An optimization framework for solving capacitated multi-level lot-sizing problems with backlogging

This paper proposes two new mixed integer programming models for capacitated multi-level lot-sizing problems with backlogging, whose linear programming relaxations provide good lower bounds on the optimal solution value. We show that both of these strong formulations yield the same lower bounds. In addition to these theoretical results, we propose a new, effective optimization framework that achieves high quality solutions in reasonable computational time. Computational results show that the proposed optimization framework is superior to other well-known approaches on several important performance dimensions

Multi-item capacitated lot-sizing problems with setup times and pricing decisions

We study a multi-item capacitated lot-sizing problem with setup times and pricing (CLSTP) over a finite and discrete planning horizon. In this class of problems, the demand for each independent item in each time period is affected by pricing decisions. The corresponding demands are then satisfied through production in a single capacitated facility or from inventory, and the goal is to set prices and determine a production plan that maximizes total profit. In contrast with many traditional lot-sizing problems with fixed demands, we cannot, without loss of generality, restrict ourselves to instances without initial inventories, which greatly complicates the analysis of the CLSTP. We develop two alternative Dantzig–Wolfe decomposition formulations of the problem, and propose to solve their relaxations using column generation and the overall problem using branch-and-price. The associated pricing problem is studied under both dynamic and static pricing strategies. Through a computational study, we analyze both the efficacy of our algorithms and the benefits of allowing item prices to vary over time. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65027/1/20394_ftp.pd

Mitigating the Cost of Anarchy in Supply Chain Systems

In a decentralized two-stage supply chain where a supplier serves a retailer who, in turn, serves end customers, operations decisions based on local incentives often lead to suboptimal system performance. Operating decisions based on local incentives may in such cases lead to a degree of system disorder or anarchy, wherein one party's decisions put the other party and/or the system at a disadvantage. While models and mechanisms for such problem classes have been considered in the literature, little work to date has considered such problems under nonstationary demands and fixed replenishment order costs. This paper models such two-stage problems as a class of Stackelberg games where the supplier announces a set of time-phased ordering costs to the retailer over a discrete time horizon of finite length, and the retailer then creates an order plan, which then serves as the supplier's demand. We provide metrics for characterizing the degree of efficiency (and anarchy) associated with a solution, and provide a set of easily understood and implemented mechanisms that can increase this efficiency and reduce the negative impacts of anarchic decisions

Improved approximation algorithm for k-level UFL with penalties, a simplistic view on randomizing the scaling parameter

The state of the art in approximation algorithms for facility location problems are complicated combinations of various techniques. In particular, the currently best 1.488-approximation algorithm for the uncapacitated facility location (UFL) problem by Shi Li is presented as a result of a non-trivial randomization of a certain scaling parameter in the LP-rounding algorithm by Chudak and Shmoys combined with a primal-dual algorithm of Jain et al. In this paper we first give a simple interpretation of this randomization process in terms of solving an aux- iliary (factor revealing) LP. Then, armed with this simple view point, Abstract. we exercise the randomization on a more complicated algorithm for the k-level version of the problem with penalties in which the planner has the option to pay a penalty instead of connecting chosen clients, which results in an improved approximation algorithm

On the equivalence of strong formulations for capacitated multi-level lot sizing problems with setup times

Several mixed integer programming formulations have been proposed for modeling capacitated multi-level lot sizing problems with setup times. These formulations include the so-called facility location formulation, the shortest route formulation, and the inventory and lot sizing formulation with (l,S) inequalities. In this paper, we demonstrate the equivalence of these formulations when the integrality requirement is relaxed for any subset of binary setup decision variables. This equivalence has significant implications for decomposition-based methods since same optimal solution values are obtained no matter which formulation is used. In particular, we discuss the relax-and-fix method, a decomposition-based heuristic used for the efficient solution of hard lot sizing problems. Computational tests allow us to compare the effectiveness of different formulations using benchmark problems. The choice of formulation directly affects the required computational effort, and our results therefore provide guidelines on choosing an effective formulation during the development of heuristic-based solution procedures

