An Integrated Framework For Configurable Product Assortment Planning

A manufacturer\u27s assortment is the set of products or product configurations that the company builds and offers to its customers. While the literature on assortment planning is growing in recent years, it is primarily aimed at non-durable retail and grocery products. In this study, we develop an integrated framework for strategic assortment planning of configurable products, with a focus on the highly complex automotive industry. The facts that automobiles are highly configurable (with the number of buildable configurations running into thousands, tens of thousands, and even millions) with relatively low sales volumes and the stock-out rates at individual dealerships (even with transshipments) are extremely high, pose significant challenges to traditional assortment planning models. This is particularly the case for markets such as the U.S. that mostly operate in a make-to-stock (MTS) environment. First, we study assortment planning models that account for exogenous demand models and stock-out based substitution while considering production and manufacturing complexity costs and economies-of-scale. We build a mathematical model that maximizes the expected profit for an Original Equipment Manufacturer (OEM) and is a mixed-integer nonlinear problem. We suggest using linear lower/upper bounds that will be solved through a Modified-Branch and Bound procedure and compare the results with commercial mixed-integer nonlinear solvers and show superiority of the proposed method in terms of solution quality as well as computational speed. We then build a modeling framework that identifies the optimal assortment for a manufacturer of automotive products under environmental considerations, in particular, Corporate Average Fuel Economy (CAFE) requirements as well as life-cycle Greenhouse Gas (GHG) emission constraints. We present a numerical experiment consisting of different vehicle propulsion technologies (conventional, Diesel, and hybrid) and study the optimal shares of different technologies for maximizing profitability under different target levels of CAFE requirements. Finally, we develop assortment planning formulations that can jointly identify optimal packages and stand-alone options over different series of the product model. Our numerical experiment reveals that product option packaging has a considerable effect on managing product complexity and profitability

Game theoretic optimisation in process and energy systems engineering: A review

Game theory is a framework that has been used by various research fields in order to represent dynamic correlation among stakeholders. Traditionally, research within the process and energy systems engineering community has focused on the development of centralised decision making schemes. In the recent years, decentralised decision-making schemes have attracted increasing attention due to their ability to capture multi-stakeholder dynamics in a more accurate manner. In this article, we survey how centralised and decentralised decision making has been facilitated by game theoretic approaches. We focus on the deployment of such methods in process systems engineering problems and review applications related to supply chain optimisation problems, design and operations, and energy systems optimisation. Finally, we analyse different game structures based on the degree of cooperation and how fairness criteria can be employed to find fair payoff allocations

Mathematics in the Supply Chain

[no abstract available

An enhanced concave program relaxation for choice network revenue management

The network choice revenue management problem models customers as choosing from an offer-set, and the firm decides the best subset to offer at any given moment to maximize expected revenue. The resulting dynamic program for the firm is intractable and approximated by a deterministic linear program called the CDLP which has an exponential number of columns. However, under the choice-set paradigm when the segment consideration sets overlap, the CDLP is difficult to solve. Column generation has been proposed but finding an entering column has been shown to be NP-hard. In this paper, starting with a concave program formulation based on segment-level consideration sets called SDCP, we add a class of constraints called product constraints, that project onto subsets of intersections. In addition we propose a natural direct tightening of the SDCP called ?SDCP, and compare the performance of both methods on the benchmark data sets in the literature. Both the product constraints and the ?SDCP method are very simple and easy to implement and are applicable to the case of overlapping segment consideration sets. In our computational testing on the benchmark data sets in the literature, SDCP with product constraints achieves the CDLP value at a fraction of the CPU time taken by column generation and we believe is a very promising approach for quickly approximating CDLP when segment consideration sets overlap and the consideration sets themselves are relatively small.discrete-choice models, network revenue management, optimization

Models and Methods for Merge-In-Transit Operations

We develop integer programming formulations and solution methods for addressing operational issues in merge-in-transit distribution systems. The models account for various complex problem features including the integration of inventory and transportation decisions, the dynamic and multimodal components of the application, and the non-convex piecewise linear structure of the cost functions. To accurately model the cost functions, we introduce disaggregation techniques that allow us to derive a hierarchy of linear programming relaxations. To solve these relaxations, we propose a cutting-plane procedure that combines constraint and variable generation with rounding and branch-and-bound heuristics. We demonstrate the effectiveness of this approach on a large set of test problems with instances with up to almost 500,000 integer variables derived from actual data from the computer industry. Key words : Merge-in-transit distribution systems, logistics, transportation, integer programming, disaggregation, cutting-plane method

