Aggregate constrained inventory systems with independent multi-product demand: control practices and theoretical limitations

In practice, inventory managers are often confronted with a need to consider one or more aggregate constraints. These aggregate constraints result from available workspace, workforce, maximum investment or target service level. We consider independent multi-item inventory problems with aggregate constraints and one of the following characteristics: deterministic leadtime demand, newsvendor, basestock policy, rQ policy and sS policy. We analyze some recent relevant references and investigate the considered versions of the problem, the proposed model formulations and the algorithmic approaches. Finally we highlight the limitations from a practical viewpoint for these models and point out some possible direction for future improvements

[[alternative]]Ordering Strategy of the Inventory System for Considering the Effect of Controllable Lead Time, Time Value of Money and Inflation

計畫編號：NSC91-2416-H032-005研究期間：200208~200307研究經費：394,000[[sponsorship]]行政院國家科學委員

The Fuzzy Economic Order Quantity Problem with a Finite Production Rate and Backorders

The track of developing Economic Order Quantity (EOQ) models with uncertainties described as fuzzy numbers has been very lucrative. In this paper, a fuzzy Economic Production Quantity (EPQ) model is developed to address a specific problem in a theoretical setting. Not only is the production time finite, but also backorders are allowed. The uncertainties, in the industrial context, come from the fact that the production availability is uncertain as well as the demand. These uncertainties will be handled with fuzzy numbers and the analytical solution to the optimization problem will be obtained. A theoretical example from the process industry is also given to illustrate the new model

The Distribution-Free Newsboy Problem with Multiple Discounts and Upgrades

Most papers on the newsboy problem assume that excess inventory is either sold after discount or discarded. In the real world, overstocks are handled with multiple discounts, upgrades, or a combination of these measures. For example, a seller may offer a series of progressively increasing discounts for units that remain on the shelf, or the seller may use incrementally applied innovations aimed at stimulating greater product sophistication. Moreover, the normal distribution does not provide better protection than other distributions with the same mean and variance. In this paper, we find the differences between normal distribution approaches and distribution-free approaches in four scenarios with mean and variance of demand as the only available data to decision-makers. First, we solve the newsboy problem by considering multiple discounts. Second, we formulate and solve the newsboy problem by considering multiple upgrades. Third, we formulate and solve a mixed newsboy problem characterized with multiple discounts and upgrades. Finally, we extend the model to solve a multiproduct newsboy problem with a storage or a budget constraint and develop an algorithm to find the solutions of the models. Concavity of the models is proved analytically. Extensive computational experiments are presented to verify the robustness of the distribution-free approach. The results show that the distribution-free approach is robust

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

Proactive management of uncertainty to improve scheduling robustness in proces industries

