Systems Statistical Engineering – Hierarchical Fuzzy Constraint Propagation

Driven by a growing requirement during the 21st century for the integration of rigorous statistical analyses in engineering research, there has been a movement within the statistics and quality communities to evolve a unified statistical engineering body of knowledge (Hoerl & Snee, 2010). Systems Statistical Engineering research seeks to integrate causal Bayesian hierarchical modeling (Pearl, 2009) and cybernetic control theory within Beer\u27s Viable System Model (S Beer, 1972; Stafford Beer, 1979, 1985) and the Complex Systems Governance framework (Keating, 2014; Keating & Katina, 2015, 2016) to produce multivariate systemic models for robust dynamic systems mission performance. (Cotter & Quigley, 2018) set forth the Bayesian systemic hierarchical constraint propagation theoretical basis for modeling the amplification and attenuation effects of environmental constraints propagated into systemic variability and variety. In their theoretical development, they simplified the analysis to only deterministic constraints, which models only the effect of statistical risks of failure. Imprecision and uncertainty in the assessment of environmental constraints will induce additional variance components in systemic variability and variety. To make causal Bayesian hierarchical modeling more capable of capturing and representing the imprecise and uncertain nature of environments, we must incorporate rough or fuzzy functions and boundaries to model imprecision and grey boundaries to model uncertainty in constraint propagation at each system level to measure the overall impact on the organization variability and variety. This paper sets forth a proposed research method to incorporate rough, fuzzy, and Grey set theories into Systems Statistical Engineering causal Bayesian hierarchical constraints modeling

A Literature Review On Combining Heuristics and Exact Algorithms in Combinatorial Optimization

There are several approaches for solving hard optimization problems. Mathematical programming techniques such as (integer) linear programming-based methods and metaheuristic approaches are two extremely effective streams for combinatorial problems. Different research streams, more or less in isolation from one another, created these two. Only several years ago, many scholars noticed the advantages and enormous potential of building hybrids of combining mathematical programming methodologies and metaheuristics. In reality, many problems can be solved much better by exploiting synergies between these approaches than by “pure” classical algorithms. The key question is how to integrate mathematical programming methods and metaheuristics to achieve such benefits. This paper reviews existing techniques for such combinations and provides examples of using them for vehicle routing problems

Electric Vehicle Routing Problem – Models and Algorithms

The transportation sector is a major greenhouse gas emitter that is heavily regulated to reduce its dependence on oil. These regulations along with the growing customer awareness of global warming have led to the investigation of new transportation problems that consider using eco-friendly vehicle fleets. Promising alternatives to traditional fleets include alternative fuel vehicles (AFVs) and electric vehicles (EVs). These twenty-first-century vehicles offer an appealing advantage of consistently reducing their environmental impact, but due to the current technology, they exhibit bothersome limitations. The short driving range along with limited charging infrastructure may consequently cause issues related to range anxiety, i.e., the fear of not having enough battery charge to reach the desired destination (or the nearest charging station). Fortunately, range anxiety can be effectively mitigated by careful route planning; for example, by planning in advance when and where to recharge the battery so that the total energy consumption and the risk of battery depletion are minimized. The last decade witnessed the investigation of many new models, formulations and solution approaches pertaining to green logistics. In this dissertation we investigated two variants of electric vehicle routing problem; namely, the Capacitated Electric Vehicle Routing Problem (C-EVRP) and the Electric Vehicle Routing Problem with Time Windows (EVRPTW). C-EVRP is a variant of the standard Capacitated Vehicle Routing Problem (CVRP), where each vehicle is powered exclusively by electricity stored in its rechargeable battery. We propose three exact approaches for solving C-EVRP. The first requires solving a compact polynomial-sized formulation, while the second is a branch-and-cut algorithm. An original feature of this algorithm is that it includes an exact separation procedure for the so-called rounded capacity constraints that is proposed for the first time in the literature. Finally, the third approach is a hybrid algorithm that requires solving an augmented variant of the compact formulation. We provide evidence that the proposed algorithms are able to solve medium-to-large size instances optimally while requiring moderate CPU times. In the case of EVRPTW, where customers should be visited only during fixed time windows, we propose a novel hybrid variable neighborhood search/tabu search metaheuristic making use of a wide range of classical and large neighborhood search operators. Moreover, our algorithm allows visiting infeasible solutions, which is achieved by means of an extended objective function for the evaluation of both feasible and infeasible solutions. In the numerical studies we demonstrate the strong performance of our metaheuristic and show that our algorithm is competitive when compared to existing methods

Exact approaches for routing capacitated electric vehicles

We investigate a variant of the standard Capacitated Vehicle Routing Problem (CVRP), where each vehicle is powered exclusively by electricity stored in its rechargeable battery. Consequently, each vehicle should visit not only customer nodes but also (possibly) some charging stations before the battery got depleted. The importance of this problem stems from the fact that logistics companies are increasingly relying on electric vehicles in urban distribution. We propose three exact approaches. The first one requires solving a compact polynomial-sized formulation. The second approach is a branch-and-cut algorithm. An original feature of this algorithm is that it embeds the first exact separation of the well-known rounded capacity constraints. Finally, the third approach is a hybrid algorithm that requires solving an augmented variant of the compact formulation. We report the results of a computational study that was carried out on a set of 125 instances, providing evidence that the polynomial-sized formulation can consistently solve instances having up to 30 customer nodes and 21 charging stations, and that the hybrid algorithm solves some instances having up to 100 customer nodes and 21 charging stations while requiring moderate CPU times. Furthermore, the proposed approach was shown to exhibit limitations in solving some large-scale tightly-constrained instances. 2020 Elsevier LtdScopu

Simultaneous control on lead time elements and ordering cost for an inflationary inventory-production model with mixture of normal distributions LTD under finite capacity

The significance of inflation and time value of money in inventory/production systems is indisputable for modern decision makers. Consequently, the paper aims to study the influence of inflationary condition on a stochastic continuous review integrated vendor–buyer inventory system in the presence of a multilevel reorder strategy for the system. It is considered that lead time components and ordering cost are controllable. Lead time is decomposed into its components: set-up time, production time and transportation time. Based on lead time components, demand during the lead time for different batches is assumed to be a mixture of normal distributions. The objective is to minimize joint inventory expected cost by simultaneously optimizing ordering quantity, reorder points of different batches, ordering cost, setup time, transportation time, production time and a number of deliveries under space constraint while the lead time demand follows a normal distribution. To minimize the expected inventory cost, a Lagrange multiplier method is applied in order to solve the problem, and an iterative algorithm is designed to find optimal values. The behavior of the model is illustrated in numerical examples. It was found that for a fixed value of transportation time, setup time and number of batches, with an augment in inflation rate, the two optimal reorder points for different batches were increased. Also, optimum joint expected annual cost with inflation for two kinds of customers’ demand is larger than one kind of customers’ demand. Furthermore, sensitivity analysis and managerial insights are given to show the applicability of the model