Analyzing the effect of the inventory policy on order and inventory variability with linear control theory

In this paper we apply linear control theory to study the effect of various inventory policies on order and inventory variability, which are key drivers of supply chain performance. In particular, we study a two-echelon supply chain with a stationary demand pattern under the influence of three inventory policies: an inventory-on-hand policy that bases orders on the visible inventory at an installation, an installation-stock policy that bases orders on the inventory position (on-hand plus on-order inventory) at an installation, and an echelon-stock policy that bases orders on the inventory position at that installation and all downstream installations. We prove analytically that the inventory-on-hand policy is unstable in practical settings, confirming analytically what has been observed in experimental settings and in practice. We also prove that the installation-stock and echelon-stock policies are stable and analyze their effect on order and inventory fluctuation. Specifically, we show the general superiority of the echelon-stock in our setting and demonstrate analytically the effect of forecasting parameters on order and inventory fluctuations, confirming the results in other research.     

2‐Cyanoprop‐2‐yl dithiobenzoate mediated reversible addition–fragmentation chain transfer polymerization of acrylonitrile targeting a polymer with a higher molecular weight

The reversible addition–fragmentation chain transfer (RAFT) polymerization of acrylonitrile (AN) mediated by 2‐cyanoprop‐2‐yl dithiobenzoate was first applied to synthesize polyacrylonitrile (PAN) with a high molecular weight up to 32,800 and a polydispersity index as low as 1.29. The key to success was ascribed to the optimization of the experimental conditions to increase the fragmentation reaction efficiency of the intermediate radical. In accordance with the atom transfer radical polymerization of AN, ethylene carbonate was also a better solvent candidate for providing higher controlled/living RAFT polymerization behaviors than dimethylformamide and dimethyl sulfoxide. The various experimental parameters, including the temperature, the molar ratio of dithiobenzoate to the initiator, the molar ratio of the monomer to dithiobenzoate, the monomer concentration, and the addition of the comonomer, were varied to improve the control of the molecular weight and polydispersity index. The molecular weights of PANs were validated by gel permeation chromatography along with a universal calibration procedure and intrinsic viscosity measurements. ¹H NMR analysis confirmed the high chain‐end functionality of the resultant polymers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1272–1281, 2007     

Capacity augmentation of a supply chain for a short lifecycle product: A system dynamics framework

For an innovative product characterized by short product lifecycle and high demand uncertainty, investment in capacity buildup has to be done cautiously. Otherwise either the product’s market diffusion is impeded or the manufacturer is left with unutilized capacity. Using the right information for making capacity augmentation decisions is critical in facing this challenge. In this paper, we propose a method for identifying critical information flows using the system dynamics model of a two-echelon supply chain. The fundamental premise of system dynamics methodology is that (system) structure determines (its) behavior. Using loop dominance analysis method we study the feedback loop structure of the supply chain system. The outcome is a set of dominant loops that determine the dynamics of capacity growth. It is revealed that the delivery delay information has little effect while the loop that connects retail sales with production order affects the dynamics significantly. Modifying this loop yields appropriate capacity augmentation decisions resulting in higher performance. What-if analyses bring out effects of modifying other structural elements. In conclusion, we claim that the information feedback based methodology is general enough to be useful in designing decision support systems for capacity augmentation. The limitations of the model are also discussed and possible extensions identified.     

Practical stopping criteria for validating safety-critical software by estimating impartial reliability

In this research, we investigate stopping rules for software testing and propose two stopping rules from the aspect of software reliability testing based on the impartial reliability model. The impartial reliability difference (IRD-MP) rule considers the difference between the impartial transition-probability reliabilities estimated for both software developer and consumers at their predetermined prior information levels. The empirical–impartial reliability difference (EIRD-MP) rule suggests stopping a software test when the computed empirical transition reliability is tending to its estimated impartial transition reliability. To insure the high-standard requirement for safety-critical software, both rules take the maximum probability (MP) of untested paths into account.     

Multi-dimensional asymptotically quasi-Toeplitz Markov chains and their application in queueing theory

Multi-dimensional asymptotically quasi-Toeplitz Markov chains with discrete and continuous time are introduced. Ergodicity and non-ergodicity conditions are proven. Numerically stable algorithm to calculate the stationary distribution is presented. An application of such chains in retrial queueing models with Batch Markovian Arrival Process is briefly illustrated. AMS Subject Classifications Primary 60K25 · 60K20     

Non-self-adjoint sturm-liouville operators with matrix potentials

We obtain asymptotic formulas for non-self-adjoint operators generated by the Sturm-Liouville system and quasiperiodic boundary conditions. Using these asymptotic formulas, we obtain conditions on the potential for which the system of root vectors of the operator under consideration forms a Riesz basis.     

Dynamic Nonlinear Modelization of Operational Supply Chain Systems

Supply Chain Management (SCM) is an important activity in all producing facilities and in many organizations to enable vendors, manufacturers and suppliers to interact gainfully and plan optimally their flow of goods and services. To realize this, a dynamic modelling approach for characterizing supply chain activities is opportune, so as to plan efficiently the set of activities over a distributed network in a formal and scientific way. The dynamical system will result so complex that it is not generally possible to specify the functional forms and the parameters of interest, relating outputs to inputs, states and stochastic terms by experiential specification methods. Thus the algorithm that will presented is Data Driven, determining simultaneously the functional forms, the parameters and the optimal control policy from the data available for the supply chain. The aim of this paper is to present this methodology, by considering dynamical aspects of the system, the presence of nonlinear relationships and unbiased estimation procedures to quantify these relations, leading to a nonlinear and stochastic dynamical system representation of the SCM problem. Moreover, the convergence of the algorithm will be proved and the satisfaction of the required statistical conditions demonstrated. Thus SCM problems may be formulated as formal scientific procedures, with well defined algorithms and a precise calculation sequence to determine the best alternative to enact. A “Certainty equivalent principle” will be indicated to ensure that the effects of the inevitable uncertainties will not lead to indeterminate results, allowing the formulation of demonstrably asymptotically optimal management plans.     

Optimal production and rationing decisions in supply chains with information sharing

This paper considers a two-echelon capacitated supply chain with two non-identical retailers and information sharing. We characterize the optimal inventory policies. We also study the benefits of the optimal stock rationing policy over the first come first served (FCFS) and the modified echelon-stock rationing (MESR) policies.     

On then-cutset property

For a partially ordered setP and an elementx ofP, a subsetS ofP is called a cutset forx inP if every element ofS is noncomparable tox and every maximal chain ofP meets {x}∪S. We letc(P) denote the smallest integerk such that every elementx ofP has a cutsetS with ‖S‖?k: Ifc(P)?n we say thatP has then-cutset property. Our results bear on the following question: givenP, what is the smallestn such thatP can be embedded in a partially ordered set having then-cutset property? As usual, 2 ⁿ denotes the Boolean lattice of all subsets of ann-element set, andB _n denotes the set of atoms and co-atoms of 2 ⁿ . We establish the following results: (i) a characterization, by means of forbidden configurations, of whichP can be embedded in a partially ordered set having the 1-cutset property; (ii) ifP contains a copy of 2 ⁿ , thenc(P)?2^[n/2]?1; (iii) for everyn>3 there is a partially ordered setP containing 2 ⁿ such thatc(P)<c(2 ⁿ ); (iv) for every positive integern there is a positive integerN such that, ifB _m is contained in a partially ordered set having then-cutset property, thenm?N.