Annals of Operations Research

, Volume 264, Issue 1–2, pp 409–433

# Dispatching algorithm for production programming of flexible job-shop systems in the smart factory industry

• Miguel A. Ortíz
• Leidy E. Betancourt
• Kevin Parra Negrete
• Fabio De Felice
• Antonella Petrillo
Original Paper

## Abstract

In today highly competitive and globalized markets, an efficient use of production resources is necessary for manufacturing enterprises. In this research, the problem of scheduling and sequencing of manufacturing system is presented. A flexible job shop problem sequencing problem is analyzed in detail. After formulating this problem mathematically, a new model is proposed. This problem is not only theoretically interesting, but also practically relevant. An illustrative example is also conducted to demonstrate the applicability of the proposed model.

## Keywords

Sequencing problem Flexible job-shop system Reconfigurable system Optimization

## Nomenclature

n

Number of pieces

m

Number of machines

G(i)

Number of operations of the piece i (i = 1...n)

H(j)

Number of operations in the tail of the machine j (j = 1 ...m).

fj

Instant the machine j is available for a new operation

pk,i,j

Processing time of operation k of the item i in the machine j

rk,i

Instant availability of operation (k, i)

Rpk,i,j

(release date o ready date) Early instant to start the operation (k, i) on the machine j: $$\hbox {rpk,i,j }= \hbox {max }\{\hbox { rk,i, fj for all (k,i) }\upepsilon \hbox { Ej}$$

fpj

Early instant to start a new operation on the machine j (if no queue, infinite value is assigned):

$$\hbox {fpj} = \hbox {min(k,i)}\upepsilon \hbox { Ej }\{\hbox { rpk,i,j }\}$$ if Ej is not empty

$$\hbox {fpj} = \infty$$ if Ej is empty

$$\hbox {t}_{\mathrm{start}}$$ (k, i)

Manufacturing start time scheduled operation

[$$\hbox {t}_{\mathrm{start}}$$] $$\hbox {(k, i)} = \hbox {rpk,i, j}$$

$$\hbox {t}_{\mathrm{end}}$$ (k, i)

Manufacturing final instant programmed operation

[$$\hbox {t}_{\mathrm{end}}$$] $$\hbox {(k, i)} = \hbox {tstart (k, i)} +\hbox { D }\cdot \hbox { pk,i,j}$$

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## Authors and Affiliations

• Miguel A. Ortíz
• 1
• Leidy E. Betancourt
• 1
• Kevin Parra Negrete
• 1
• Fabio De Felice
• 2
• Antonella Petrillo
• 3
1. 1.Department of Industrial EngineeringUniversidad de la Costa CUCBarranquillaColombia
2. 2.Department of Civil and Mechanical EngineeringUniversity of Cassino and Southern LazioCassinoItaly
3. 3.Department of EngineeringUniversity of Naples “Parthenope”NaplesItaly