# Supply Chain

In: Science

Submitted By clairebrbs123
Words 1127
Pages 5
Lecture 4 for IE4350 on 2/5/2015
Topics: Goal Programming, and Stochastic Optimization 1. Multi-Objective Optimizations (Goal Programming) Many times, the decision process involves multiple, yet conflicting objectives. As a simple example, when you approach the car dealer for a new car, there are several objective functions in your minds: (1) low price; (2) high performance; and (3) latest technology, etc. Unfortunately, these objectives may conflict with each other. If you want to spend less money, you may not able to purchase a car equipped with the lasted technology (GPS, collision avoidance, and hybrid, just name a few). Now let us re-exam the PC/Laptop/Work Station problem again. Recall the problem is formulated as (x1 represents the weekly quality for PC, x2 for LT and x3 for WS) Problem P1 Maximize Subject to

P  350 x1  470 x2  610 x3 x1  x2  120

(1.1) (1.2) (1.3) (1.4)

x3  48 10 x1  15 x2  20 x3  2000
All x’s are non-negative Using the simplex’ method, we have x1=120, x2=0, and x3=40. The max profit P=\$66,400.

The marketing and sale manger may decline this production planning because it entails much heavier sales on PC (120) than the Work Stations (40), and no laptops. If the market fluctuates with less demand on PC, the manufacturer will carry excessive PC inventory, blocking the cash flowing. To express his concern, the market manager proposes the following condition: The number of PC/LT produced cannot be larger than the WS sold plus a constant Q. Mathematically,

x1  x2  x3  Q
Or

(1.5) (1.6)

x1  x2  x3  Q

Equations (1) or (2) can be treated as the GOAL CONSTRAINT. This constraint can also be viewed as the objective function to be achieved by the computer producer. However, (1) or (2) can be incorporated into Problem P5, and the new formulation becomes Problem P2 Maximize Subject to

P  350 x1  470 x2  610 x3…...

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