Question 2. Transshipment type problem. You are given the following transshipmen

Question

Question 2. Transshipment type problem. You are given the following transshipment problem. The supply is depicted at auto plants 1 and 2, there are two transshipment centers at nodes 3 and 4 and demand is depicted at the three dealers at nodes 5 6,7. As you may have noticed, the transshipment centers are connected to each other and cars can be transported from center 3 to center 4 as necessary. Also the dealerships at 5 and 7 can receive cars from dealer 6. The transfer center 3 has a capacity of 1500 autos. The transfer center 4 has a capacity of 1600 autos. The corresponding travel costs are depicted at each roadway link in Figure 1 below: a) 20 points - Formulate the problem as an LP, b) 5 points - Assume that the auto plant one (1) has increased its capability to produce an additional 100 autos to a total of 1500 autos. Show the change in the constraints because of this extra capability of auto plant 1. Dealers 1200 Transfer Centers Auto Plants 1400 1000 1600 800 Figure 1. Auto transport from two auto plants to three dealerships

Explanation / Answer

a) Formulate LP model

Decision variables: Xij = Number of autos supplied from node i to node j in th network

Objective: Min Z = 5X13 + 3X14 + 4X23 + 6X24 + 7X34 + 6X35 + 9X36 + 8X37 + 5X45 + 4X46 + 3X47 + 5X65 + 4X67

s.t. Constraints:

X13 + X14 = 1400

X23 + X24 = 1600

X13 + X23 = X34 + X35 + X36 + X37

X14 + X24 + X34 = X45 + X46 + X47

X34 + X35 + X36 + X37 <= 1500

X45 + X46 + X47 <= 1600

X35 + X45 + X65 = 1200

X36 + X46 - X65 - X67 = 1100

X37 + X47 + X67 = 800

Xij >= 0

b) The first two constraints change as below

X13 + X14 <= 1500

X23 + X24 <= 1600

All other constraints remain same.

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.