Stochastic Reorder Point-Lot Size (r,Q) Inventory Model under Maximum Entropy Principle

This paper takes into account the continuous-review reorder point-lot size (r,Q) inventory model under stochastic demand, with the backorders-lost sales mixture. Moreover, to reflect the practical circumstance in which full information about the demand distribution lacks, we assume that only an estimate of the mean and of the variance is available. Contrarily to the typical approach in which the lead-time demand is supposed Gaussian or is obtained according to the so-called minimax procedure, we take a different perspective. That is, we adopt the maximum entropy principle to model the lead-time demand distribution. In particular, we consider the density that maximizes the entropy over all distributions with given mean and variance. With the aim of minimizing the expected total cost per time unit, we then propose an exact algorithm and a heuristic procedure. The heuristic method exploits an approximated expression of the total cost function achieved by means of an ad hoc first-order Taylor polynomial. We finally carry out numerical experiments with a twofold objective. On the one hand we examine the efficiency of the approximated solution procedure. On the other hand we investigate the performance of the maximum entropy principle in approximating the true lead-time demand distribution

Weighted Round Robin (WRR) Based Replenishment Model in Vendor Managed Inventory (VMI) System

Vendor managed inventory (VMI) is a popular supply chain system where vendor or supplier take responsibility and decision in managing its customers’ inventory. Two important goals of the VMI are improving service level and maintaining inventory still low and available. Many studies in VMI compare their performance with the traditional system. Unfortunately, studies in improving VMI performance are rare. This work aims to improve VMI by implementing Weighted Round Robin (WRR), a popular scheduling model in computer system, in the replenishment model in VMI. WRR is popular because of its load balancing nature. Environment in this work is two-echelon supply chain. The vendor is a multi-product manufacturer. The customers are retailers. This WRR based replenishment model is then compared with two common replenishment models: (s, S) model and (r, Q) model. In this work, we observe two performance parameters: sales and inventory condition. Based on the simulation result, it is shown that the WRR model performs better than the existing (s, S) model and (r, Q) model and it occurs in most of the observed variables. In the certain condition, performance of the WRR model compared with the (s, S) model and the (r, Q) model is as follows. The WRR model performs 31 percent better than the (s, S) model and 12 percent better than the (r, Q) model in success ratio. Manufacturer’s stock in the WRR model is only 36 percent than in the (s, S) model and 40 percent than in the (r, Q) model. Total stock in the supply chain in the WRR model is only 63 percent than in the (s, S) model and 89 percent than in the (r, Q) model

Weighted Round Robin (WRR) Based Replenishment Model in Vendor Managed Inventory (VMI) System

Vendor managed inventory (VMI) is a popular supply chain system where vendor or supplier take responsibility and decision in managing its customers’ inventory. Two important goals of the VMI are improving service level and maintaining inventory still low and available. Many studies in VMI compare their performance with the traditional system. Unfortunately, studies in improving VMI performance are rare. This work aims to improve VMI by implementing Weighted Round Robin (WRR), a popular scheduling model in computer system, in the replenishment model in VMI. WRR is popular because of its load balancing nature. Environment in this work is two-echelon supply chain. The vendor is a multi-product manufacturer. The customers are retailers. This WRR based replenishment model is then compared with two common replenishment models: (s, S) model and (r, Q) model. In this work, we observe two performance parameters: sales and inventory condition. Based on the simulation result, it is shown that the WRR model performs better than the existing (s, S) model and (r, Q) model and it occurs in most of the observed variables. In the certain condition, performance of the WRR model compared with the (s, S) model and the (r, Q) model is as follows. The WRR model performs 31 percent better than the (s, S) model and 12 percent better than the (r, Q) model in success ratio. Manufacturer’s stock in the WRR model is only 36 percent than in the (s, S) model and 40 percent than in the (r, Q) model. Total stock in the supply chain in the WRR model is only 63 percent than in the (s, S) model and 89 percent than in the (r, Q) model

Optimising replenishment policy in an integrated supply chain with controllable lead time and backorders-lost sales mixture

This paper aims to optimize the inventory replenishment policy in an integrated supply chain consisting of a single supplier and a single buyer. The system under consideration has the features such as backorders-lost sales mixture, controllable lead time, stochastic demand, and stockout costs. The underlying problem has not been studied in the literature. We present a novel approach to formulate the optimization problem, which is able to satisfy the constraint on the number of admissible stockouts per time unit. To solve the optimization problem, we propose two algorithms: an exact algorithm and a heuristic algorithm. These two algorithms are developed based on some analytical properties that we established by analysing the cost function in relation to the decision variables. The heuristic algorithm employs an approximation technique based on an ad-hoc Taylor series expansion. Extensive numerical experiments are provided to demonstrate the effectiveness of the proposed algorithms

