# Multi-Objective Optimization of the Organization’s Performance for Sustainable Development

^{*}

## Abstract

**:**

## 1. Introduction

- Evaluating (DEMATEL, ISM, SEM);
- Weighting (analytic hierarchy process);
- Normalization (TOPSIS, SAW, ELECTRE);
- MODM–multi-attribute utility analysis.

- Multi-attribute utility analysis;
- Goal programming;
- Genetic algorithm and neural network.

## 2. Literature Review

## 3. Materials and Methods

#### 3.1. Methods

_{1}, X

_{2}, …, X

_{n}, which generally represents the quantities to be manufactured from n products in a production system (workshop, section, enterprise) in which m resources (raw materials, energy, machinery, human resources) are limited to bi, i = 1, 2, …, m, and the specific consumption is a

_{ij}, a vector function f(X) with components that must be maximized or minimized.

_{ij}—is the consumption of the resource R

_{i}available in the quantity b

_{i}, b

_{i}≥ 0, of product unit P

_{j}, a

_{ij}≥ 0, i = 1, 2, …, m, j = 1, 2, …, n,

- profit, which will be maximized;
- turnover, which will be maximized;
- production costs, which will be minimized;
- the time of non-use of the equipment, which will be minimized;
- labor productivity, which will be maximized;
- working capital, which must be minimized.

_{k}(X), a component of f(X), can have other concrete meanings. In general, an optimal solution to the linear-programming problem with a single objective function f

_{k}(X), of those p of f(X), is not optimal for the other (p − 1) objective functions, since as components of the vector function f(X), they can be conflicting and very unfavorable.

_{k}were determined using the vector of importance coefficients.

_{ij}elements of the matrix B have the properties:

_{ij}= 1/b

_{ij},

b

_{ij}= b

_{ik}/b

_{jk}, i, j, k = 1,2,…, n.

^{T}= mP

^{T}

^{T}is the column vector:

^{T}= 0, where E is the unit matrix. The P

^{T}vector is an eigenvector of matrix B. The P

^{T}values are obtained as follows:

^{T}= λ

_{max}P

^{T},

_{max}is its highest value.

#### 3.2. Materials

## 4. Results

- Turnover, in order to maximize sales volume;
- Delivery costs, in order to minimize the consumption of materials, energy, and fuel;
- Productivity, in order to maximize the added value achieved by employees.

_{max}= 3.135 and the matrix equation BP

^{T}= λ

_{max}P

^{T}results:

- Maximizing turnover

_{1}+ 1320x

_{2}+ 1167x

_{3}+ 1820x

_{4}+ 1097x

_{5}+ 1085x

_{6}+ 1094x

_{7}+ 1030x

_{8}+ 1007x

_{9}+ 1203x

_{10}+ 1119x

_{11}+ 928x

_{12}− 32700000

- 2.
- Minimizing delivery costs, minimizing used resources

_{1}+ 75x

_{2}+ 70x

_{3}+ 65x

_{4}+ 60x

_{5}+ 55x

_{6}+ 50x

_{7}+ 45x

_{8}+ 40x

_{9}+ 35x

_{10}+ 30x

_{11}+ 25x

_{12}− 172961230,

- 3.
- Maximizing productivity

_{1}+ 10924x

_{2}+ 12131x

_{3}+ 11081x

_{4}+ 11625x

_{5}+ 11499x

_{6}+ 11082x

_{7}+ 11127x

_{8}+ 10943x

_{9}+ 13441x

_{10}+ 12180x

_{11}+ 10342x

_{12}− 32700000

_{1}+ 1320000 x

_{2}+ 1167000 x

_{3}+ 1820000 x

_{4}+ 1097000 x

_{5}+ 1085000 x

_{6}+ 1094000 x

_{7}+ 1030000 x

_{8}+ 1007000 x

_{9}+ 1203000 x

_{10}+ 1119000 x

_{11}+ 92800 x

_{12}− 32700000) − 0.612 (80 x

_{1}+ 75 x

_{2}+ 70 x

_{3}+ 65 x

_{4}+ 60 x

_{5}+ 55 x

_{6}+ 50 x

_{7}+ 45 x

_{8}+ 40 x

_{9}+ 35 x

_{10}+ 30 x

_{11}+ 25 x

_{12}− 172961230) + 0.256 (9676 x

_{1}+ 10924 x

_{2}+ 12131 x

_{3}+ 1081 x

_{4}+ 11625 x

_{5}+ 11499 x

_{6}+ 11082 x

_{7}+ 11127 x

_{8}+ 10943 x

_{9}+ 13441 x

_{10}+ 12180 x

_{11}+ 10342 x

_{12}− 32700000),

_{1}+ 176990.6x

_{2}+ 157106.7x

_{3}+ 243037.9x

_{4}+ 147743.3x

_{5}+ 146130.1x

_{6}+ 147214.4x

_{7}+ 138780.9x

_{8}+ 135700.9x

_{9}+ 138455.58x

_{10}+ 150807.7x

_{11}+ 125128.3x

_{12}+ 107561230,

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**The optimization results obtained for each objective function by linear programming and by multi-objective linear programming.

