scholarly journals Integrated Scheduling of Production and Distribution with Release Dates and Capacitated Deliveries

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Xueling Zhong ◽  
Dakui Jiang
Keyword(s):  
Arrival Time ◽  
Exact Algorithm ◽  
Distribution Model ◽  
Objective Functions ◽  
Release Date ◽  
Worst Case ◽  
Integrated Scheduling ◽  
Worst Case Ratio ◽  
Production And Distribution ◽  
Distribution Cost

This paper investigates an integrated scheduling of production and distribution model in a supply chain consisting of a single machine, a customer, and a sufficient number of homogeneous capacitated vehicles. In this model, the customer places a set of orders, each of which has a given release date. All orders are first processed nonpreemptively on the machine and then batch delivered to the customer. Two variations of the model with different objective functions are studied: one is to minimize the arrival time of the last order plus total distribution cost and the other is to minimize total arrival time of the orders plus total distribution cost. For the former one, we provide a polynomial-time exact algorithm. For the latter one, due to its NP-hard property, we provide a heuristic with a worst-case ratio bound of 2.

scholarly journals Parallel Machine Scheduling with Batch Delivery to Two Customers

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Xueling Zhong ◽  
Dakui Jiang
Keyword(s):  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Variable Cost ◽  
Worst Case ◽  
Batch Delivery ◽  
Worst Case Ratio ◽  
Processing Facility ◽  
Production And Distribution ◽  
Distribution Cost

In some make-to-order supply chains, the manufacturer needs to process and deliver products for customers at different locations. To coordinate production and distribution operations at the detailed scheduling level, we study a parallel machine scheduling model with batch delivery to two customers by vehicle routing method. In this model, the supply chain consists of a processing facility withmparallel machines and two customers. A set of jobs containingn1jobs from customer 1 andn2jobs from customer 2 are first processed in the processing facility and then delivered to the customers directly without intermediate inventory. The problem is to find a joint schedule of production and distribution such that the tradeoff between maximum arrival time of the jobs and total distribution cost is minimized. The distribution cost of a delivery shipment consists of a fixed charge and a variable cost proportional to the total distance of the route taken by the shipment. We provide polynomial time heuristics with worst-case performance analysis for the problem. Ifm=2and(n1-b)(n2-b)<0, we propose a heuristic with worst-case ratio bound of 3/2, wherebis the capacity of the delivery shipment. Otherwise, the worst-case ratio bound of the heuristic we propose is2-2/(m+1).

Fast closed testing for exchangeable local tests

Biometrika ◽  
2020 ◽  
Vol 107 (3) ◽  
pp. 761-768 ◽  
Author(s):  
E Dobriban
Keyword(s):  
Error Rate ◽  
Multiple Testing ◽  
Exact Algorithm ◽  
Multiple Hypothesis Testing ◽  
Test Statistics ◽  
Familywise Error Rate ◽  
Closure Principle ◽  
Worst Case ◽  
Higher Criticism ◽  
False Discovery

Summary Multiple hypothesis testing problems arise naturally in science. This note introduces a new fast closed testing method for multiple testing which controls the familywise error rate. Controlling the familywise error rate is state-of-the-art in many important application areas and is preferred over false discovery rate control for many reasons, including that it leads to stronger reproducibility. The closure principle rejects an individual hypothesis if all global nulls of subsets containing it are rejected using some test statistics. It takes exponential time in the worst case. When the tests are symmetric and monotone, the proposed method is an exact algorithm for computing the closure, is quadratic in the number of tests, and is linear in the number of discoveries. Our framework generalizes most examples of closed testing, such as Holm’s method and the Bonferroni method. As a special case of the method, we propose the Simes and higher criticism fusion test, which is powerful both for detecting a few strong signals and for detecting many moderate signals.

Integrated Scheduling of Production and Distribution Operations

2005 ◽  
Vol 51 (4) ◽  
pp. 614-628 ◽  
Author(s):  
Zhi-Long Chen ◽  
George L. Vairaktarakis
Keyword(s):  
Integrated Scheduling ◽  
Production And Distribution ◽  
Distribution Operations

scholarly journals On Rectilinear Distance-Preserving Trees

VLSI Design ◽  
1998 ◽  
Vol 7 (1) ◽  
pp. 15-30
Author(s):  
Gustavo E. Téllez ◽  
Majid Sarrafzadeh
Keyword(s):  
Approximation Algorithm ◽  
Heuristic Algorithm ◽  
Time Complexity ◽  
High Performance ◽  
Exact Algorithm ◽  
Wire Length ◽  
Worst Case ◽  
Rectilinear Distance ◽  
Source To Sink ◽  
Linear Delay

Given a set of terminals on the plane N={s,ν1,…,νn}, with a source terminal s, a Rectilinear Distance-Preserving Tree (RDPT) T(V, E) is defined as a tree rooted at s, connecting all terminals in N. An RDPT has the property that the length of every source to sink path is equal to the rectilinear distance between that source and sink. A Min- Cost Rectilinear Distance-Preserving Tree (MRDPT) minimizes the total wire length while maintaining minimal source to sink linear delay, making it suitable for high performance interconnect applications.This paper studies problems in the construction of RDPTs, including the following contributions. A new exact algorithm for a restricted version of the problem in one quadrant with O(n2) time complexity is proposed. A novel heuristic algorithm, which uses optimally solvable sub-problems, is proposed for the problem in a single quadrant. The average and worst-case time complexity for the proposed heuristic algorithm are O(n3/2) and O(n3), respectively. A 2-approximation of the quadrant merging problem is proposed. The proposed algorithm has time complexity O(α2T(n)+α3) for any constant α > 1, where T(n) is the time complexity of the solution of the RDPT problem on one quadrant. This result improves over the best previous quadrant merging solution which has O(n2T(n)+n3) time complexity.We test our algorithms on randomly uniform point sets and compare our heuristic RDPT construction against a Minimum Cost Rectilinear Steiner (MRST) tree approximation algorithm. Our results show that RDPTs are competitive with Steiner trees in total wire-length when the number of terminals is less than 32. This result makes RDPTs suitable for VLSI routing applications. We also compare our algorithm to the Rao-Shor RDPT approximation algorithm obtaining improvements of up to 10% in total wirelength. These comparisons show that the algorithms proposed herein produce promising results.

SCHEDULING FILE TRANSFERS UNDER PORT AND CHANNEL CONSTRAINTS

1993 ◽  
Vol 04 (02) ◽  
pp. 101-115 ◽  
Author(s):  
SHIN-ICHI NAKANO ◽  
TAKAO NISHIZEKI
Keyword(s):  
Communication Channel ◽  
Edge Coloring ◽  
Large Collection ◽  
File Transfer ◽  
Worst Case ◽  
File Transfers ◽  
Worst Case Ratio ◽  
Efficient Approximation Algorithm ◽  
New Type ◽  
Efficient Approximation

The file transfer scheduling problem was introduced and studied by Coffman, Garey, Johnson and LaPaugh. The problem is to schedule transfers of a large collection of files between various nodes of a network under port constraint so as to minimize the overall finishing time. This paper extends their model to include communication channel constraint in addition to port constraint. We formulate the problem with both port and channel constraints as a new type of edge-coloring of multigraphs, called an fg-edge-coloring, and give an efficient approximation algorithm with absolute worst-case ratio 3/2.

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