Supplier Choice: Market Selection under Uncertainty.

Suppliers and Manufacturers generally have some say in which subset of all possible demand they will meet. In some cases that choice is implicit through pricing decisions and feature selection. Other times it is made explicitly by choosing only specific regions to stock a product in. This thesis includes models using both approaches and incorporates random demands. We present several methods for choosing a subset of all candidate customers given uncertain demands. In this thesis we consider four models of demand selection. The first two research problems consider market selection, which has been studied in the literature. The Selective Newsvendor Problem (SNP) looks at a decision maker choosing a subset of candidate markets to serve, and then receiving revenues and paying newsvendor-type costs based on the selected collection. In this thesis we consider a generalization with normally distributed demands which includes a multi-period problem as a special case and develop both exact and heuristic algorithms to solve it. When demands are not normally distributed, the problem is considerably more complex and is in general NP-hard. We develop an approximation algorithm using sample average approximation and a rounding approach to efficiently solve the problem. In addition to the work on market selection, we propose two other models for demand selection. We study auctions as a tool for a supplier with a fixed capacity to allocate the limited supply to retailers with newsvendor-type costs. Finally, we present a model for a supplier who must ensure demand is met in all markets, but has the option to work with subsidiary suppliers to meet that demand.PhDIndustrial and Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120864/1/zstrinka_1.pd

Fuzzy Transfer Pricing World: On the Analysis of Transfer Pricing with Fuzzy Logic Techniques

The arm’s length analysis of international transfer prices of multinational firms lacks sound methodological approach of the so-called function and risk analysis. In practice, such analyses are descriptive. Derived from Zadeh’s mathematical theory of fuzzy sets, this paper investigates a quantitative approach to identify the function and risk pattern of related parties of multinational companies. We illustrate our fuzzy logic approach with a simple case.

The boomerang returns? Accounting for the impact of uncertainties on the dynamics of remanufacturing systems

Recent years have witnessed companies abandon traditional open-loop supply chain structures in favour of closed-loop variants, in a bid to mitigate environmental impacts and exploit economic opportunities. Central to the closed-loop paradigm is remanufacturing: the restoration of used products to useful life. While this operational model has huge potential to extend product life-cycles, the collection and recovery processes diminish the effectiveness of existing control mechanisms for open-loop systems. We systematically review the literature in the field of closed-loop supply chain dynamics, which explores the time-varying interactions of material and information flows in the different elements of remanufacturing supply chains. We supplement this with further reviews of what we call the three ‘pillars’ of such systems, i.e. forecasting, collection, and inventory and production control. This provides us with an interdisciplinary lens to investigate how a ‘boomerang’ effect (i.e. sale, consumption, and return processes) impacts on the behaviour of the closed-loop system and to understand how it can be controlled. To facilitate this, we contrast closed-loop supply chain dynamics research to the well-developed research in each pillar; explore how different disciplines have accommodated the supply, process, demand, and control uncertainties; and provide insights for future research on the dynamics of remanufacturing systems

A proof of convergence of a finite volume scheme for modified steady Richards’ equation describing transport processes in the pressing section of a paper machine

A number of water flow problems in porous media are modelled by Richards’ equation [1]. There exist a lot of different applications of this model. We are concerned with the simulation of the pressing section of a paper machine. This part of the industrial process provides the dewatering of the paper layer by the use of clothings, i.e. press felts, which absorb the water during pressing [2]. A system of nips are formed in the simplest case by rolls, which increase sheet dryness by pressing against each other (see Figure 1). A lot of theoretical studies were done for Richards’ equation (see [3], [4] and references therein). Most articles consider the case of x-independent coefficients. This simplifies the system considerably since, after Kirchhoff’s transformation of the problem, the elliptic operator becomes linear. In our case this condition is not satisfied and we have to consider nonlinear operator of second order. Moreover, all these articles are concerned with the nonstationary problem, while we are interested in the stationary case. Due to complexity of the physical process our problem has a specific feature. An additional convective term appears in our model because the porous media moves with the constant velocity through the pressing rolls. This term is zero in immobile porous media. We are not aware of papers, which deal with such kind of modified steady Richards’ problem. The goal of this paper is to obtain the stability results, to show the existence of a solution to the discrete problem, to prove the convergence of the approximate solution to the weak solution of the modified steady Richards’ equation, which describes the transport processes in the pressing section. In Section 2 we present the model which we consider. In Section 3 a numerical scheme obtained by the finite volume method is given. The main part of this paper is theoretical studies, which are given in Section 4. Section 5 presents a numerical experiment. The conclusion of this work is given in Section 6

