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Generating order policies by SDP: non-stationary demand and service level constraints

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Figure

Fig. 1. All possible states of inventory levels and all possible paths
Table 1. SDP order quantities given the inventory level I t−1 Q 1 Q 2 Q 3 Q 4 Q 5 Q 6 0 6 2 4 8 6 4 1 0 1 3 7 5 3 2 0 0 2 6 4 2 3 0 0 1 5 3 1 4 0 0 0 4 2 0 5 0 0 0 3 1 0 6 0 0 0 2 0 0 7 0 0 0 1 0 0 8 0 0 0 0 0 0
Fig. 2. Possible inventory development given demand paths
Table 2. SDP order policy and its reached service levels (required α = 0.8) k = 5; E(T C) = 37.95 k = 50; E(T C) = 129.01 Qˆ t 5 2 4 7 5 4 5 2 4 7 5 4 I t−1 Q 1 Q 2 Q 3 Q 4 Q 5 Q 6 I t−1 Q 1 Q 2 Q 3 Q 4 Q 5 Q 6 0 5 2 4 7 5 4 0 18 16 16 15 10 4 1 0 1 3 6 4
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