Tham khảo tài liệu 'supply chain, the way to flat organisation part 11', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Distributed Supply Chain Planning for Multiple Companies with Limited Local Information 291 L EE fa - Su r EE I S - Sb I 22 i t i 1 i t I v ieP t ieP t The penalty parameter r for a linear penalty term is gradually increased in each iteration. By applying the linear approximation technique around a tentative solution for the proposed method the solutions derived by solving subproblem for each company cannot provide an exact lower bound of the original problem. Coordination of supply chain planning among multiple companies A sequence of optimization problems Ek can be given by 23 where L is given by 14 . Ek min L rt ESỊ -E S 23 ceZs c eZc The decomposed subproblem for each company is reformulated as 24 and 25 by applying the first order Taylor series of expansion around a tentative solution. For supplier company c e Zs ÍJĨPk mínVVÍ Yc vc Ì n V lirWI. V c V vc I rozfl EP0c minEE J .Et - j rkEE S t E -E 24 ieP t ieP t c eZs c c eZc For vendor company d e Zc ppk minW J fdf d Yd Ydì ỉ .ỢdU WIỸd X V ọc _ V .ợc I OCX EP0c minEEy ASt J rkEE s E E Su 1 25 ieP t ieP t c eZc d c eZs subject to 1 4 - 11 The subproblem for each company is an MILP problem which can be solved by a commercial solver. rk represents a weighting factor for penalty function. To derive near-optimal solution for the proposed method the weighting factor rk must be gradually increased according to the following equation. r rk r 26 A r is the step size parameter for penalty weighting coefficient which should be determined by preliminary tests. Even though the objective function includes a linear penalty function for each subproblem a lower bound of the original problem can be obtained by calculating L for the solution of subproblem when rk is set to zero. Scenario of planning coordination for multiple companies The system generates near-optimal plan in the following steps. Step 1 Initialization k 0 . The multipliers Ằlt and the weighting factor rk are set to .