Approximation for Batching via Priorities

We consider here the one-machine serial batching problem under weighted average completion. This problem is known to be $cal Ncal P$-hard and no good approximation algorithms are known. Batching has wide application in manufacturing, decision management, and scheduling in information technology. We give an approximation algorithm with approximation ratio of $2$; the algorithm is a priority algorithm, which batches jobs in decreasing order of priority. We also give a lower bound of $frac{2 +sqrt{6}}{4} approx 1.1124$ on the approximation ratio of any priority algorithm and conjecture that there is a priority algorithm which matches this bound. Adaptive algorithm experiments are used to support the conjecture. An easier problem is the list version of the problem where the order of the jobs is given. We give a new linear time algorithm for the list batching problem

Order batching in multi-server pick-and-sort warehouses.

In many warehouses, customer orders are batched to profit from a reduction in the order picking effort. This reduction has to be offset against an increase in sorting effort. This paper studies the impact of the order batching policy on average customer order throughput time, in warehouses where the picking and sorting functions are executed separately by either a single operator or multiple parallel operators. We present a throughput time estimation model based on Whitt's queuing network approach, assuming that the number of order lines per customer order follows a discrete probability distribution and that the warehouse uses a random storage strategy. We show that the model is adequate in approximating the optimal pick batch size, minimizing average customer order throughput time. Next, we use the model to explore the different factors influencing optimal batch size, the optimal allocation of workers to picking and sorting, and the impact of different order picking strategies such as sort-while-pick (SWP) versus pick-and-sort (PAS)Order batching; Order picking and sorting; Queueing; Warehousing;

Product Return Handling

In this article we focus on product return handling and warehousingissues. In some businesses return rates can be well over 20% andreturns can be especially costly when not handled properly. In spiteof this, many managers have handled returns extemporarily. The factthat quantitative methods barely exist to support return handlingdecisions adds to this. In this article we bridge those issues by 1)going over the key decisions related with return handling; 2)identifying quantitative models to support those decisions.Furthermore, we provide insights on directions for future research.reverse logistics;decision-making;quantitative models;retailing and warehousing

Batching Problems with Constraints

There is an increasing demand for a phenomenon that can manifest benefits gained from grouping similar jobs together and then scheduling these groups efficiently. Batching is the decision of whether or not to put the jobs into same group based on certain criteria. Batching plays a major role in job scheduling in Information Technology, traffic controlling systems, and goods-flow management. A list batching problem refers to batching a list of jobs in the same order or priority as given in the problem. In this thesis we consider a one-machine list batching problem under weighted average completion. Given sequence of jobs are scheduled on single machine into distinct batches. Constraint is to batch these jobs into a fixed but arbitrary number ‘k’ of batches. Each batch can have any number of jobs (within the given list) grouped without changing the order of jobs. We call it a k-Batch problem. This is offline form of the batching problems, and is solved by reducing to a shortest path problem. We give an improved and faster version of the algorithm to solve k-Batch problem in O(n2) time

Heuristics for batching jobs under weighted average completion time

Batching problems are machine scheduling problems, where a set of jobs with given processing requirements has to be scheduled on a single machine. The set of jobs has to be partitioned into subsets to form a sequence of batches. A batch combines jobs to run jointly, and each job\u27s completion time is defined to be the completion time of the entire batch. For a batching problem, it is also assumed that when each batch is scheduled, it requires a setup time. One seeks to find a schedule that minimizes the total weighted completion time; This problem is NP-complete, but the problem can be solved efficiently in O(n log (n)) time if the order of the jobs is given. This is accomplished through a non-trivial reduction to on-line matrix searching in a totally monotone array. An implementation of this algorithm is part of the thesis work; To remove the requirement of a fixed order and thus to solve the original NP-complete batching problem, the space of permutations is searched using a genetic algorithm technique. The implementation uses a library of object-oriented functions, GAlib, to implement genetic algorithms. This highly versatile library was written by Mathew Wall of MIT; The thesis also seeks to find techniques to obtain an upper bound, which can be used to measure the quality of the solutions found by the heuristic

Design and Control of Warehouse Order Picking: a literature review

Order picking has long been identified as the most labour-intensive and costly activity for almost every warehouse; the cost of order picking is estimated to be as much as 55% of the total warehouse operating expense. Any underperformance in order picking can lead to unsatisfactory service and high operational cost for its warehouse, and consequently for the whole supply chain. In order to operate efficiently, the orderpicking process needs to be robustly designed and optimally controlled. This paper gives a literature overview on typical decision problems in design and control of manual order-picking processes. We focus on optimal (internal) layout design, storage assignment methods, routing methods, order batching and zoning. The research in this area has grown rapidly recently. Still, combinations of the above areas have hardly been explored. Order-picking system developments in practice lead to promising new research directions.Order picking;Logistics;Warehouse Management