Dinamisme, capacitat de resposta i flexibilitat són característiques essencials en el desenvolupament de la societat actual. Les noves tendències de globalització i els avenços en tecnologies de la informació i comunicació fan que s'evolucioni en un entorn altament dinàmic i incert. La incertesa present en tot procés esdevé un factor crític a l'hora de prendre decisions, així com un repte altament reconegut en l'àrea d'Enginyeria de Sistemes de Procés (PSE). En el context de programació de les operacions, els models de suport a la decisió proposats fins ara, així com també software comercial de planificació i programació d'operacions avançada, es basen generalment en dades estimades, assumint implícitament que el programa d'operacions s'executarà sense desviacions. La reacció davant els efectes de la incertesa en temps d'execució és una pràctica habitual, però no sempre resulta efectiva o factible. L'alternativa és considerar la incertesa de forma proactiva, és a dir, en el moment de prendre decisions, explotant el coneixement disponible en el propi sistema de modelització.Davant aquesta situació es plantegen les següents preguntes: què s'entén per incertesa? Com es pot considerar la incertesa en el problema de programació d'operacions? Què s'entén per robustesa i flexibilitat d'un programa d'operacions? Com es pot millorar aquesta robustesa? Quins beneficis comporta? Aquesta tesi respon a aquestes preguntes en el marc d'anàlisis operacionals en l'àrea de PSE. La incertesa es considera no de la forma reactiva tradicional, sinó amb el desenvolupament de sistemes proactius de suport a la decisió amb l'objectiu d'identificar programes d'operació robustos que serveixin com a referència pel nivell inferior de control de planta, així com també per altres centres en un entorn de cadenes de subministrament. Aquest treball de recerca estableix les bases per formalitzar el concepte de robustesa d'un programa d'operacions de forma sistemàtica. Segons aquest formalisme, els temps d'operació i les ruptures d'equip són considerats inicialment com a principals fonts d'incertesa presents a nivell de programació de la producció. El problema es modelitza mitjançant programació estocàstica, desenvolupant-se finalment un entorn d'optimització basat en simulació que captura les múltiples fonts d'incertesa, així com també estratègies de programació d'operacions reactiva, de forma proactiva. La metodologia desenvolupada en el context de programació de la producció s'estén posteriorment per incloure les operacions de transport en sistemes de múltiples entitats i incertesa en els temps de distribució. Amb aquesta perspectiva més àmplia del nivell d'operació s'estudia la coordinació de les activitats de producció i transport, fins ara centrada en nivells estratègic o tàctic. L'estudi final considera l'efecte de la incertesa en la demanda en les decisions de programació de la producció a curt termini. El problema s'analitza des del punt de vista de gestió del risc, i s'avaluen diferents mesures per controlar l'eficiència del sistema en un entorn incert.En general, la tesi posa de manifest els avantatges en reconèixer i modelitzar la incertesa, amb la identificació de programes d'operació robustos capaços d'adaptar-se a un ampli rang de situacions possibles, enlloc de programes d'operació òptims per un escenari hipotètic. La metodologia proposada a nivell d'operació es pot considerar com un pas inicial per estendre's a nivells de decisió estratègics i tàctics. Alhora, la visió proactiva del problema permet reduir el buit existent entre la teoria i la pràctica industrial, i resulta en un major coneixement del procés, visibilitat per planificar activitats futures, així com també millora l'efectivitat de les tècniques reactives i de tot el sistema en general, característiques altament desitjables per mantenir-se actiu davant la globalitat, competitivitat i dinàmica que envolten un procés.Dynamism, responsiveness, and flexibility are essential features in the development of the current society. Globalization trends and fast advances in communication and information technologies make all evolve in a highly dynamic and uncertain environment. The uncertainty involved in a process system becomes a critical problem in decision making, as well as a recognized challenge in the area of Process Systems Engineering (PSE). In the context of scheduling, decision-support models developed up to this point, as well as commercial advanced planning and scheduling systems, rely generally on estimated input information, implicitly assuming that a schedule will be executed without deviations. The reaction to the effects of the uncertainty at execution time becomes a common practice, but it is not always effective or even possible. The alternative is to address the uncertainty proactively, i.e., at the time of reasoning, exploiting the available knowledge in the modeling procedure itself. In view of this situation, the following questions arise: what do we understand for uncertainty? How can uncertainty be considered within scheduling modeling systems? What is understood for schedule robustness and flexibility? How can schedule robustness be improved? What are the benefits? This thesis answers these questions in the context of operational analysis in PSE. Uncertainty is managed not from the traditional reactive viewpoint, but with the development of proactive decision-support systems aimed at identifying robust schedules that serve as a useful guidance for the lower control level, as well as for dependent entities in a supply chain environment. A basis to formalize the concept of schedule robustness is established. Based on this formalism, variable operation times and equipment breakdowns are first considered as the main uncertainties in short-term production scheduling. The problem is initially modeled using stochastic programming, and a simulation-based stochastic optimization framework is finally developed, which captures the multiple sources of uncertainty, as well as rescheduling strategies, proactively. The procedure-oriented system developed in the context of production scheduling is next extended to involve transport scheduling in multi-site systems with uncertain travel times. With this broader operational perspective, the coordination of production and transport activities, considered so far mainly in strategic and tactical analysis, is assessed. The final research point focuses on the effect of demands uncertainty in short-term scheduling decisions. The problem is analyzed from a risk management viewpoint, and alternative measures are assessed and compared to control the performance of the system in the uncertain environment.Overall, this research work reveals the advantages of recognizing and modeling uncertainty, with the identification of more robust schedules able to adapt to a wide range of possible situations, rather than optimal schedules for a hypothetical scenario. The management of uncertainty proposed from an operational perspective can be considered as a first step towards its extension to tactical and strategic levels of decision. The proactive perspective of the problem results in a more realistic view of the process system, and it is a promising way to reduce the gap between theory and industrial practices. Besides, it provides valuable insight on the process, visibility for future activities, as well as it improves the efficiency of reactive techniques and of the overall system, all highly desirable features to remain alive in the global, competitive, and dynamic process environment

