Introduction to mathematical programming
Introduction to mathematical programming
4th Edition
ISBN: 9780534359645
Author: Jeffrey B. Goldberg
Publisher: Cengage Learning
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Chapter 4.16, Problem 12P

Explanation of Solution

Selecting the project using the preemptive goal programming:

Consider the following variables x1,x2,........,x8,

xi={1      If project i is build0      otherwise

For every project values related to each attribute are tabulated.

The table is given below,

 12345678
ROI20704566703504953801500480
Cost900240335700410190500160
Productivity improvement32201032
Manpower needed181827364264824
Degree of risk32411023

The company has the following goals.

Goal 1: Archive a return on investment of at least $3,250. Thus the constraint formed is,

2070x1+456x2+670x3+350x4+495x5+380x6+1500x7+480x83250

Goal 2: Limit cost to $1300. Thus the constraint formed is,

900x1+240x2+335x3+700x4+410x5+190x6+500x7+160x81300

Goal 3: Archive a productivity improvement of at least 6. Thus the constraint formed is,

3x1+2x2+2x3+x5+3x7+2x86

Goal 4: Limit manpower use to 108. Thus the constraint formed is,

18x1+18x2+27x3+36x4+42x5+6x6+48x7+24x8108

Goal 5: Limit technological risk to a total of 4. Thus the constraint formed is

3x1+2x2+4x3+x4+x5+6x6+2x7+3x84

Hence the linear programming can be formulated as given below,

Minimize z=x1+x2+x3+x4+x5+x6+x7+x8

Subject to the constraints,

2070x1+456x2+670x3+350x4+495x5+380x6+1500x7+480x83250900x1+240x2+335x3+700x4+410x5+190x6+500x7+160x813003x1+2x2+2x3+x5+3x7+2x8618x1+18x2+27x3+36x4+42x5+6x6+48x7+24x8108

3x1+2x2+4x3+x4+x5+6x6+2x7+3x84xi0

Here, it is observed that for these set of constraints, there is no region which is feasible. That is all the constraints cannot be met. Hence e assign a cost value incurred if any of the goal is not meet. So introduce deviational variables as follows

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Chapter 4 Solutions

Introduction to mathematical programming

Ch. 4.5 - Prob. 1PCh. 4.5 - Prob. 2PCh. 4.5 - Prob. 3PCh. 4.5 - Prob. 4PCh. 4.5 - Prob. 5PCh. 4.5 - Prob. 6PCh. 4.5 - Prob. 7PCh. 4.6 - Prob. 1PCh. 4.6 - Prob. 2PCh. 4.6 - Prob. 3PCh. 4.6 - Prob. 4PCh. 4.7 - Prob. 1PCh. 4.7 - Prob. 2PCh. 4.7 - Prob. 3PCh. 4.7 - Prob. 4PCh. 4.7 - Prob. 5PCh. 4.7 - Prob. 6PCh. 4.7 - Prob. 7PCh. 4.7 - Prob. 8PCh. 4.7 - Prob. 9PCh. 4.8 - Prob. 1PCh. 4.8 - Prob. 2PCh. 4.8 - Prob. 3PCh. 4.8 - Prob. 4PCh. 4.8 - Prob. 5PCh. 4.8 - Prob. 6PCh. 4.10 - Prob. 1PCh. 4.10 - Prob. 2PCh. 4.10 - Prob. 3PCh. 4.10 - Prob. 4PCh. 4.10 - Prob. 5PCh. 4.11 - Prob. 1PCh. 4.11 - Prob. 2PCh. 4.11 - Prob. 3PCh. 4.11 - Prob. 4PCh. 4.11 - Prob. 5PCh. 4.11 - Prob. 6PCh. 4.12 - Prob. 1PCh. 4.12 - Prob. 2PCh. 4.12 - Prob. 3PCh. 4.12 - Prob. 4PCh. 4.12 - Prob. 5PCh. 4.12 - Prob. 6PCh. 4.13 - Prob. 2PCh. 4.14 - Prob. 1PCh. 4.14 - Prob. 2PCh. 4.14 - Prob. 3PCh. 4.14 - Prob. 4PCh. 4.14 - Prob. 5PCh. 4.14 - Prob. 6PCh. 4.14 - Prob. 7PCh. 4.16 - Prob. 1PCh. 4.16 - Prob. 2PCh. 4.16 - Prob. 3PCh. 4.16 - Prob. 5PCh. 4.16 - Prob. 7PCh. 4.16 - Prob. 8PCh. 4.16 - Prob. 9PCh. 4.16 - Prob. 10PCh. 4.16 - Prob. 11PCh. 4.16 - Prob. 12PCh. 4.16 - Prob. 13PCh. 4.16 - Prob. 14PCh. 4.17 - Prob. 1PCh. 4.17 - Prob. 2PCh. 4.17 - Prob. 3PCh. 4.17 - Prob. 4PCh. 4.17 - Prob. 5PCh. 4.17 - Prob. 7PCh. 4.17 - Prob. 8PCh. 4 - Prob. 1RPCh. 4 - Prob. 2RPCh. 4 - Prob. 3RPCh. 4 - Prob. 4RPCh. 4 - Prob. 5RPCh. 4 - Prob. 6RPCh. 4 - Prob. 7RPCh. 4 - Prob. 8RPCh. 4 - Prob. 9RPCh. 4 - Prob. 10RPCh. 4 - Prob. 12RPCh. 4 - Prob. 13RPCh. 4 - Prob. 14RPCh. 4 - Prob. 16RPCh. 4 - Prob. 17RPCh. 4 - Prob. 18RPCh. 4 - Prob. 19RPCh. 4 - Prob. 20RPCh. 4 - Prob. 21RPCh. 4 - Prob. 22RPCh. 4 - Prob. 23RPCh. 4 - Prob. 24RPCh. 4 - Prob. 26RPCh. 4 - Prob. 27RPCh. 4 - Prob. 28RP
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