193 X Lab X P Pea X help x Mes X Pea X Cor u.edu/courses/185255/assignments/5088447 merA-X-IEE376-... > Assignments > Lab 10: Network Optimiza... Lab 10: Network Optimization in AMPL A+ X P Pea X Das X Stu ASU Home My ASU Start Assignment Lab Objectives In this lab, you will: • Formulate a network optimization problem using AMPL. • Coe a network optimization problem using sets, indices, summations, and "for all" notation. Understand the importance of separating data and models. Problem Statement Suppose you manage a manufacturing plant that produces 450K of Personal Computers per week, and two distribution centers. The two distribution centers are located in the northeast and southeast, and they receive computers from the manufacturing plant. The distribution centers transship them to warehouses located in the following cities: Boston, Newark, Baltimore, Atlanta, and Orlando. A network representation, including the cost and capacity of each arc, can be seen below. The numbers outside of the nodes are production amount (for PITT) and demand (for each city). The objective is to formulate and code in AMPL the optimization problem that minimizes the total cost and satisfies the total demand of the customer. BOS 90 1.7,100 Capacity Cost 0.7.100 NE WR 130 (93 X Lab X P Pea X help x Mes .edu/courses/185255/assignments/5088447 Lab Objectives In this lab, you will: x 3 Pea X 0 Formulate a network optimization problem using AMPL. Cor X P Pea X 9 Day • Coe a network optimization problem using sets, indices, summations, and "for all" notation. Understand the importance of separating data and models. X Sta Problem Statement Suppose you manage a manufacturing plant that produces 450K of Personal Computers per week, and two distribution centers. The two distribution centers are located in the northeast and southeast, and they receive computers from the manufacturing plant. The distribution centers transship them to warehouses located in the following cities: Boston, Newark, Baltimore, Atlanta, and Orlando. A network representation, including the cost and capacity of each arc, can be seen below. The numbers outside of the nodes are production amount (for PITT) and demand (for each city). The objective is to formulate and code in AMPL the optimization problem that minimizes the total cost and satisfies the total demand of the customer. BOS 90 1.7, 100 Capacity Cost 0.7,100 NE EWR) 120 2.5, 250 1.3, 100 450 PITT BWI 120 1.3, 100 3.5, 250 0.8, 100 SE ATL 70 0.2, 100 2.1, 100 MCO 50 (93 X 5 Lab × Pea X help x Mes X Pea X Cor X P Pea X Dat X .edu/courses/185255/assignments/5088447 distribution centers. The two distribution centers are located in the northeast and southeast, and they receive computers from the manufacturing plant. The distribution centers transship them to warehouses located in the following cities: Boston, Newark, Baltimore, Atlanta, and Orlando. A network representation, including the cost and capacity of each arc, can be seen below. The numbers outside of the nodes are production amount (for PITT) and demand (for each city). The objective is to formulate and code in AMPL the optimization problem that minimizes the total cost and satisfies the total demand of the customer. BOS 90 1.7, 100 Capacity Cost NE 0.7, 100 EWR) 120 2.5, 250 1.3, 100 450 PITT BWI 120 1.3.100 3.5, 250 0.8, 100 SE ATL 70 0.2, 100 2.1, 100 MCO 50 Figure 15-1: A directed network. The formulation for this problem is as follows: • Parameters • I: Set of cities • A: Set of arcs U₁: Capacity on the arc (i, j) Є A Cij: Cost to transfer one unit of product from city i to city j on the arc (i, j) = A b(i): Supply if b(i)>0 Vie I and demand if b(i) < 0 ViЄ I • Decision variables Number of products shipped from city & I to city ie J 193 X Lab X Pea X help X Mes X Pea u.edu/courses/185255/assignments/5088447 X CORD BLOOD 200 Con X Pea X Figure 15-1: A directed network. The formulation for this problem is as follows: Parameters • I: Set of cities • A: Set of arcs 0 Uij: Capacity on the arc (i, j) Є A A Das o Cij: Cost to transfer one unit of product from city i to city j on the arc (i, j) Є A b(i): Supply if b(i)>0 Vi Є I and demand if b(i) < 0 ViЄ I • Decision variables xij: Number of products shipped from city i Є I to city jЄ J • Constraints 0 Σ(A - E)EA j = b(i) ViЄ I 0≤ j ≤Uij V(i, j) E A Objective function (maximize the profits) Minimize (i)EA Cijij In order to help you code the mod and .dat files, here are the components of the .dat file. set cities := PITT NE SE BOS EWR BWI ATL MCO ; set arcs := (PITT, NE) (PITT, SE) (NE,BOS) (NE, EWR) (NE, BWI) (SE, EWR) (SE, BWI) (SE, ATL) (SE,MCO); param: b:= PITT 450 NE 0 SE O BOS -90 EWR -120 BWI -120 ATL -70 (03x Lab X Pea help x Me X Pea X Cor X P Pea K Das .edu/courses/185255/assignments/5088447 0≤ j ≤Uij V(i, j) Є A Objective function (maximize the profits) Minimize ΣEA Cijij In order to help you code the .mod and .dat files, here are the components of the .dat file. set cities := PITT NE SE BOS EWR BWI ATL MCO ; set arcs := (PITT, NE) (PITT, SE) (NE,BOS) (NE, EWR) (NE, BWI) (SE, EWR) (SE, BWI) (SE, ATL) (SE, MCO); param: b:= PITT 450 NE O SE O BOS -90 EWR -120 BWI -120 ATL -70 MCO -50%; param: cu := PITT NE 2.5 250 PITT SE 3.5 250 NE BOS 1.7 100 NE EWR 0.7 100 NE BWI 1.3 100 SE EWR 1.3 100 SE BWI 0.8 100 CF ATY 100