E-supply chain integration adoption: examination of buyer–supplier relationships

The purpose of this study is to empirically examine the adoption of e-supply chain integration by electrical and electronic industry suppliers. This study has integrated both the transaction cost and resource-dependence models in understanding the influence of buyer–seller relationships on e-supply chain integration. Hypotheses were developed based on the proposed model. Data were collected from 122 electrical and electronic suppliers located in Malaysia. The data was examined using multiple regression analysis. The results showed that Asset Specificity, Product Technological Uncertainty, Transaction frequency, Proportion of sales to e-supply chain integration promoter, and number of customers are able to explain suppliers’ decisions to adopt e-supply chain integrations with their buyers. Buyers that would like to improve the adoptions of e-supply chain integration will be able to formulate and plan strategies from the buyer–seller relationships perspectives

Integrated market selection and production planning: complexity and solution approaches

Emphasis on effective demand management is becoming increasingly recognized as an important factor in operations performance. Operations models that account for supply costs and constraints as well as a supplier's ability to in°uence demand characteristics can lead to an improved match between supply and demand. This paper presents a new class of optimization models that allow a supplier to select, from a set of potential markets, those markets that provide maximum profit when production/procurement economies of scale exist in the supply process. The resulting optimization problem we study possesses an interesting structure and we show that although the general problem is NP-complete, a number of relevant and practical special cases can be solved in polynomial time. We also provide a computationally very effcient and intuitively attractive heuristic solution procedure that performs extremely well on a large number of test instances

Exact algorithms for integrated facility location and production planning problems

We consider a class of facility location problems with a time dimension, which requires assigning every customer to a supply facility in each of a finite number of periods. Each facility must meet all assigned customer demand in every period at a minimum cost via its production and inventory decisions. We provide exact branch‐and‐price algorithms for this class of problems and several important variants. The corresponding pricing problem takes the form of an interesting class of production planning and order selection problems. This problem class requires selecting a set of orders that maximizes profit, defined as the revenue from selected orders minus production‐planning‐related costs incurred in fulfilling the selected orders. We provide polynomial‐time dynamic programming algorithms for this class of pricing problems, as well as for generalizations thereof. Computational testing indicates the advantage of our branch‐and‐price algorithm over various approaches that use commercial software packages. These tests also highlight the significant cost savings possible from integrating location with production and inventory decisions and demonstrate that the problem is rather insensitive to forecast errors associated with the demand streams. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86850/1/20458_ftp.pd

Integrated market selection and production planning: Complexity and solution approaches

Emphasis on effective demand management is becoming increasingly recognized as an important factor in operations performance. Operations models that account for supply costs and constraints as well as a supplier's ability to influence demand characteristics can lead to an improved match between supply and demand. This paper presents a class of optimization models that allow a supplier to select, from a set of potential markets, those markets that provide maximum profit when production/procurement economies of scale exist in the supply process. The resulting optimization problem we study possesses an interesting structure and we show that although the general problem is NP -complete, a number of relevant and practical special cases can be solved in polynomial time. We also provide a computationally very efficient and intuitively attractive heuristic solution procedure that performs extremely well on a large number of test instances

Automated Analysis of Cryptococcal Macrophage Parasitism Using GFP-Tagged Cryptococci

The human fungal pathogens Cryptococcus neoformans and C. gattii cause life-threatening infections of the central nervous system. One of the major characteristics of cryptococcal disease is the ability of the pathogen to parasitise upon phagocytic immune effector cells, a phenomenon that correlates strongly with virulence in rodent models of infection. Despite the importance of phagocyte/Cryptococcus interactions to disease progression, current methods for assaying virulence in the acrophage system are both time consuming and low throughput. Here, we introduce the first stable and fully characterised GFP–expressing derivatives of two widely used cryptococcal strains: C. neoformans serotype A type strain H99 and C. gattii serotype B type strain R265. Both strains show unaltered responses to environmental and host stress conditions and no deficiency in virulence in the macrophage model system. In addition, we report the development of a method to effectively and rapidly investigate macrophage parasitism by flow cytometry, a technique that preserves the accuracy of current approaches but offers a four-fold improvement in speed