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Supply Chain, The Way to Flat Organisation Part 4

Tham khảo tài liệu 'supply chain, the way to flat organisation part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Optimization Based e-Sourcing 81 - Supply Constraint For every winning bid j e J qj e aj Zj and for losing bids qj 0. - Demand Constraint The total quantity procured should satisfy the demand of the buyer J - B. The WDP is a nonconvex piecewise linear knapsack problem Kameshwaran Narahari 2009a which is NP-hard. It is a minimization version of a nonlinear knapsack problem with a demand of B units. Each bid corresponds to an item in the knapsack. Unlike traditional knapsack problems each item j can be included in the knapsack in a pre-specified range ữj Zj and the cost Qj is a function of quantity included. The cost function Qj of Figure 3 is nonlinear but due to the piecewise linear nature the WDP can be modelled as the following MILP. miny n0d0 y nSdS PSSSxS 1 j j j j j jI jeJ V s 1 subject to d 1 d0 Vj e J 2 xS d Vj e J 1 s lj 3 Xs - ds 1 Vj e J 1 s lj 4 z Hjdj x0SjXSj I- B 5 jeJV s 1 J ds e 0 1 Vj e J 0 s lj 6 xsj e 0 1 Vj e J 1 s lj 7 The decision variable Xs denotes the fraction of goods chosen from the linear segment s of bid j. For this setup to make sense whenever xsj 0 then Xs-1 0 for all s. To enable this binary decision variable dSj is used for each segment to denote the selection or rejection of segment s . of bid j. The winning quantity for bid j is a d0 y7 od with cost n n l -V g q y J ÌÌ 1 j j n0d0 X nd BSd . The binary decision variable d0 is also used as an indicator j j j j r-j j j ị y 0 j variable for selecting or rejecting bid j as d0 0 implies that no quantity is selected for trading from bid j. 3.4 Business constraints The business rules and purchasing logic can be added as side constraints to the WDP. For the above procurement scenario the relevant business constraints are restricting the number of winning suppliers in a given range LB ƯB and guaranteeing a minimum volume or monetary business worth MIN_QTY MIN_VAL for a set of incumbent suppliers J c J . 82 Supply Chain The Way to Flat Organisation LB J UB 8 YI 70 Y Sjxsị MIN _ QTY 9 7J s l J