Multi-agent supply chain scheduling problem by considering resource allocation and transportation
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: (Index of batches) (Index of orders) (Index of agent type or customer) = 1,…, (Index of orders of agent) Index of order belonging to agent Sets: (The set of orders) (The set of first-type customer's orders) (The set of second-type customer's orders) Parameters Due date of order Delivery cost of each batch
Mixed integer non-linear programming
The definition of Mixed Integer Non-Linear Programming model for the problem is as follows:
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
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