Multi-agent supply chain scheduling problem by considering resource allocation and transportation

https://doi.org/10.1016/j.cie.2019.106003Get rights and content

Highlights

  • The problem of supply chain scheduling for two types of agents is studied.

  • Two mathematical programming models are proposed.

  • An Adaptive Genetic Algorithm (AGA), Ant Lion Optimization (ALO) and a heuristic algorithm are proposed.

  • The results indicate that AGA performs better than the other algorithms.

Abstract

Today in the global market competition, integration issue in supply chain is considered as an important principle. In this study, for the first time, different requirements of the customers and different aims of the manufacturer are simultaneously addressed in an integrated problem of production scheduling, transportation, and resource allocation. The problem consists of two types of customers, considered as the agents. The first agent accepts tardiness in delivery of orders provided that the manufacturer pays the tardiness penalty; whereas, the second agent does not accept the tardy orders. The purpose is to minimize the sum of batch delivery cost, resource allocation, tardiness penalty cost, and lost sale cost (the total number of tardy orders). To solve the problem, two mathematical programming models, including a Mixed Integer Non-Linear Programming (MINLP) and a Mixed Integer Linear Programming (MILP) are proposed. Also, due to NP-hard nature of the problem, two meta-heuristic algorithms of Adaptive Genetic Algorithm (AGA) and Ant Lion Optimization (ALO), as well as a heuristic algorithm are proposed. To assess the merits of the solution methods, small and large-scale tests are designed. The results indicate the superiority of adaptive genetic algorithm in comparison with other algorithms.

Introduction

In a production system, many decisions in operational level must be made in a simultaneous manner, such as acceptance of orders, supply of resource planning, outsourcing, transportation planning, and delivery scheduling. Integrating different decisions is an important issue, since it can lead to significant reduction in total cost of supply chain scheduling (Rasti-Barzoki, Hejazi, & Mazdeh, 2013).

Production scheduling is one of the important issues of a supply chain. In classical production scheduling problems, decisions on job scheduling and machine assignment are made with different assumptions in processing and delivery times. Resource allocation is the problem of allocating limited resources based on different sets of constraints. Delivery scheduling is considered as the problem of transportation and logistics planning. Selection of the transportation system and vehicles, finding appropriate routes, and assigning products to the vehicles are some essential issues associated to the delivery scheduling.

When a set of orders are available, it is possible that a subset of orders follows a specific index and another subset follows an index different from the first one. The decision maker should design scheduling in a way that all types of orders would obtain their best amount of index. This type of decision making is called “multi-agent scheduling” (Yin, 2016).

Coordination of production and transportation plans can result in saving energy and reducing fuel consumption (Barzoki & Hejazi, 2017). In the problem introduced in this paper, important factors of the supply chain, including batch delivery cost, tardiness penalty cost, total number of tardy orders, and resource allocation, are considered. Each one of these factors plays a key role in optimizing the production system. Consideration of all these factors together can lead to an efficient scheduling plan and substantially reduce the supply chain costs (Sarkar & Giri, 2018).

In supply chains, the behaviors of different customers are not necessarily the same. A group of customers are sensitive to delay of delivering their orders; so, manufacturers tend to minimize sum of weighted tardiness in the supply chain scheduling problem (Akturk & Ilhan, 2011). On the other hand, the purpose of minimizing number of tardy orders is a widely used objective function, since there exists another group of customers that do not accept tardy orders at all. The rejection of tardy orders leads to lost sales and loss of customer goodwill (Gonçalves, Valente, & Schaller, 2016). In case the customers of a manufacturer consist of both groups, the application of a production system that simultaneously considers the above-mentioned factors is crucial.

Section snippets

Literature review

According to our literature review, the objective functions of the related problems can be divided into five categories: total weight of tardiness, total number of tardy orders, resource allocation cost, distribution cost and multi-agent functions. In the following, some of the studies associated to these categories are addressed.

Problem description

The most important signs applied in this study are introduced as follows:

Index:
bb=1,2,,N (Index of batches)
jj=1,2,,N (Index of orders)
kk=1,2 (Index of agent type or customer)
ii = 1,…,nk (Index of orders of agentk)
JikIndex of order i belonging to agentk
Sets:
ΩΩ=J11,J21,,Jn11,J12,J22,,Jn22,jΩ (The set of orders)
Ω1Ω1=j11,j21,,jn11 (The set of first-type customer's orders)
Ω2Ω2=j12,,jn22 (The set of second-type customer's orders)
Parameters
djDue date of jth order
θDelivery cost of each batch
e