Cyber-Physical Systems Design: Electricity Markets and Network Security

This thesis presents Cyber-Physical Systems Design (CPS Design). Design of CPS is challenging and requires interdisciplinary studies of engineering and economics because of the distinguishing features of CPS: strategic (self profit-maximizing) decision makers, complex physical constraints, and large-scale networked systems. We study these features by focusing on designing markets with complex constraints including both policy and physical constraints, and decomposing large-scale CPS within the context of electricity markets and network security. We first study market design for implementation of complex electricity policy targets, i.e. sustainability, reliability, and price efficiency, by efficient design of spot, carbon, and capacity markets that correct the deficiencies of the current electricity markets; this design does not take into account the network constraints due to the Kirchhoff's laws. To address this problem, we develop a framework based on the design of efficient auctions with constraints. Our market design sheds light on major debates in electricity policy including capacity-and-energy vs energy-only markets, carbon market vs carbon tax, and use of price or offer caps. Second, we add network constraints due to Kirchhoff's laws of current and voltage, which are unique to electricity networks, to the design of electricity spot markets with complex physical constraints. To address this problem, we develop a framework for the design of networked markets based on the ideas from local public goods. Finally, we study the design of defense policies for large-scale network security. Our approach is to design approximately optimal defense policies that are computable. We develop a framework based on the notion of influence graph, which captures the connectivity of the security states of the system elements, to decompose the system into subsystems. We then design approximately optimal defense policies for each sub-system. We consider non-Bayesian uncertainty and even though we do not model the attacker as a strategic decision maker, we compensate (in part) for the lack of this feature by adopting a minmax performance criterion.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/144165/1/rasouli_1.pd

IMPOSING MONOTONICITY AND CURVATURE ON FLEXIBLE FUNCTIONAL FORMS

Replaced with revised version of paper 05/29/04.Research Methods/ Statistical Methods,

An enhanced concave program relaxation for choice network revenue management

The network choice revenue management problem models customers as choosing from an offer set, and the firm decides the best subset to offer at any given moment to maximize expected revenue. The resulting dynamic program for the firm is intractable and approximated by a deterministic linear program called the CDLP which has an exponential number of columns. However, under the choice-set paradigm when the segment consideration sets overlap, the CDLP is difficult to solve. Column generation has been proposed but finding an entering column has been shown to be NP-hard. In this paper, starting with a concave program formulation called SDCP that is based on segment-level consideration sets, we add a class of constraints called product constraints (σPC), that project onto subsets of intersections. In addition we propose a natural direct tightening of the SDCP called ESDCPκ, and compare the performance of both methods on the benchmark data sets in the literature. In our computational testing on the benchmark data sets in the literature, 2PC achieves the CDLP value at a fraction of the CPU time taken by column generation. For a large network our 2PC procedure runs under 70 seconds to come within 0.02% of the CDLP value, while column generation takes around 1 hour; for an even larger network with 68 legs, column generation does not converge even in 10 hours for most of the scenarios while 2PC runs under 9 minutes. Thus we believe our approach is very promising for quickly approximating CDLP when segment consideration sets overlap and the consideration sets themselves are relatively small

Approximate Dynamic Programming Algorithms for United States Air Force Officer Sustainment

The United States Air Force (USAF) officer sustainment system involves making accession and promotion decisions for nearly 64 thousand officers annually. We formulate a discrete time stochastic Markov decision process model to examine this military workforce planning problem. The large size of the motivating problem suggests that conventional exact dynamic programming algorithms are inappropriate. As such, we propose two approximate dynamic programming (ADP) algorithms to solve the problem. We employ a least-squares approximate policy iteration (API) algorithm with instrumental variables Bellman error minimization to determine approximate policies. In this API algorithm, we use a modified version of the Bellman equation based on the post-decision state variable. Approximating the value function using a post-decision state variable allows us to find the best policy for a given approximation using a decomposable mixed integer nonlinear programming formulation. We also propose an approximate value iteration algorithm using concave adaptive value estimation (CAVE). The CAVE algorithm identities an improved policy for a test problem based on the current USAF officer sustainment system. The CAVE algorithm obtains a statistically significant 2.8% improvement over the currently employed USAF policy, which serves as the benchmark