Order Acceptance and Scheduling: A Taxonomy and Review

Over the past 20 years, the topic of order acceptance has attracted considerable attention from those who study scheduling and those who practice it. In a firm that strives to align its functions so that profit is maximized, the coordination of capacity with demand may require that business sometimes be turned away. In particular, there is a trade-off between the revenue brought in by a particular order, and all of its associated costs of processing. The present study focuses on the body of research that approaches this trade-off by considering two decisions: which orders to accept for processing, and how to schedule them. This paper presents a taxonomy and a review of this literature, catalogs its contributions and suggests opportunities for future research in this area

Fully polynomial time approximation schemes for sequential decision problems

Thesis (S.M.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2005.Includes bibliographical references (p. 65-67).This thesis is divided into two parts sharing the common theme of fully polynomial time approximation schemes. In the first part, we introduce a generic approach for devising fully polynomial time approximation schemes for a large class of problems that we call list scheduling problems. Our approach is simple and unifying, and many previous results in the literature follow as direct corollaries of our main theorem. In the second part, we tackle a more difficult problem; the stochastic lot sizing problem, and give the first fully polynomial time approximation scheme for it. Our approach is based on simple techniques that could arguably have wider applications outside of just designing fully polynomial time approximation schemes.by Mohamed Mostagir.S.M

A dynamic programming approach for a class of robust optimization problems

Common approaches to solving a robust optimization problem decompose the problem into a master problem (MP) and adversarial problems (APs). The MP contains the original robust constraints, written, however, only for nite numbers of scenarios. Additional scenarios are generated on the y by solving the APs. We consider in this work the budgeted uncertainty polytope from Bertsimas and Sim, widely used in the literature, and propose new dynamic programming algorithms to solve the APs that are based on the maximum number of deviations allowed and on the size of the deviations. Our algorithms can be applied to robust constraints that occur in various applications such as lot-sizing, the traveling salesman problem with time windows, scheduling problems, and inventory routing problems, among many others. We show how the simple version of the algorithms leads to a fully polynomial time approximation scheme when the deterministic problem is convex. We assess numerically our approach on a lot-sizing problem, showing a comparison with the classical mixed integer linear programming reformulation of the AP

Green Lot-Sizing

The lot-sizing problem concerns a manufacturer that needs to solve a production planning problem. The producer must decide at which points in time to set up a production process, and when he/she does, how much to produce. There is a trade-off bet

A Framework for Approximate Optimization of BoT Application Deployment in Hybrid Cloud Environment

We adopt a systematic approach to investigate the efficiency of near-optimal deployment of large-scale CPU-intensive Bag-of-Task applications running on cloud resources with the non-proportional cost to performance ratios. Our analytical solutions perform in both known and unknown running time of the given application. It tries to optimize users' utility by choosing the most desirable tradeoff between the make-span and the total incurred expense. We propose a schema to provide a near-optimal deployment of BoT application regarding users' preferences. Our approach is to provide user with a set of Pareto-optimal solutions, and then she may select one of the possible scheduling points based on her internal utility function. Our framework can cope with uncertainty in the tasks' execution time using two methods, too. First, an estimation method based on a Monte Carlo sampling called AA algorithm is presented. It uses the minimum possible number of sampling to predict the average task running time. Second, assuming that we have access to some code analyzer, code profiling or estimation tools, a hybrid method to evaluate the accuracy of each estimation tool in certain interval times for improving resource allocation decision has been presented. We propose approximate deployment strategies that run on hybrid cloud. In essence, proposed strategies first determine either an estimated or an exact optimal schema based on the information provided from users' side and environmental parameters. Then, we exploit dynamic methods to assign tasks to resources to reach an optimal schema as close as possible by using two methods. A fast yet simple method based on First Fit Decreasing algorithm, and a more complex approach based on the approximation solution of the transformed problem into a subset sum problem. Extensive experiment results conducted on a hybrid cloud platform confirm that our framework can deliver a near optimal solution respecting user's utility function

Advances and Novel Approaches in Discrete Optimization

Discrete optimization is an important area of Applied Mathematics with a broad spectrum of applications in many fields. This book results from a Special Issue in the journal Mathematics entitled ‘Advances and Novel Approaches in Discrete Optimization’. It contains 17 articles covering a broad spectrum of subjects which have been selected from 43 submitted papers after a thorough refereeing process. Among other topics, it includes seven articles dealing with scheduling problems, e.g., online scheduling, batching, dual and inverse scheduling problems, or uncertain scheduling problems. Other subjects are graphs and applications, evacuation planning, the max-cut problem, capacitated lot-sizing, and packing algorithms

SUPPLY CHAIN SCHEDULING FOR MULTI-MACHINES AND MULTI-CUSTOMERS

Manufacturing today is no longer a single point of production activity but a chain of activities from the acquisition of raw materials to the delivery of products to customers. This chain is called supply chain. In this chain of activities, a generic pattern is: processing of goods (by manufacturers) and delivery of goods (to customers). This thesis concerns the scheduling operation for this generic supply chain. Two performance measures considered for evaluation of a particular schedule are: time and cost. Time refers to a span of the time that the manufacturer receives the request of goods from the customer to the time that the delivery tool (e.g. vehicle) is back to the manufacturer. Cost refers to the delivery cost only (as the production cost is considered as fi xed). A good schedule is thus with short time and low cost; yet the two may be in conflict. This thesis studies the algorithm for the supply chain scheduling problem to achieve a balanced short time and low cost. Three situations of the supply chain scheduling problem are considered in this thesis: (1) a single machine and multiple customers, (2) multiple machines and a single customer and (3) multiple machines and multiple customers. For each situation, di fferent vehicles characteristics and delivery patterns are considered. Properties of each problem are explored and algorithms are developed, analysed and tested (via simulation). Further, the robustness of the scheduling algorithms under uncertainty and the resilience of the scheduling algorithms under disruptions are also studied. At last a case study, about medical resources supply in an emergency situation, is conducted to illustrate how the developed algorithms can be applied to solve the practical problem. There are both technical merits and broader impacts with this thesis study. First, the problems studied are all new problems with the particular new attributes such as on-line, multiple-customers and multiple-machines, individual customer oriented, and limited capacity of delivery tools. Second, the notion of robustness and resilience to evaluate a scheduling algorithm are to the best of the author's knowledge new and may be open to a new avenue for the evaluation of any scheduling algorithm. In the domain of manufacturing and service provision in general, this thesis has provided an e ffective and effi cient tool for managing the operation of production and delivery in a situation where the demand is released without any prior knowledge (i.e., on-line demand). This situation appears in many manufacturing and service applications