Mixed integer non-linear programming

The definition of Mixed Integer Non-Linear Programming model for the problem is as follows:Minimizθb=1NYb+ejΩfj+jΩ2αjUj+jΩ1WjTjb=1NXjb=1jΩ1b=1NXjb=1-UjjΩ2jΩXjbNYbb=1,2,3,NTjXjbCb-djjΩ1,b=1,2,3,NCb=Cb-1+jΩXjbpjb=2,3,4,NC1=jΩXjbpjb=1XjbCb-djMUjjΩ2,b=1,2,3,Npj=pjn-LjfjjΩfjfjujΩpjlpjjΩXjb,Yb,Uj0.1pj,Cb,Tj0fj0integer

The objective function considered in relation (2) is to minimize batch delivery, additional resource allocation, the total penalty resulting from

The proposed inexact solution approaches

As demonstrated in Section 3, the problem focused in this research is NP-hard. For such problems, it is known that the exact solution methods are incapable to achieve the optimal solutions of the large-scale samples (Tamannaei and Irandoost, 2019, Tamannaei and Rasti-Barzoki, 2019, Falsafain and Tamannaei, 2019). Thus, we have proposed one heuristic and two meta-heuristic algorithms to find the appropriate solutions for the large-scale samples in reasonable performance times. Based on solution

Parameters setting

In this study, the complete design of experiments is applied by means of Minitab 2016 environment. The orthogonal array defined for parameters in each one of both proposed meta-heuristics is L9 provided that each parameter contains three levels. The developed AGA consists of two parameters, each of which includes three levels: the initial population and the termination condition. In this method, the initial population and the number of generation are considered the same. To adjust the

Computational results

In this section, the performance of the MIP mathematical model, the heuristic algorithm (HU), and the two developed AGA and ALO meta-heuristic algorithms are evaluated. Heuristic and meta-heuristic methods are implemented in MATLAB 2010 environment, and the proposed mathematical model is coded in GAMS 24.1 environment, and solved in CPLEX solver. To do this, we used a PC with Intel(R) Pentium(R) CPU G840 @ 2.8 GHz, RAM 4 GB, Window 7 (64-bit) specifications.

Statistical analysis

In this section, the statistical results are presented to support the results shown in the previous section.

Conclusion

In this study, we focus on supply chain scheduling problem, aimed to minimize the sum of resource allocation, transportation cost, tardiness penalty cost, and lost sale cost. The problem includes two types of agents as the customers. The first type accepts tardiness in delivery of orders; whereas the second type does not accept the tardy orders. To tackle the problem, two mathematical programming models, including a Mixed Integer Non-Linear Programming (MINLP) and a Mixed Integer Linear

References (47)

  • W.-C. Lee et al.

    Branch-and-bound and simulated annealing algorithms for a two-agent scheduling problem

    Expert Systems with Applications

    (2010)
  • S.-W. Lin et al.

    Order acceptance and scheduling to maximize total net revenue in permutation flowshops with weighted tardiness

    Applied Soft Computing

    (2015)
  • Q. Liu

    Novel multi-objective resource allocation and activity scheduling for fourth party logistics

    Computers & Operations Research

    (2014)
  • R. M’Hallah et al.

    Minimizing the weighted number of tardy jobs on a single machine

    European Journal of Operational Research

    (2003)
  • R. M’Hallah et al.

    Minimizing the weighted number of tardy jobs on a single machine with release dates

    European Journal of Operational Research

    (2007)
  • S. Mirjalili

    The ant lion optimizer

    Advances in Engineering Software

    (2015)
  • S. Polyakovskiy et al.

    A multi-agent system for the weighted earliness tardiness parallel machine problem

    Computers & Operations Research

    (2014)
  • M. Rasti-Barzoki et al.

    Minimizing the weighted number of tardy jobs with due date assignment and capacity-constrained deliveries for multiple customers in supply chains

    European Journal of Operational Research

    (2013)
  • M. Rasti-Barzoki et al.

    Pseudo-polynomial dynamic programming for an integrated due date assignment, resource allocation, production, and distribution scheduling model in supply chain scheduling

    Applied Mathematical Modelling

    (2015)
  • M. Rasti-Barzoki et al.

    A branch and bound algorithm to minimize the total weighed number of tardy jobs and delivery costs

    Applied Mathematical Modelling

    (2013)
  • D. Shabtay

    Optimal due date assignment and resource allocation in a group technology scheduling environment

    Computers & Operations Research

    (2010)
  • D. Shabtay et al.

    A bicriteria approach to maximize the weighted number of just-in-time jobs and to minimize the total resource consumption cost in a two-machine flow-shop scheduling system

    International Journal of Production Economics

    (2012)
  • T. Soares

    Cost allocation model for distribution networks considering high penetration of distributed energy resources

    Electric Power Systems Research

    (2015)
  • Cited by (0)

    View full text