Approximation of the k-batch consolidation problem
نویسندگان
چکیده
We consider a problem of minimizing the number of batches of a fixed capacity processing the orders of various sizes on a finite set of items. This batch consolidation problem is motivated by the production system typical in raw material industries in which multiple items can be processed in the same batch if they share sufficiently close production parameters. If the number of items processed in a batch is restricted to being up to some fixed integer k, the problem is referred to as the k-batch consolidation problem. We will show that the k-batch consolidation problem admits an approximation whose factor is twice that of the k-set cover problem. In particular, this implies an upper bound on the approximation factor, 2Hk − 1, where Hk = 1+ 1 2 + · · · + 1 k . © 2008 Elsevier B.V. All rights reserved.
منابع مشابه
Approximation of k-batch consolidation problem
We consider a problem of minimizing the number of batches of a fixed capacity processing the orders of various sizes on a finite set of items. This batch consolidation problem is motivated by the production system typical in raw material industries in which multiple items can be processed in the same batch in case they share sufficiently close production parameters. If the number of items proce...
متن کاملApproximation of a batch consolidation problem
In batch production systems, multiple items can be processed in the same batch if they share sufficiently similar production parameters. We consider the batch consolidation problem of minimizing the number of batches of a finite set of items. This article focuses on the case in which only one or two items can be processed in a single batch. The problem is NP-hard and cannot be approximated with...
متن کاملA Genetic Based Scheduling Algorithm for the PHSP with Unequal Batch Size Inbound Trailers
This paper considers the parcel hub scheduling problem (PHSP) with unequal batch size inbound trailers, which is a combinatorial optimization problem commonly found in a parcel consolidation terminal in the parcel delivery industry (PDI). The problem consists of processing a large number of inbound trailers at a much smaller number of unload docks. The parcels in the inbound trailers must be un...
متن کاملOrder Consolidation for Batch Processing
We consider the batch processing of orders where either whole or part of a single order or a specific pair of different orders may be grouped in a batch with a fixed capacity. The problem can be modelled by a graph G = (V, E), where each node v ∈ V corresponds to an order, its weight w(v) corresponds to the amount of ordered quantity and a pair of orders, say u and v may be grouped in a batch i...
متن کاملApproximation Solutions for Time-Varying Shortest Path Problem
Abstract. Time-varying network optimization problems have tradition-ally been solved by specialized algorithms. These algorithms have NP-complement time complexity. This paper considers the time-varying short-est path problem, in which can be optimally solved in O(T(m + n)) time,where T is a given integer. For this problem with arbitrary waiting times,we propose an approximation algorithm, whic...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Theor. Comput. Sci.
دوره 410 شماره
صفحات -
تاریخ انتشار 2009