Efficient near-optimal procedures for some inventory models with backorders-lost sales mixture and controllable lead time, under continuous or periodic review

This paper considers a number of inventory models with backorders-lost sales mixture, stockout costs, and controllable lead time. The lead time is a linear function of the lot size and includes a constant term that is made of several components. These lot-size-independent components are assumed to be controllable. Both single- and double-echelon inventory systems, under periodic or continuous review, are considered. To authors knowledge, these models have never been previously studied in literature. The purpose of this paper is to analyse and optimize these novel inventory models. The optimization is carried out by means of heuristics that work on an ad hoc approximation of the cost functions. This peculiarity permits to exploit closed-form expressions that make the optimization procedure simpler and more readily applicable in practice than standard approaches. Finally, numerical experiments investigate the efficiency of the proposed heuristics and the sensitivity of the developed models

Confidence-based Optimization for the Newsvendor Problem

We introduce a novel strategy to address the issue of demand estimation in single-item single-period stochastic inventory optimisation problems. Our strategy analytically combines confidence interval analysis and inventory optimisation. We assume that the decision maker is given a set of past demand samples and we employ confidence interval analysis in order to identify a range of candidate order quantities that, with prescribed confidence probability, includes the real optimal order quantity for the underlying stochastic demand process with unknown stationary parameter(s). In addition, for each candidate order quantity that is identified, our approach can produce an upper and a lower bound for the associated cost. We apply our novel approach to three demand distribution in the exponential family: binomial, Poisson, and exponential. For two of these distributions we also discuss the extension to the case of unobserved lost sales. Numerical examples are presented in which we show how our approach complements existing frequentist - e.g. based on maximum likelihood estimators - or Bayesian strategies.Comment: Working draf

Sustainable Inventory Management Model for High-Volume Material with Limited Storage Space under Stochastic Demand and Supply

Inventory management and control has become an important management function, which is vital in ensuring the efficiency and profitability of a company’s operations. Hence, several research studies attempted to develop models to be used to minimise the quantities of excess inventory, in order to reduce their associated costs without compromising both operational efficiency and customers’ needs. The Economic Order Quantity (EOQ) model is one of the most used of these models; however, this model has a number of limiting assumptions, which led to the development of a number of extensions for this model to increase its applicability to the modern-day business environment. Therefore, in this research study, a sustainable inventory management model is developed based on the EOQ concept to optimise the ordering and storage of large-volume inventory, which deteriorates over time, with limited storage space, such as steel, under stochastic demand, supply and backorders. Two control systems were developed and tested in this research study in order to select the most robust system: an open-loop system, based on direct control through which five different time series for each stochastic variable were generated, before an attempt to optimise the average profit was conducted; and a closed-loop system, which uses a neural network, depicting the different business and economic conditions associated with the steel manufacturing industry, to generate the optimal control parameters for each week across the entire planning horizon. A sensitivity analysis proved that the closed-loop neural network control system was more accurate in depicting real-life business conditions, and more robust in optimising the inventory management process for a large-volume, deteriorating item. Moreover, due to its advantages over other techniques, a meta-heuristic Particle Swarm Optimisation (PSO) algorithm was used to solve this model. This model is implemented throughout the research in the case of a steel manufacturing factory under different operational and extreme economic scenarios. As a result of the case study, the developed model proved its robustness and accuracy in managing the inventory of such a unique industry

Quantitative Models in Life Science Business

This open access book explores the field of life science business from a multidisciplinary perspective. Applying statistical, mathematical, game-theoretic, and data science tools to pharmaceutical and biotechnology business endeavors, the book describes value creation, value maintenance, and value realization in the life sciences as a sequence of processes using the quantitative language of applied mathematics. Written by experts from a variety of fields, the contributions illustrate the shift from a deterministic to a stochastic view of the processes involved, offering a new perspective on life sciences economics. The book covers topics such as valuing and managing intellectual property in life science, licensing in the pharmaceutical business, outsourcing pharmaceutical R&D, and stochastic modelling of a pharmaceutical supply chain. The book will appeal to scholars of economics and the life sciences, as well as to professionals in chemical and pharmaceutical industries