"Minimization of the picking time of a warehouse in the Batch Assignment and Sequencing problem with a simulation model"
Liany Tobon-Castro and Daniel Mendoza-Caseres

This paper addresses the Batch Assignment and Sequencing problem considering multiple pickers and due dates of the orders that must be delivered in a warehouse. Order-picking systems in warehouses have been widely studied in the literature given their importance of making them more efficient due to the high costs and consumption of resources. In the process the orders are grouped in batches to be assigned and sequenced by the pickers equipped with a roll cage that will make tours through the warehouse where they must make stops in each of the storage locations of the items found in the batch they are recovering. 

This research seeks to minimize the tardiness of the order picking process. The batches are organized considering the due dates of the orders to avoid incurring delays and cost overruns. The problem represents how and in what sequence the batches should be assigned to the available pickers to improve warehouse performance. 
Batch Assignment and Sequencing problems are NP-hard, due to the fact that no exact algorithms are found that allow solving them for large instances in acceptable computational times. This has led different authors to treat the problem through the use of different metaheuristics such as Genetic Algorithms (GA), Variable Neighborhood Search, Ant Colony Optimization (ACO), Seed Algorithm, Taboo Search, among others. 

The literature consulted does not evidence studies that provide a solution to the Batch Assignment and Sequencing problem through the use of Simulation Optimization techniques. The simulation has been a method of solution used ultimately. However, with the development of new technologies and the arrival of computers with more powerful hardware and specialized simulation software, they have made it possible to obtain solutions for large instances of NP-hard problems by providing shorter computational times for investigations. 
This work, in progress, considers Batch Assignment and Sequencing problem to minimize the total tardiness of the order picking process considering due dates of the orders. Each batch is assigned in a single sequencing position that the pickers have, to then perform the corresponding routing. It is assumed that the batches have been previously processed by grouping orders whose sum of the number of items does not exceed the capacity of the picking device with which the pickers have to carry out their tours. 

In the use of the metaheuristic, each batch must be assigned to a single picker and have only one sequencing position. The pickers do not have a limit number of positions so they can do the collection of any number of batches existing in the warehouse following the established order. Subsequently, the picker proceeds to make the corresponding tour leaving the depot and return-ing when he has visited all the storage positions of the items contained in the batches. Therefore, it is understood that the processing time of the orders corresponds to the time elapsed since they are grouped until the picker returns to the depot with the batch in which they are assigned. In this way the tardiness of each order is the positive difference between the moment of the processing of the batch containing the order ended and its due date. 

The warehouse that considers this research consists of a manual order picking system including two blocks, five selection aisles, three cross aisles and a depot where once the batches have been obtained and made their assignment and sequencing, the pickers are prepared to perform the tours for the batches that they will recover. 
To minimize the picking time, in conjunction with the Flexsim 2019 simulation software, two metaheuristics are being used: A Seed Algorithm for the initial solution of the problem and a Var-iable Neighborhood Search to improve the initial solution. It was found that with the use of Simu-lation Optimization it is possible to reduce the picking time between 10 and 20 percent when due dates are loose. However, in order to simulate a more realistic order-picking system, it is necessary to evaluate larger instances with more tight due dates as they are normally in the different ware-houses. It is for this reason that this research is ongoing in order to achieve better solutions for the problem posed. 
When addressing the problem of the way described above, a methodology is applied that al-lows dealing with more real instances considering stochastic aspects through the use of a simulation model. In this sense, with the implementation of simulation techniques it is possible to ob-serve measures of system performance such as the percentage of resource utilization, service level, process response time and other variables that cannot be easily observed when only metaheuristics are used to find a solution.