Method | Advantages | Disadvantages/Limits | Main Areas of Application |
---|---|---|---|

Analytic Hierarchy Process (AHP) | Easy to use; scalable; hierarchy structure can easily adjust to fit many sized problems; possibility of integration with other methods; not data intensive. | Problems due to interdependence between criteria and alternatives; can lead to inconsistencies between judgment and ranking criteria. | Performance-type problems, resource management, political strategy, and planning. |

Technique for Order Preferences by Similarity to Ideal Solutions (TOPSIS) | Has a simple process; easy to use and program; the number of steps remains the same regardless of the number of attributes. | Difficult to weight and keep consistency of judgment. | Supply chain management and logistics, engineering, manufacturing systems, business, marketing, and environment. |

Linear Programming (LP) | Capable of handling large-scale problems; can produce infinite alternatives. | Needs to be used in combination with other MCDM methods to weight coefficients. | Production planning, scheduling, distribution systems, energy planning, scheduling, and wildlife management. |

PROMETHEE | Easy to use; possibility of taking into account both quantitative and qualitative criteria; does not require assumption that criteria are proportionate; possibility of integration with other methods. | Does not provide a clear method by which to assign weights; need to weigh decision factors using other methods. | Environmental, hydrology, water management, business and finance, chemistry, logistics, transportation, and manufacturing. |

Author | MCDM/MCDA Methods Used | Main Subject of the Research |
---|---|---|

Behzadian, M. et al. [5] | TOPSIS | A state-of-the-art literature survey to taxonomize the research on TOPSIS applications and methodologies. |

Broniewicz, E.; Ogrodnik, K. A. [6] | DEMATEL, REMBRANDT, and VIKOR | The utilization of the application potential of MCDM/MCDA methods in decision-making problems in the field of transport, in light of sustainable development. |

Halffmann, P. et al. [11] | Multi-objective mixed-integer and integer linear | State-of-the-art multiobjective mixed-integer programming. |

Li, C.-M. et al. [12] | Linear programming | Optimal decision model for diversified industrial management (optimal scales of coal, electric power, chemical, and equipment manufacturing). |

Gupta, S. et al. [13] | Fuzzy goal programming | A fuzzy goal programming model to study the sustainable development goals of GDP growth, electricity consumption, and GHG emission across different economic sectors of India by the year 2030. |

Zhao, X. et al. [15] | Mixed-integer non-linear programming | Model for the green lock-scheduling problem at the Three Gorges Dam (minimizing the carbon emissions and the waiting time in the lockage process). |

Zhou, W. et al. [16] | Mixed-integer linear programming | Multi-periodic train timetabling and routing, by optimizing the routes of trains at stations and their entering time and leaving time on each chosen arrival–departure track at each visited station. |

Sarwar, S. et al. [17] | Mixed-integer linear programming | Providing an efficient load-shedding technique for an islanded distribution system. |

Al-Quradaghi, S. et al. [18] | Mixed-integer programming | Optimizing the exchange of material flows in the network (maximize reusable/recyclable material output, while minimizing network costs) |

Fechete, F.; Nedelcu, A. | AHP and multi-objective linear programming | Optimization model that integrates three major objectives of organizational performance: maximizing sales, minimizing expenses, and maximizing productivity, all combined for the sustainable development of the organization. |

Intensity of Importance $({\mathit{w}}_{\mathit{i}}$$/{\mathit{w}}_{\mathit{j}})$ | Definition | Explanation |
---|---|---|

1 | Equal importance | The two criteria contribute equally to the goal. |

3 | Weak importance | Experience shows the slight importance of one criterion over another. |

5 | Strong importance | Experience demonstrates the stronger importance of one criterion over another. |

7 | Demonstrated importance | Practice has proven the importance of one criterion over another. |

9 | Absolute importance | Obviously one criterion is more important than another. |

2, 4, 6, 8 | Importance of intermediate values | Used when a compromise is needed. |

Month | Sales Volume Achieved [T-Ron] | Customer Orders [pcs] | Production Capacity [pcs] |
---|---|---|---|

