Mathematical Optimization Models
Fatemeh Nikkhoo; Ali Hosseinzadeh Kashan; Bakhtiar Ostadi; Ehsan Nikbakhsh
Abstract
Purpose: The order-picking problem is important as one of the warehouse's logistics activities. This problem is defined as collecting orders from different warehouse locations to respond to customers' orders quickly. This paper aims to provide a multi-objective mathematical programming model for integrating ...
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Purpose: The order-picking problem is important as one of the warehouse's logistics activities. This problem is defined as collecting orders from different warehouse locations to respond to customers' orders quickly. This paper aims to provide a multi-objective mathematical programming model for integrating the decisions of batching, routing, and scheduling of selectors with the packaging problem in a multi-warehouse environment. The objective functions include depreciation of the delivery times and total order picking costs.Methodology: In this research, first, by reviewing the literature in the field of order picking, the research gaps of the problem have been identified. Then, taking into account the main constraints of the problem, a multi-objective mathematical model has been formulated for the multi-warehouse order-picking problem. The classic Benders decomposition algorithm and the accelerated Benders decomposition algorithm have been used to solve the problem. The data related to the warehouses of a company producing sanitary products in Iran was used as a case study to validate the applicability of the proposed model, and its results were reported in the article.Findings: The proposed model's results indicate that CPLEX can solve these problems up to small sizes in an acceptable time. Also, the numerical results show the performance of the Benders decomposition algorithm and the accelerated Benders algorithm as suitable alternatives for solving the model in large-sized problems. The calculation results obtained from the implementation of the solution methods for the proposed model showed that in terms of the number of iterations and the calculation time, the accelerated Benders algorithm had better results than the classic Benders algorithm.Originality/Value: In this research, the order-picking problem with the integrity of operational decisions has been formulated as a multi-objective mathematical model for a multi-warehouse environment for the first time. Also, in this article regarding the solution method, exact solution approaches have been used for the first time considering the structure of the problem. The computation results show that the proposed algorithms are efficient and suitable methods for problem-solving.
Scheduling Modeling
Morteza Farhadi Sartangi; Ali Husseinzadeh Kashan; Hassan Haleh; Abolfazl Kazemi
Abstract
Purpose: Order picking operation is one of the most well-known labor and cost intensive internal logistics processes. Withdrawal of the order in response to customer need is defined in order to collect a set of orders from storage zone in the shortest possible time. The purpose of this research is to ...
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Purpose: Order picking operation is one of the most well-known labor and cost intensive internal logistics processes. Withdrawal of the order in response to customer need is defined in order to collect a set of orders from storage zone in the shortest possible time. The purpose of this research is to provide a scientific and practical basis considering the constraints that enforce to achieve an acceptable level of performance in order picking systems. This is done by building a Mixed Integer Linear Programming (MILP) formulation and developing an adapted solution method suited to the structure of the problemMethodology: First, by reviewing the literature in the field of order picking systems, sufficient knowledge has been obtained at the operational level, and with emphasis on warehouse management constraints, a MILP formulation is proposed by integrating order batching and picker routing. After validating the model and solving it through GAMS software, due to the nature of the problem, which is an NP-hard type, the problem is solved with an efficient algorithm, which is a grouping version of the league championship algorithm, and the results are compared. To develop the algorithm, operators are fit to the specific structure of the problem, i.e., the assignment of orders (items) to order pickers (groups)Findings: Developing a multi-period MILP formulation for multi-trip picker routing, assuming for the first time the possibility of product replenishment and limited access to pickers. For large-scale problem instances, the league championship algorithm is used. The results indicate the effective capability and efficiency of this algorithm for solving large test problem instances.Originality/Value: The issue of multi-period order picking and multi-trip routing of pickers is considered for the first time in this paper. Because of the limited number of pickers, this must be taken into account in modeling. The assumption of product replenishment is also considered for the first time in this article and its modeling has been done. In this way, orders enter the warehouse over time, during different periods, and are placed in a predetermined positions. The limited access to pickers in each period is also discussed for the first time in this paper. Finally, the objective function of minimizing the total tardiness, which is in line with the needs of the industry, is also introduced in this paper. Regarding the solution method, a league championship metaheuristic algorithm is presented which takes into account the problem structure (which corresponds to the structure of grouping problems) and solution generation operators have been developed to maintain the new solution.