DYNAMIC LOT-SIZING PROBLEMS: A Review on Model and Efficient Algorithm

Due to their importance in industry, dynamic demand lot-sizing problems are frequently studied.This study consider dynamic lot-sizing problems with recent advances in problem and modelformulation, and algorithms that enable large-scale problems to be effectively solved.Comprehensive review is given on model formulation of dynamic lot-sizing problems, especiallyon capacitated lot-sizing (CLS) problem and the coordinated lot-sizing problem. Bothapproaches have their intercorrelated, where CLS can be employed for single or multilevel/stage, item, and some restrictions. When a need for joint setup replenishment exists, thenthe coordinated lot-sizing is the choice. Furthermore, both algorithmics and heuristics solutionin the research of dynamic lot sizing are considered, followed by an illustration to provide anefficient algorithm

A review of multi-component maintenance models with economic dependence

In this paper we review the literature on multi-component maintenance models with economic dependence. The emphasis is on papers that appeared after 1991, but there is an overlap with Section 2 of the most recent review paper by Cho and Parlar (1991). We distinguish between stationary models, where a long-term stable situation is assumed, and dynamic models, which can take information into account that becomes available only on the short term. Within the stationary models we choose a classification scheme that is primarily based on the various options of grouping maintenance activities: grouping either corrective or preventive maintenance, or combining preventive-maintenance actions with corrective actions. As such, this classification links up with the possibilities for grouped maintenance activities that exist in practice

(s, S) Policies for a Dynamic Inventory Model with Stochastic Lead Times

This study analyzes a stochastic lead time inventory model under the assumptions that (a) replenishment orders do not cross in time and (b) the lead time distribution for a given order is independent of the number and sizes of outstanding orders. The study extends the existing literature on the finite horizon version of the model and yields an intuitively appealing dynamic program that is nearly identical to one that would apply in a transformed model with all lead times fixed at zero. Hence, many results that have been derived for fixed lead time models generalize easily. Conditions for the optimality of myopic base stock policies, and for the optimality of (s, S) policies are established for both finite and infinite planning horizons. The infinite-horizon model analysis is extended by adapting the fixed lead time results for the efficient computation of optimal and approximately optimal (s, S) policies

Application of Markov Decision Processes (MDPs) in Petroleum Industry

Gasoline and diesel fuel is the lifeblood that keeps ourdaily life moving forward. Inefficient operation of fuel supplyleads to unsatisfactory service, time consuming, as well as loweconomic benefits. Exploring the optimal timing for gas stations toreplenish gasoline and diesel is of importance. We propose to applyinfinite-horizon Markov Decision Processes (MDPs) to thisdynamic problem. Compared with traditional methods fordetermining the optimal timing of replenishment, such as IB,EOQ, EB, etc., MDPs are better in accurately modeling thesituation which needs sequential decision making underuncertainties. For the MDPs modelling gas station replenishmentproblem, the rewards for any actions taken in the states (theremaining gasoline and diesel inventory status in the oil tank of thegas station) is to keep the duration for stockout and the tankertrucks’ waiting time as low as possible. The optimal policy is tomaximize the rewards. A real world case study was presented anda revised infinite-horizon MDPs model was constructed tooptimize the time for replenishment. Managerial insights guidingthe actions gas stations should take to optimize theirreplenishment strategies are gained

Lp-Based Artificial Dependency for Probabilistic Etail Order Fulfillment

We consider an online multi-item retailer with multiple fulfillment facilities and finite inventory, with the objective of minimizing the expected shipping cost of fulfilling customer orders over a finite horizon. We approximate the stochastic dynamic programming formulation of the problem with an equivalent deterministic linear program, which we use to develop a probabilistic fulfillment heuristic that is provably optimal in the asymptotic sense. This first heuristic, however, relies on solving an LP that is exponential in the size of the input. Therefore, we subsequently provide another heuristic which solves an LP that is polynomial in the size of the input, and prove an upper bound on its asymptotic competitive ratio. This heuristic works by modifying the LP solution with artificial dependencies, with the resulting fractional variables used to probabilistically fulfill orders. A hardness result shows that asymptotically optimal policies that are computationally efficient cannot exist. Finally, we conduct numerical experiments that show that our heuristic's performance is very close to optimal for a range of parameters.http://deepblue.lib.umich.edu/bitstream/2027.42/108712/1/1250_ASinha.pd

A Dynamic inventory optimization method applied to printer fleet management

Current optimization methods for inventory management of toner cartridges for printer fleets typically focus on aggregate cartridge demand. However, with the development of printer technology, toner consumption algorithms are being developed which can accurately quantify the amount of toner that has been consumed over time, based on print job characteristics. This research introduces a dynamic inventory optimization approach for a fleet of printers over a rolling time horizon. Given, the consumption algorithm for the printer system, the cumulative toner consumed per cartridge per printer can be tracked. A forecasting method is developed which utilizes this toner consumption data for individual printers to forecast toner cartridge replacement times. Taking into account the uncertainty related to demand, demand forecast and lead time, an optimization model has been developed to determine the order placement times and order quantities to minimize the total cost subject to a specified service level. An experimental performance evaluation has been conducted on the parameters of the dynamic inventory management algorithm. Based on the results of this evaluation, the implementation of this dynamic inventory optimization methodology could have a positive impact on printer fleet management

Dynamic pricing models for electronic business

Dynamic pricing is the dynamic adjustment of prices to consumers depending upon the value these customers attribute to a product or service. Today’s digital economy is ready for dynamic pricing; however recent research has shown that the prices will have to be adjusted in fairly sophisticated ways, based on sound mathematical models, to derive the benefits of dynamic pricing. This article attempts to survey different models that have been used in dynamic pricing. We first motivate dynamic pricing and present underlying concepts, with several examples, and explain conditions under which dynamic pricing is likely to succeed. We then bring out the role of models in computing dynamic prices. The models surveyed include inventory-based models, data-driven models, auctions, and machine learning. We present a detailed example of an e-business market to show the use of reinforcement learning in dynamic pricing