tailieunhanh - Supply Chain Management New Perspectives Part 20

Tham khảo tài liệu 'supply chain management new perspectives part 20', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Districting and Customer Clustering Within Supply Chain Planning A Review of Modeling and Solution Approaches 747 Stp Std Stopping time per pickup and delivery respectively in each node. dik Distance from point i to point k i k e V Ả Scale factor 0 1 1. doi Distance from the depot to the point i i e V. Sp Average speed. Nz Normalization parameter for the compactness metric. Nw Normalization parameter for the workload metric. The following decision variables are defined Xij Binary variable. 1 indicates that customer i is assigned to district j. And the following auxiliary variables are defined W Continuous variable that represent the maximum workload content assigned to a district. z Continuous variable that measure the compactness as the maximum travel time between the furthest apart points of a district. Dj Continuous variable that takes the value of the traveling time from the depot to the farthest point of district j. Mj Continuous variable that takes the value of the traveling time between the two furthest apart points of district j. The mathematical formulation model is as follows Min OF1 W 1_ Nw Nz Subject to s j1 jeJ Vi eV GR- 1 GR- 2 s wPiXij a ieV Vj e J GR- 3 s wdX p z .Jik X Xkj -1 Vj e J GR- 4 Vj e J i e I k i eV GR- 5 j Sp Z Mị Vj e J GR- 6 Dj d X Vi e V Vj e J GR- 7 W Stds . StpS wpXj Dj Sp ieV ieV Vj e J GR- 8 X e 1 0 Vi e V Vj e J GR- 9 Equation GR- 1 is the objective function that minimizes a weighted average of the maximum workload and maximum compactness metrics. The objectives are normalized and the relative weighting is given by Ấ. Constraints GR- 2 guarantee that each demand point is assigned to only one district. Constraints GR- 3 and GR- 4 guarantee that each district has a maximum of a pickups and p deliveries respectively. These constraints help to balance the number of pickups and deliveries allocated to a district so that the capacity of the vehicles is not exceeded. Constraints GR- 5 guarantee that Mj takes the value of the maximum