By Sanjay Sharma
Sharma S. utilized Nonlinear Programming (New Age foreign (P) Ltd, 2006)(ISBN 812241771X)
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In order to find out the value of h, expand f(a + h) using Taylor’s theorem and ignore higher powers of h. 6. 3. Solution. 3 + 2133. 33 22222. 396 This value is used as a in the next iteration. 396 + 713. 07 9661. 497 The process is continued to achieve any desired accuracy. In a complex manufacturing-inventory model, all the shortage quantities are not assumed to be completely backordered. A fraction of shortage quantity is not backlogged. Total annual cost function is formulated as the sum of procurement cost, setup cost, inventory holding cost and backordering cost.
A fraction of shortage quantity is not backlogged. Total annual cost function is formulated as the sum of procurement cost, setup cost, inventory holding cost and backordering cost. , lot size. Newton-Raphson method may be successfully applied in order to obtain the optimum lot size using an initial value as the batch size for the situation in which all the shortages are assumed to be completely backordered. 12) This value of x is used in the next iteration as an approximate value, a. The process is continued until the difference between two successive values of x becomes very small.
X1*a11 . x2*a21 ... 11) w1 . x1* a12 . x2* a22 ... xn* an2 OP Q w2 ... 52 APPLIED NONLINEAR PROGRAMMING LM C Nw N LM C OP LM C OP ... LM C OP Nw Q Nw Q Nw Q w1 * or f = w2 1 2 N 1 2 N . a1 N x1* . a2 N x2* anN ... xn* N wN OP Q wN ( x1* ) a11w1 + a12w2 + ... a1 N wN ( x2* )a21w1 + a22w2 + ... + a2 NwN ... ( xn* )an1w1 + an2w2 + ... + anNwN L ∑ L L C O LC O C O M (x ) = M P M P ... 10), f * LC O = M P Nw Q LC O = M P Nw Q 1 w1 or f * 1 1 LM C OP Nw Q LM C OP Nw Q w1 1 2 w2 2 2 L C OP ... M Nw Q L C OP ...
Applied nonlinear programming by Sanjay Sharma