On the polyhedral structure of two‐level lot‐sizing problems with supplier selection

In this article, we study a two‐level lot‐sizing problem with supplier selection (LSS), which is an NP‐hard problem arising in different production planning and supply chain management applications. After presenting various formulations for LSS, and computationally comparing their strengths, we explore the polyhedral structure of one of these formulations. For this formulation, we derive several families of strong valid inequalities, and provide conditions under which they are facet‐defining. We show numerically that incorporating these valid inequalities within a branch‐and‐cut framework leads to significant improvements in computation. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 647–666, 2017     

Controlling rates in a double queue

A double-ended queue with a Poisson arrival pattern is examined in a situation where the rates depend (in a restricted sense) on both the time and the state of the system. Under some circumstances, the rates can be controlled. This article studies the distribution of the difference in queue sizes for each member of a large class of control strategies and introduces the problem of determining the optimal times at which the control should be in effect in order to maximize certain objective functions.     

Algorithmic insights and a convergence analysis for a Karmarkar-type of algorithm for linear programming problems

This paper is concerned with a modification of a recently proposed variant of Karmarkar's algorithm for solving linear programming problems. In analyzing this variant, we exhibit interesting and useful relationships of these types of algorithms with barrier function methods, and subgradient optimization procedures involving space dilation techniques, which subsume the well-known ellipsoidal type of algorithms. Convergence of this variant is established under certain regularity conditions. We also provide remarks on how to obtain dual variables or Lagrange multipliers at optimality.     

Estimating the probability of a diffusing target encountering a stationary sensor

The problem addressed is that of estimating the probability of a moving particle (called the target) avoiding detection by a stationary sensor to time t. The target follows a diffusion path and is constrained to remain within a square region R. The detecting sensor is fixed at the center of A. Two expressions for this probability are given. The first results from an approximation to the exact solution of the diffusion equation and the second from experimentation with a Monte Carlo simulation of the diffusion process.     

The cost of production breaks

Disruptions in the production process can have a serious impact on production costs. Most of the previous literature which addresses the cost impact of production breaks attributes the observed increase in costs solely to “loss of learning.” We develop a mathematical model which implies that breaks in the unit learning curve can occur because of a production break, even under the assumption of no forgetting. In such cases, increases in unit cost can be caused by decreasing returns as the amount of time available to meet the delivery schedule decreases due to the production break.     

A method for estimating the parameters of reliability models

The maximum likelihood estimates (MLE) of transition rates in a finite-state continuous-time Markov process with an absorbing state are obtained, when there are a number of independent realizations of the process. This process is explained as a model for deteriorating systems of reliability theory through example. The asymptotic properties of MLES as the observed number of realizations tend to infinity are studied. Extension of these results to semi-Markov processes is discussed.     

Finite Markov chain models skip-free in one direction

Finite Markov processes are considered, with bidimensional state space, such that transitions from state (n, i) to state (m, j) are possible only if m ≤ n + 1. The analysis leads to efficient computational algorithms, to determine the stationary probability distribution, and moments of first passage times.