By Thi Thu Thuy Huynh.
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Extra info for Capacity constraints in multi-stage production-inventory systems applying material requirements planning theory
This is a heuristic method for finding the best solution for the production quantity of each item in each period. The method involves four procedures, of which the first is finding a starting solution. The three others are named “Moving”, “Reduction” and “Improvement” and are explained after the outline of the algorithm is described. We introduce some additional notation: m = iteration counter S[m] = set of solution variables obtained at iteration m NPV(S[m]) = expected net present value of S[m] mmax = maximum number of iterations of the heuristic.
1. Flowchart of the fundamental equations of MRP Theory (Grubbström and Tang 2000). The fundamental equations of MRP Theory are balance equations describing the time development of total inventory, available inventory, backlogs, and allocations (see Grubbström and Tang, 2000). With the policies we are studying, backlogs will not occur in deterministic demand cases. 2) where S is the column vector of items in inventory (including is the column vector of items in available inventory allocations), R is the vector of external demand, P (total inventory less allocations), D is the vector of items produced, H is the input matrix (the Bill of Materials), and I is the identity matrix.
On differentiating NPV with respect to Q we obtain ( cQ + K ) f ( ρ )Q ln f ( ρ ) = ∂NPV c + = 2 ∂Q 1 − f ( ρ )Q 1 − f ( ρ )Q = ( ) ( ) c 1 − f ( ρ )Q + ( cQ + K ) f ( ρ )Q ln f ( ρ ) (1 − f ( ρ ) ) Q 2 39 =0. 60) which is the necessary optimisation condition. 61) which has the standard format. Instead, in the fixed period requirement (FPR) case, the quantity Qn = D(tn + T ) − D(tn ) is ordered at the beginning of each interval of length T. Expected production will then be: ⎡∞ ⎤ E ⎣⎡ P ( s ) ⎤⎦ = E ⎢ ( D(tn + T ) − D(tn ) ) e stn ⎥ = ⎣ n =0 ⎦ T 1 .
Capacity constraints in multi-stage production-inventory systems applying material requirements planning theory by Thi Thu Thuy Huynh.