Applying fuzzy PERT in cycle time management for supply chain system

As the fast technology evolution and the globalization trend, the competition among businesses transform into supply chain network gradually. However, the operation performance of the supply chain network influenced by many uncertain factors. These uncertain influence factors include the demand of the customer, the response time of delivery, operation lead time, stock level and cost. Under foregoing conditions, enterprises cannot control the variations in actual environment precisely and satisfy customers’ requirements. Therefore, the linguistic variables are used to express these uncertainties in this paper. First, this paper presents a procedure to transform the operation processes of the supply chain network into a diagram to indicate the activities among members of supply chain. Second, combining fuzzy set theory with the program evaluation and review technique (PERT) to estimate the cycle time of supply chain system. According to the fuzzy PERT model, we can calculate the cycle time and find out the critical path of a supply chain system. Furthermore, we can compute the possibility of the order fulfillment of a supply chain system. Finally, a numerical simulation is presented to illustrate the procedure of this proposed model

A Fuzzy Economic Order Quantity (EOQ) Model with Consideration of Quality Items, Inspection Errors and Sales Return

In this paper, we develop an economic order quantity model with imperfect quality, inspection errors and sales returns, where upon the arrival of order lot, 100% screening process is performed and the items of imperfect quality are sold as a single batch at a lessen price, prior to receiving the next shipment. The screening process to remove the defective items may involve two types of errors. In this article we extend the Khan et al. (2011) model by considering demand and defective rate in fuzzy sense and also sales return in our model. The objective is to determine the optimal order lot size to maximize the total profit. We use the signed distance, a ranking method for fuzzy numbers, to find the approximate of total profit per unit time in the fuzzy sense. The impact of fuzziness of fraction of defectives and demand rate on optimal solution is showed by numerical example

Supply chain management for the process industry

This thesis investigates some important problems in the supply chain management (SCM) for the process industry to fill the gap in the literature work, covering production planning and scheduling, production, distribution planning under uncertainty, multiobjective supply chain optimisation and water resources management in the water supply chain planning. To solve these problems, models and solution approaches are developed using mathematical programming, especially mixed-integer linear programming (MILP), techniques. First, the medium-term planning of continuous multiproduct plants with sequence-dependent changeovers is addressed. An MILP model is developed using Travelling Salesman Problem (TSP) classic formulation. A rolling horizon approach is also proposed for large instances. Compared with several literature models, the proposed models and approaches show significant computational advantage. Then, the short-term scheduling of batch multiproduct plants is considered. TSP-based formulation is adapted to model the sequence-dependent changeovers between product groups. An edible-oil deodoriser case study is investigated. Later, the proposed TSP-based formulation is incorporated into the supply chain planning with sequence-dependent changeovers and demand elasticity of price. Model predictive control (MPC) is applied to the production, distribution and inventory planning of supply chains under demand uncertainty. A multiobjective optimisation problem for the production, distribution and capacity planning of a global supply chain of agrochemicals is also addressed, considering cost, responsiveness and customer service level as objectives simultaneously. Both ε- constraint method and lexicographic minimax method are used to find the Pareto-optimal solutions Finally, the integrated water resources management in the water supply chain management is addressed, considering desalinated water, wastewater and reclaimed water, simultaneously. The optimal production, distribution and storage systems are determined by the proposed MILP model. Real cases of two Greek islands are studied