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A Pareto approach for the multi-factory supply chain scheduling and distribution problem

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Abstract

Integrated decisions in the supply chain are one of the most attractive topics for researchers. But to get closer to the real-world problems, other real assumptions should be considered. One of these assumptions is the multi-agent view in which several sets of customers or agents with their own objective compete with each other to acquire the supply chain resources. Here, an integrated supply chain scheduling problem along with the batch delivery consideration in a series multi-factory environment is investigated and the routing decisions among customers are considered. A mathematical model is presented for this problem. Due to the complexity, a novel ant colony optimization algorithm is developed to obtain Pareto solutions. Also, a simulated annealing based local search is used to improve the quality of solutions. The performance of the algorithm is compared with three well-known multi-objective algorithms. Results show the proper performance of the proposed algorithm compared to the other algorithms.

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Abbreviations

J :

Set of jobs or customers (\(i, j \in J\))

F :

Set of factories (\(f \in F\))

K :

Set of vehicles (\(\in K\))

G :

Set of agents (\(agent1,agent2 \in G\))

n :

Number of customers (jobs)

|F|:

Number of factories

M :

A positive big number

\(p_i^f\) :

Processing time of job i in factory f

\(d_i\) :

Due date of job i

\(q_i\) :

Size of job i

\(t_{ij}\) :

Transportation time between customer i and j

\(t_{i}^F\) :

Transportation time between customer i and the last factory

\(t^f\) :

Transportation time between factories f and \(f+\) 1

\(r_{ij}\) :

Distance between customer i and j

\(r_{i}^F\) :

Distance between customer i and the last factory

\(r^f\) :

Distance between factories f and \(f+\) 1

FCI :

Fixed inbound transportation cost

FCO :

Fixed outbound transportation cost

Q :

Capacity of each vehicle

\(X_{ij}\) :

is 1 if partial sequence (i, j) exists in the optimal solution, otherwise 0

\(Y_{j}^{kf}\) :

is 1 if job j is allocated to vehicle k in factory f, otherwise 0

\(B^{kf}\) :

is 1 if at least one job exists in vehicle k of factory f, otherwise 0

\(Z_{ij}^{k}\) :

is 1 if partial delivery (i, j) is delivered by vehicle k in the last factory, otherwise 0

\(C_j^f\) :

Processing completion time of job j in factory f

\(CB^{kf}\) :

Processing completion time of total assigned jobs of vehicle k of factory f

\(Ar^{kf}\) :

Arrival time of the batch k in factory f

\(A_j\) :

Delivery time of job j

\(T_j\) :

Tardiness of job j

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Authors and Affiliations

  1. School of Industrial Engineering, College of Engineering, University of Tehran, Alborz Campus, Tehran, Iran

    Ali Gharaei

  2. School of Industrial Engineering, College of Engineering, University of Tehran, P.O. Box: 11155/4563, Tehran, Iran

    Fariborz Jolai

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  1. Ali Gharaei
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Gharaei, A., Jolai, F. A Pareto approach for the multi-factory supply chain scheduling and distribution problem. Oper Res Int J 21, 2333–2364 (2021). https://doi.org/10.1007/s12351-019-00536-7

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