Approximation Algorithms for the Stochastic Lot-Sizing Problem with Order Lead Times

We develop new algorithmic approaches to compute provably near-optimal policies for multiperiod stochastic lot-sizing inventory models with positive lead times, general demand distributions, and dynamic forecast updates. The policies that are developed have worst-case performance guarantees of 3 and typically perform very close to optimal in extensive computational experiments. The newly proposed algorithms employ a novel randomized decision rule. We believe that these new algorithmic and performance analysis techniques could be used in designing provably near-optimal randomized algorithms for other stochastic inventory control models and more generally in other multistage stochastic control problems.National Science Foundation (U.S.) (Grant DMS-0732175)National Science Foundation (U.S.) (CAREER Award CMMI-0846554)United States. Air Force Office of Scientific Research (Award FA9550-08-1-0369)United States. Air Force Office of Scientific Research (Award FA9550-11-1-0150)Singapore-MIT AllianceSolomon Buchsbaum AT&T Research Fun

Evaluation of cost balancing policies in multi-echelon stochastic inventory control problems

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2010.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 67-68).We study a periodic-reviewed, infinite horizon serial network inventory control problem. The demands in different periods are independent of each other and follow an identical Poisson distribution. Unsatisfied demands are backlogged until they are satisfied by supply units. In each period, there is a per-unit holding cost is incurred for each unit of supply that stays in the system and a per-unit backorder cost is incurred for each unsatisfied unit of demand. The objective of the inventory control policy is to minimize the long-run expected average cost over an infinite horizon. The goal of the thesis is to evaluate the empirical performance of the dual balancing policy and several other variants of cost balancing policies through numerical simulations. The dual-balancing policy is based on two novel ideas: the marginal cost accounting scheme, which assigns to each decision all the costs that are made inevitable after that decision is made; and the cost balancing idea to balance opposing costs.(cont.) The dual-balancing policy can be modified in several ways to get other cost balancing policies. It has been proven that the dual-balancing policy has a worst-case guarantee of 2 but this does not indicate the empirical performance. An approximately optimal policy is considered as the benchmark to test the quality of the cost balancing policies. In the computational experiments, the dual-balancing policy shows an average error of 7.74% compared to the approximately optimal policy, much better than the theoretical worst-case guarantee. The three variants of cost balancing policies have made significant improvement on the performance of the dual-balancing policy. The accuracy of the dual-balancing policy is also affected by the system parameters. In addition, with high demand rate and long lead times, we have observed several scenarios when the cost balancing policies dominate the approximately optimal policy.by Qian Yu.S.M

Provably near-optimal algorithms for multi-stage stochastic optimization models in operations management

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 157-165).Many if not most of the core problems studied in operations management fall into the category of multi-stage stochastic optimization models, whereby one considers multiple, often correlated decisions to optimize a particular objective function under uncertainty on the system evolution over the future horizon. Unfortunately, computing the optimal policies is usually computationally intractable due to curse of dimensionality. This thesis is focused on providing provably near-optimal and tractable policies for some of these challenging models arising in the context of inventory control, capacity planning and revenue management; specifically, on the design of approximation algorithms that admit worst-case performance guarantees. In the first chapter, we develop new algorithmic approaches to compute provably near-optimal policies for multi-period stochastic lot-sizing inventory models with positive lead times, general demand distributions and dynamic forecast updates. The proposed policies have worst-case performance guarantees of 3 and typically perform very close to optimal in extensive computational experiments. We also describe a 6-approximation algorithm for the counterpart model under uniform capacity constraints. In the second chapter, we study a class of revenue management problems in systems with reusable resources and advanced reservations. A simple control policy called the class selection policy (CSP) is proposed based on solving a knapsack-type linear program (LP). We show that the CSP and its variants perform provably near-optimal in the Halfin- Whitt regime. The analysis is based on modeling the problem as loss network systems with advanced reservations. In particular, asymptotic upper bounds on the blocking probabilities are derived. In the third chapter, we examine the problem of capacity planning in joint ventures to meet stochastic demand in a newsvendor-type setting. When resources are heterogeneous, there exists a unique revenue-sharing contract such that the corresponding Nash Bargaining Solution, the Strong Nash Equilibrium, and the system optimal solution coincide. The optimal scheme rewards every participant proportionally to her marginal cost. When resources are homogeneous, there does not exist a revenue-sharing scheme which induces the system optimum. Nonetheless, we propose provably good revenue-sharing contracts which suggests that the reward should be inversely proportional to the marginal cost of each participant.by Cong Shi.Ph.D

Data-Driven Algorithms for Stochastic Supply Chain Systems: Approximation and Online Learning

In the era of Big Data, with new and emerging technologies, data become easily attainable for companies. However, acquiring data is only the first step for the company. The second and more important step is to effectively integrate the data through the learning process (mining the data) in the decision-making process, and to utilize the information extracted from data to improve the efficiency of the company’s supply chain operation. The primary focus of this dissertation is on multistage stochastic optimization problems arising in the context of supply chains and inventory control problems, and on the design of efficient algorithms to solve the respective models. This dissertation can be categorized into two broad areas as follows. The first part of this dissertation focuses on the design of non-parametric learning algorithms for complex inventory systems with censored data. We address two challenging stochastic inventory control models: the periodic-review perishable inventory system and the periodic-review inventory control problem with lost-sales and positive lead times. We assume that the decision maker has no demand distribution information available a priori and can only observe past realized sales (censored demand) information to optimize the system's performance on the fly. For each of the problems, we design a learning algorithm that can coverage to the best base-stock policy with tight regret rate. The second part of this dissertation focuses on the design of approximation algorithms for stochastic perishable inventory systems with correlated demand. In this part, we consider the perishable inventory system from the optimization perspective. Different from traditional perishable inventory literature, we allow demands to be arbitrarily correlated and nonstationary, which means we can capture the seasonality nature of the economy, and allow the decision makers to effectively incorporate demand forecast. For this problem, we develop two approximation algorithms with worst-case performance guarantees. Through comprehensive numerical experiments, we have shown that the numerical performances of the approximation algorithms are very close to optimal.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138697/1/zhanghn_1.pd

Multiple sourcing in single- and multi-echelon inventory systems

This thesis deals with stochastic inventory models that focus on the following two aspects in particular: (i) the coordination of multiple supply sources and (ii) the optimization of the inventory allocation and sizing in multi-echelon systems. Initially, single-echelon inventory models with multiple sourcing and multi-echelon inventory models with single sourcing are analyzed separately. In the former case, the goal is the identification of effective inventory control policies. In the latter case, the focus lies on the development of a new multi-echelon approach, which combines the two major frameworks currently available in the literature. Subsequently, both aspects are integrated into a multi-echelon inventory model with multiple sourcing