Essays on Shipment Consolidation Scheduling and Decision Making in the Context of Flexible Demand

This dissertation contains three essays related to shipment consolidation scheduling and decision making in the presence of flexible demand. The first essay is presented in Section 1. This essay introduces a new mathematical model for shipment consolidation scheduling for a two-echelon supply chain. The problem addresses shipment coordination and consolidation decisions that are made by a manufacturer who provides inventory replenishments to multiple downstream distribution centers. Unlike previous studies, the consolidation activities in this problem are not restricted to specific policies such as aggregation of shipments at regular times or consolidating when a predetermined quantity has accumulated. Rather, we consider the construction of a detailed shipment consolidation schedule over a planning horizon. We develop a mixed-integer quadratic optimization model to identify the shipment consolidation schedule that minimizes total cost. A genetic algorithm is developed to handle large problem instances. The other two essays explore the concept of flexible demand. In Section 2, we introduce a new variant of the vehicle routing problem (VRP): the vehicle routing problem with flexible repeat visits (VRP-FRV). This problem considers a set of customers at certain locations with certain maximum inter-visit time requirements. However, they are flexible in their visit times. The VRP-FRV has several real-world applications. One scenario is that of caretakers who provide service to elderly people at home. Each caretaker is assigned a number of elderly people to visit one or more times per day. Elderly people differ in their requirements and the minimum frequency at which they need to be visited every day. The VRP-FRV can also be imagined as a police patrol routing problem where the customers are various locations in the city that require frequent observations. Such locations could include known high-crime areas, high-profile residences, and/or safe houses. We develop a math model to minimize the total number of vehicles needed to cover the customer demands and determine the optimal customer visit schedules and vehicle routes. A heuristic method is developed to handle large problem instances. In the third study, presented in Section 3, we consider a single-item cyclic coordinated order fulfillment problem with batch supplies and flexible demands. The system in this study consists of multiple suppliers who each deliver a single item to a central node from which multiple demanders are then replenished. Importantly, demand is flexible and is a control action that the decision maker applies to optimize the system. The objective is to minimize total system cost subject to several operational constraints. The decisions include the timing and sizes of batches delivered by the suppliers to the central node and the timing and amounts by which demanders are replenished. We develop an integer programing model, provide several theoretical insights related to the model, and solve the math model for different problem sizes

Internalizing negative externalities in vehicle routing problems through green taxes and green tolls

Road freight transportation includes various internal and external costs that need to be accounted for in the construction of efficient routing plans. Typically, the resulting optimization problem is formulated as a vehicle routing problem in any of its variants. While the traditional focus of the vehicle routing problem was the minimization of internal routing costs such as travel distance or duration, numerous approaches to include external factors related to environmental routing aspects have been recently discussed in the literature. However, internal and external routing costs are often treated as competing objectives. This paper discusses the internalization of external routing costs through the consideration of green taxes and green tolls. Numeric experiments with a biased-randomization savings algorithm, show benefits of combining internal and external costs in delivery route planning.Peer Reviewe

Using the Sharp Operator for edge detection and nonlinear diffusion

In this paper we investigate the use of the sharp function known from functional analysis in image processing. The sharp function gives a measure of the variations of a function and can be used as an edge detector. We extend the classical notion of the sharp function for measuring anisotropic behaviour and give a fast anisotropic edge detection variant inspired by the sharp function. We show that these edge detection results are useful to steer isotropic and anisotropic nonlinear diffusion filters for image enhancement

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes