A forward with backward inventory policy algorithm for nonlinear increasing demand and shortage backorders

The traditional inventory policies have been developed for constant demand processes. In reality, demand is not always stable; it might have an increasing pattern. In this paper, a forward with backward inventory policy algorithm is developed to determine the operational parameters of an inventory system with a nonlinear increasing demand rate, shortage backorders and a finite planning horizon. Numerical experiments are also conducted to compare the results with the existing techniques and to illustrate the applicability of the proposed technique

Inventory Policy for Dependent Demand Where Parent Demand Has Decreasing Pattern

When a product reaches its maturity in its life cycle, some innovations have to be put in that product in order to lengthen its life cycle. Otherwise, that product will be perceived as obsolete. It might affect the demand of that product i.e. the demand become decreasing. Based on the observation that we conducted over two smart phone brands, the phenomena that the demand has declining pattern really happened in the real situation. In addition, the observation shows that the product life cycle is getting shorter. This implies that the manufacturer has to deal with decreasing demand more often. A case study is presented in this paper, in which manufacturer experienced final product with decreasing demand pattern. Some lot sizing techniques, such as Lot for Lot, Silver Meal 1, Silver Meal 2, Least Unit Cost, Part Period Balancing, and Incremental, are tested to solve the inventory policy for both final product (parent) and its components (child). It is concluded that a company should not consider only one component or one level whenever deciding the inventory policy, i.e. production lot size. It is shown by the case study that the best lot sizing technique for a particular parent of product whenever the company only consider the parent is different with the best lot sizing technique whenever the company consider the parent and its child. For the case presented, it is shown that the smallest total cost of parent and child is most likely occurred whenever Silver Meal 2 lot sizing technique is applied in the parent with decreasing demand pattern.

Multi-Echelon Inventory Optimization and Demand-Side Management: Models and Algorithms

Inventory management is a fudamental problem in supply chain management. It is widely used in practice, but it is also intrinsically hard to optimize, even for relatively simple inventory system structures. This challenge has also been heightened under the threat of supply disruptions. Whenever a supply source is disrupted, the inventory system is paralyzed, and tremenduous costs can occur as a consequence. Designing a reliable and robust inventory system that can withstand supply disruptions is vital for an inventory system\u27s performance.First we consider a basic type of inventory network, an assembly system, which produces a single end product from one or several components. A property called long-run balance allows an assembly system to be reduced to a serial system when disruptions are not present. We show that a modified version is still true under disruption risk. Based on this property, we propose a method for reducing the system into a serial system with extra inventory at certain stages that face supply disruptions. We also propose a heuristic for solving the reduced system. A numerical study shows that this heuristic performs very well, yielding significant cost savings when compared with the best-known algorithm.Next we study another basic inventory network structure, a distribution system. We study continuous-review, multi-echelon distribution systems subject to supply disruptions, with Poisson customer demands under a first-come, first-served allocation policy. We develop a recursive optimization heuristic, which applies a bottom-up approach that sequentially approximates the base-stock levels of all the locations. Our numerical study shows that it performs very well.Finally we consider a problem related to smart grids, an area where supply and demand are still decisive factors. Instead of matching supply with demand, as in the first two parts of the dissertation, now we concentrate on the interaction between supply and demand. We consider an electricity service provider that wishes to set prices for a large customer (user or aggregator) with flexible loads so that the resulting load profile matches a predetermined profile as closely as possible. We model the deterministic demand case as a bilevel problem in which the service provider sets price coefficients and the customer responds by shifting loads forward in time. We derive optimality conditions for the lower-level problem to obtain a single-level problem that can be solved efficiently. For the stochastic-demand case, we approximate the consumer\u27s best response function and use this approximation to calculate the service provider\u27s optimal strategy. Our numerical study shows the tractability of the new models for both the deterministic and stochastic cases, and that our pricing scheme is very effective for the service provider to shape consumer demand

Development of an Optimal Replenishment Policy for Human Capital Inventory

A unique approach is developed for evaluating Human Capital (workforce) requirements. With this approach, new ways of measuring personnel availability are proposed and available to ensure that an organization remains ready to provide timely, relevant, and accurate products and services in support of its strategic objectives over its planning horizon. The development of this analysis and methodology was established as an alternative approach to existing studies for determining appropriate hiring and attrition rates and to maintain appropriate personnel levels of effectiveness to support existing and future missions. The contribution of this research is a prescribed method for the strategic analyst to incorporate a personnel and cost simulation model within the framework of Human Resources Human Capital forecasting which can be used to project personnel requirements and evaluate workforce sustainment, at least cost, through time. This will allow various personnel managers to evaluate multiple resource strategies, present and future, maintaining near “perfect” hiring and attrition policies to support its future Human Capital assets

실시간 동적 계획법 및 강화학습 기반의 공공자전거 시스템의 동적 재배치 전략

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 건설환경공학부, 2020. 8. 고승영.The public bicycle sharing system is one of the modes of transportation that can help to relieve several urban problems, such as traffic congestion and air pollution. Because users can pick up and return bicycles anytime and anywhere a station is located, pickup or return failure can occur due to the spatiotemporal imbalances in demand. To prevent system failures, the operator should establish an appropriate repositioning strategy. As the operator makes a decision based on the predicted demand information, the accuracy of forecasting demand is an essential factor. Due to the stochastic nature of demand, however, the occurrence of prediction errors is inevitable. This study develops a stochastic dynamic model that minimizes unmet demand for rebalancing public bicycle sharing systems, taking into account the stochastic demand and the dynamic characteristics of the system. Since the repositioning mechanism corresponds to the sequential decision-making problem, this study applies the Markov decision process to the problem. To solve the Markov decision process, a dynamic programming method, which decomposes complex problems into simple subproblems to derive an exact solution. However, as a set of states and actions of the Markov decision process become more extensive, the computational complexity increases and it is intractable to derive solutions. An approximate dynamic programming method is introduced to derive an approximate solution. Further, a reinforcement learning model is applied to obtain a feasible solution in a large-scale public bicycle network. It is assumed that the predicted demand is derived from the random forest, which is a kind of machine learning technique, and that the observed demand occurred along the Poisson distribution whose mean is the predicted demand to simulate the uncertainty of the future demand. Total unmet demand is used as a key performance indicator in this study. In this study, a repositioning strategy that quickly responds to the prediction error, which means the difference between the observed demand and the predicted demand, is developed and the effectiveness is assessed. Strategies developed in previous studies or applied in the field are also modeled and compared with the results to verify the effectiveness of the strategy. Besides, the effects of various safety buffers and safety stock are examined and appropriate strategies are suggested for each situation. As a result of the analysis, the repositioning effect by the developed strategy was improved compared to the benchmark strategies. In particular, the effect of a strategy focusing on stations with high prediction errors is similar to the effect of a strategy considering all stations, but the computation time can be further reduced. Through this study, the utilization and reliability of the public bicycle system can be improved through the efficient operation without expanding the infrastructure.공공자전거 시스템은 교통혼잡과 대기오염 등 여러 도시문제를 완화할 수 있는 교통수단이다. 대여소가 위치한 곳이면 언제 어디서든 이용자가 자전거를 이용할 수 있는 시스템의 특성상 수요의 시공간적 불균형으로 인해 대여 실패 또는 반납 실패가 발생한다. 시스템 실패를 예방하기 위해 운영자는 적절한 재배치 전략을 수립해야 한다. 운영자는 예측 수요 정보를 전제로 의사결정을 하므로 수요예측의 정확성이 중요한 요소이나, 수요의 불확실성으로 인해 예측 오차의 발생이 불가피하다. 본 연구의 목적은 공공자전거 수요의 불확실성과 시스템의 동적 특성을 고려하여 불만족 수요를 최소화하는 재배치 모형을 개발하는 것이다. 공공자전거 재배치 메커니즘은 순차적 의사결정 문제에 해당하므로, 본 연구에서는 순차적 의사결정 문제를 모형화할 수 있는 마르코프 결정 과정을 적용한다. 마르코프 결정 과정을 풀기 위해 복잡한 문제를 간단한 부문제로 분해하여 정확해를 도출하는 동적 계획법을 이용한다. 하지만 마르코프 결정 과정의 상태 집합과 결정 집합의 크기가 커지면 계산 복잡도가 증가하므로, 동적 계획법을 이용한 정확해를 도출할 수 없다. 이를 해결하기 위해 근사적 동적 계획법을 도입하여 근사해를 도출하며, 대규모 공공자전거 네트워크에서 가능해를 얻기 위해 강화학습 모형을 적용한다. 장래 공공자전거 이용수요의 불확실성을 모사하기 위해, 기계학습 기법의 일종인 random forest로 예측 수요를 도출하고, 예측 수요를 평균으로 하는 포아송 분포를 따라 수요를 확률적으로 발생시켰다. 본 연구에서는 관측 수요와 예측 수요 간의 차이인 예측오차에 빠르게 대응하는 재배치 전략을 개발하고 효과를 평가한다. 개발된 전략의 우수성을 검증하기 위해, 기존 연구의 재배치 전략 및 현실에서 적용되는 전략을 모형화하고 결과를 비교한다. 또한, 재고량의 안전 구간 및 안전재고량에 관한 민감도 분석을 수행하여 함의점을 제시한다. 개발된 전략의 효과를 분석한 결과, 기존 연구의 전략 및 현실에서 적용되는 전략보다 개선된 성능을 보이며, 특히 예측오차가 큰 대여소를 탐색하는 전략이 전체 대여소를 탐색하는 전략과 재배치 효과가 유사하면서도 계산시간을 절감할 수 있는 것으로 나타났다. 공공자전거 인프라를 확대하지 않고도 운영의 효율화를 통해 공공자전거 시스템의 이용률 및 신뢰성을 제고할 수 있고, 공공자전거 재배치에 관한 정책적 함의점을 제시한다는 점에서 본 연구의 의의가 있다.Chapter 1. Introduction １ 1.1 Research Background and Purposes １ 1.2 Research Scope and Procedure ７ Chapter 2. Literature Review １０ 2.1 Vehicle Routing Problems １０ 2.2 Bicycle Repositioning Problem １２ 2.3 Markov Decision Processes ２３ 2.4 Implications and Contributions ２６ Chapter 3. Model Formulation ２８ 3.1 Problem Definition ２８ 3.2 Markov Decision Processes ３４ 3.3 Demand Forecasting ４０ 3.4 Key Performance Indicator (KPI) ４５ Chapter 4. Solution Algorithms ４７ 4.1 Exact Solution Algorithm ４７ 4.2 Approximate Dynamic Programming ５０ 4.3 Reinforcement Learning Method ５２ Chapter 5. Numerical Example ５５ 5.1 Data Overview ５５ 5.2 Experimental Design ６１ 5.3 Algorithm Performance ６６ 5.4 Sensitivity Analysis ７４ 5.5 Large-scale Cases ７６ Chapter 6. Conclusions ８２ 6.1 Conclusions ８２ 6.2 Future Research ８３ References ８６ 초 록 ９２Docto

Constructive solution methodologies to the capacitated newsvendor problem and surrogate extension

The newsvendor problem is a single-period stochastic model used to determine the order quantity of perishable product that maximizes/minimizes the profit/cost of the vendor under uncertain demand. The goal is to fmd an initial order quantity that can offset the impact of backlog or shortage caused by mismatch between the procurement amount and uncertain demand. If there are multiple products and substitution between them is feasible, overstocking and understocking can be further reduced and hence, the vendor\u27s overall profit is improved compared to the standard problem. When there are one or more resource constraints, such as budget, volume or weight, it becomes a constrained newsvendor problem. In the past few decades, many researchers have proposed solution methods to solve the newsvendor problem. The literature is first reviewed where the performance of each of existing model is examined and its contribution is reported. To add to these works, it is complemented through developing constructive solution methods and extending the existing published works by introducing the product substitution models which so far has not received sufficient attention despite its importance to supply chain management decisions. To illustrate this dissertation provides an easy-to-use approach that utilizes the known network flow problem or knapsack problem. Then, a polynomial in fashion algorithm is developed to solve it. Extensive numerical experiments are conducted to compare the performance of the proposed method and some existing ones. Results show that the proposed approach though approximates, yet, it simplifies the solution steps without sacrificing accuracy. Further, this dissertation addresses the important arena of product substitute models. These models deal with two perishable products, a primary product and a surrogate one. The primary product yields higher profit than the surrogate. If the demand of the primary exceeds the available quantity and there is excess amount of the surrogate, this excess quantity can be utilized to fulfill the shortage. The objective is to find the optimal lot sizes of both products, that minimize the total cost (alternatively, maximize the profit). Simulation is utilized to validate the developed model. Since the analytical solutions are difficult to obtain, Mathematical software is employed to find the optimal results. Numerical experiments are also conducted to analyze the behavior of the optimal results versus the governing parameters. The results show the contribution of surrogate approach to the overall performance of the policy. From a practical perspective, this dissertation introduces the applications of the proposed models and methods in different industries such as inventory management, grocery retailing, fashion sector and hotel reservation

Three Essays on Energy Economics

This dissertation focuses on the economics of electricity generation. I aim to answer three main questions: After controlling for outside market forces, how did acid rain regulation impact Eastern coal production? How have the fundamental relationships in the natural gas market changed since deregulation, especially given the rise of production from shale resources? And how have sub-state policies affected the adoption of residential solar generation installations? For each question, I use economic tools to provide empirical answers which will contribute both to the academic literature as well as energy policy.;My first essay looks at the coal production in the Eastern US from 1983-2012. It is widely understood that the quantity of coal produced in this region declined during this time period, though its causes are debated. While some have identified the cause to be outside economic forces, the prevailing view is that federal regulation was the main driver. By controlling for outside market forces, this paper is able to estimate the effect that the differing regulatory periods have had on coal production. Results demonstrate how in general the regulatory phases of the Acid Rain Program are associated with decreases in production in the Illinois and Appalachian basins, however with varying magnitudes. Further, there are some areas that saw some increases. The essay also measure the mitigating impact that the installation of \u27scrubber\u27 units had on production. Overall, this essay provides a more nuanced look at the relationship between coal production and regulation during this time period.;The second essay in this dissertation models the natural gas market. Since the complete deregulation of the market in 1993, there have been significant changes. Most notably, the rapid rise of production from shale resources has greatly increased the supply and decreased the price of the commodity. Where for many years a net importer, the US is now predicted to be a net exporter of natural gas within the next year. This massive change has altered the fundamental relationships in the market. This essay utilizes recently developed methodology to estimate how these relationships have changed over time. Further, given our research design we are able to estimate how the supply and demand elasticities have been influenced in the new era of abundant and cheap natural gas. Results provide a more nuanced view of the natural gas market, and allow for a better understanding of its drivers.;My third essay measures the impact that certain policies have had in the residential solar market. Specifically, I estimate the impact on residential solar adoption associated with sub-state policies, enacted at the municipal, county, or utility level. To capture the clustering and peer effects in the adoption of residential solar that have been described in the literature, I utilize spatial econometric methods. To better model the nested nature of state and county renewable policies, a Bayesian hierarchical model is used. Results suggest that sub-state policies are associated with positive and significant increases in per-capita residential solar installations and capacity additions

Algorithmes d'approximation pour la gestion de stock

Nous considérons des problèmes de gestion des stocks multi-échelon à temps périodique avec des demandes non stationnaires. Ces hypothèses sur la demande apparaissent notamment lorsque des prévisions sur la demande sont utilisées dynamiquement (de nouvelles prévisions sont fournies à chaque période). La structure des coûts comprend des coûts fixes et variables d approvisionnement, des coûts de stockage et des coûts de mise en attente des demandes. Le délai d approvisionnement est supposé constant. Le problème consistant à déterminer la politique optimale qui minimise les coûts sur un horizon fini peut être formulé grâce à un programme dynamique. Dans le cadre déterministe, les problèmes auxquels nous nous intéressons sont le plus souvent NP-difficiles, ce qui fait rapidement exploser l espace d état. Il devient alors nécessaire de recourir à des heuristiques. Nous nous orientons vers la recherche d'algorithmes d'approximation combinatoires pour le problème One Warehouse Multi Retailers et plus généralement pour des systèmes de distribution divergents. Nous nous intéresserons dans un premier temps à des systèmes de distribution à deux étages avec un entrepôt central et des entrepôts secondaires qui voient la demande finale. Dans un deuxième temps, des structures logistiques plus complexes pourront être considérées. L objectif sera de proposer des heuristiques originales, basées sur des techniques de répartition des coûts, de les comparer numériquement à la politique optimale sur de petites instances et, si possible, d établir des garanties de performance.Inventory management has always been a major component of the field of operations research and numerous models derived from the industry aroused the interest of both the researchers and the practitioners. Within this framework, our work focuses on several classical inventory problems, for which no tractable method is known to compute an optimal solution. Specifically, we study deterministic models, in which the demands of the customers are known in advance, and we propose approximation techniques for each of the corresponding problems that build feasible approximate solutions while remaining computationally tractable. We first consider continuous-time models with a single facility when demand and holding costs are time-dependent. We present a simple technique that balances the different costs incurred by the system and we use this concept to build approximation methods for a large class of such problems. The second part of our work focuses on a discrete time model, in which a central warehouse supplies several retailers facing the final customers demands. This problem is known to be NP-hard, thus finding an optimal solution in polynomial time is unrealistic unless P=NP. We introduce a new decomposition of the system into simple subproblems and a method to recombine the solutions to these subproblems into a feasible solution to the original problem. The resulting algorithm has a constant performance guarantee and can be extended to several generalizations of the system, including more general cost structures and problems with backlogging or lost-sales.SAVOIE-SCD - Bib.électronique (730659901) / SudocGRENOBLE1/INP-Bib.électronique (384210012) / SudocGRENOBLE2/3-Bib.électronique (384219901) / SudocSudocFranceF

Computing policy parameters for stochastic inventory control using stochastic dynamic programming approaches

The objective of this work is to introduce techniques for the computation of optimal and near-optimal inventory control policy parameters for the stochastic inventory control problem under Scarf’s setting. A common aspect of the solutions presented herein is the usage of stochastic dynamic programming approaches, a mathematical programming technique introduced by Bellman. Stochastic dynamic programming is hybridised with branch-and-bound, binary search, constraint programming and other computational techniques to develop innovative and competitive solutions. In this work, the classic single-item, single location-inventory control with penalty cost under the independent stochastic demand is extended to model a fixed review cost. This cost is charged when the inventory level is assessed at the beginning of a period. This operation is costly in practice and including it can lead to significant savings. This makes it possible to model an order cancellation penalty charge. The first contribution hereby presented is the first stochastic dynamic program- ming that captures Bookbinder and Tan’s static-dynamic uncertainty control policy with penalty cost. Numerous techniques are available in the literature to compute such parameters; however, they all make assumptions on the de- mand probability distribution. This technique has many similarities to Scarf’s stochastic dynamic programming formulation, and it does not require any ex- ternal solver to be deployed. Memoisation and binary search techniques are deployed to improve computational performances. Extensive computational studies show that this new model has a tighter optimality gap compared to the state of the art. The second contribution is to introduce the first procedure to compute cost- optimal parameters for the well-known (R, s, S) policy. Practitioners widely use such a policy; however, the determination of its parameters is considered com- putationally prohibitive. A technique that hybridises stochastic dynamic pro- gramming and branch-and-bound is presented, alongside with computational enhancements. Computing the optimal policy allows the determination of op- timality gaps for future heuristics. This approach can solve instances of consid- erable size, making it usable by practitioners. The computational study shows the reduction of the cost that such a system can provide. Thirdly, this work presents the first heuristics for determining the near-optimal parameters for the (R,s,S) policy. The first is an algorithm that formally models the (R,s,S) policy computation in the form of a functional equation. The second is a heuristic formed by a hybridisation of (R,S) and (s,S) policy parameters solvers. These heuristics can compute near-optimal parameters in a fraction of time compared to the exact methods. They can be used to speed up the optimal branch-and-bound technique. The last contribution is the introduction of a technique to encode dynamic programming in constraint programming. Constraint programming provides the user with an expressive modelling language and delegates the search for the solution to a specific solver. The possibility to seamlessly encode dynamic programming provides new modelling options, e.g. the computation of optimal (R,s,S) policy parameters. The performances in this specific application are not competitive with the other techniques proposed herein; however, this encoding opens up new connections between constraint programming and dynamic programming. The encoding allows deploying DP based constraints in modelling languages such as MiniZinc. The computational study shows how this technique can outperform a similar encoding for mixed-integer programming