z_ (i) (t) \ right) + \ sum _ (i) \ sum _ (t = 1) ^ (T) h'_ (i) (t) x'_ (i) (t)) </Dd> </Dl> <Dd> m i n ∑ i ∑ t = 0 T − 1 (k i (t) δ (z i (t)) + c i (t) z i (t)) + ∑ i ∑ t = 1 T h i ′ (t) x i ′ (t) (\ displaystyle min \ sum _ (i) \ sum _ (t = 0) ^ (T - 1) \ left (k_ (i) (t) \ delta (z_ (i) (t)) + c_ (i) (t) z_ (i) (t) \ right) + \ sum _ (i) \ sum _ (t = 1) ^ (T) h'_ (i) (t) x'_ (i) (t)) </Dd> <P> Where x' is local inventory (the state), z the order size (the control), d is local demand, k represents fixed order costs, c variable order costs, h local inventory holding costs . δ () is the Heaviside function . Changing the dynamics of the problem leads to a multi-item analogue of the dynamic lot - size model . </P>

Material requirement planning is more than an inventory system