January | 1438 | 2,548,556 | 2,700,000 |

February | 1309 | 2,550,855 | 2,500,000 |

March | 1157 | 2,735,389 | 2,700,000 |

April | 1811 | 2,503,787 | 2,800,000 |

May | 1089 | 2,750,643 | 2,800,000 |

June | 1078 | 2,624,632 | 2,700,000 |

July | 1088 | 2,682,187 | 2,800,000 |

August | 1025 | 2,563,748 | 3,000,000 |

September | 1003 | 2,451,276 | 2,800,000 |

October | 1200 | 2,992,994 | 3,000,000 |

November | 1117 | 2,761,731 | 2,800,000 |

December | 927 | 2,258,991 | 2,100,000 |

Orders Delivered per Month (Pieces/Month) | |
---|---|

X_{1} | 2,548,556 |

X_{2} | 2,550,855 |

X_{3} | 2,735,389 |

X_{4} | 2,865,200 |

X_{5} | 2,750,643 |

X_{6} | 2,624,632 |

X_{7} | 2,682,187 |

X_{8} | 2,563,748 |

X_{9} | 2,451,276 |

X_{10} | 3,906,792 |

X_{11} | 2,761,731 |

X_{12} | 2,258,991 |

Month | Customer Orders [pcs] | Production Capacity [pcs] | Total Cost/min (RON/min) |
---|---|---|---|

January | 2,548,556 | 2,700,000 | 25 |

February | 2,550,855 | 2,500,000 | 25 |

March | 2,735,389 | 2,700,000 | 25 |

April | 2,503,787 | 2,800,000 | 25 |

May | 2,750,643 | 2,800,000 | 25 |

June | 2,624,632 | 2,700,000 | 25 |

July | 2,682,187 | 2,800,000 | 25 |

August | 2,563,748 | 3,000,000 | 25 |

September | 2,451,276 | 2,800,000 | 25 |

October | 2,992,994 | 3,000,000 | 25 |

November | 2,761,731 | 2,800,000 | 25 |

December | 2,258,991 | 2,100,000 | 25 |

Orders Delivered per Month (Pieces/Month) | |
---|---|

X_{1} | 2,634,800 |

X_{2} | 2,500,000 |

X_{3} | 2,700,000 |

X_{4} | 2,503,790 |

X_{5} | 2,750,640 |

X_{6} | 2,624,630 |

X_{7} | 2,682,190 |

X_{8} | 2,563,750 |

X_{9} | 2,564,990 |

X_{10} | 3,000,000 |

X_{11} | 2,800,000 |

X_{12} | 2,100,000 |

Month | Productivity [Pieces/Worker] | Customer Orders [pcs] | Production Capacity [Pieces] |
---|---|---|---|

January | 9664 | 2,548,556 | 2,700,000 |

February | 10,913 | 2,550,855 | 2,500,000 |

March | 12,121 | 2,735,389 | 2,700,000 |

April | 11,072 | 2,503,787 | 2,800,000 |

May | 11,617 | 2,750,643 | 2,800,000 |

June | 11,492 | 2,624,632 | 2,700,000 |

July | 11,706 | 2,682,187 | 2,800,000 |

August | 11,122 | 2,563,748 | 3,000,000 |

September | 10,939 | 2,451,276 | 2,800,000 |

October | 13,438 | 2,992,994 | 3,000,000 |

November | 12,178 | 2,761,731 | 2,800,000 |

December | 10,341 | 2,258,991 | 2,100,000 |

Orders Delivered per Month (Pieces/Month) | |
---|---|

X_{1} | 2,548,556 |

X_{2} | 2,550,855 |

X_{3} | 2,735,389 |

X_{4} | 2,503,787 |

X_{5} | 2,750,643 |

X_{6} | 2,624,632 |

X_{7} | 2,682,187 |

X_{8} | 2,563,748 |

X_{9} | 2,451,276 |

X_{10} | 4,268,205 |

X_{11} | 2,761,731 |

X_{12} | 2,258,991 |

Variable | Orders Delivered per Month (Pieces/Month) |
---|---|

X_{1} | 2,700,000 |

X_{2} | 2,500,000 |

X_{3} | 2,634,800 |

X_{4} | 2,865,200 |

X_{5} | 2,389,230 |

X_{6} | 3,110,770 |

X_{7} | 2,800,000 |

X_{8} | 3,000,000 |

X_{9} | 1,411,070 |

X_{10} | 2,993,000 |

X_{11} | 4,195,930 |

X_{12} | 2,100,000 |

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**MDPI and ACS Style**

Fechete, F.; Nedelcu, A.
Multi-Objective Optimization of the Organization’s Performance for Sustainable Development. *Sustainability* **2022**, *14*, 9179.
https://doi.org/10.3390/su14159179

**AMA Style**

Fechete F, Nedelcu A.
Multi-Objective Optimization of the Organization’s Performance for Sustainable Development. *Sustainability*. 2022; 14(15):9179.
https://doi.org/10.3390/su14159179

**Chicago/Turabian Style**

Fechete, Flavia, and Anișor Nedelcu.
2022. "Multi-Objective Optimization of the Organization’s Performance for Sustainable Development" *Sustainability* 14, no. 15: 9179.
https://doi.org/10.3390/su14159179