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

A non-calculus approach to solving the utility maximization problem using the Cobb-Douglas and CES utility function

This paper proposes a new original non-calculus method to solving the utility maximization problem using the Cobb-Douglas and the CES utility functions, and incorporating the weighted arithmetic-geometric-mean inequality (weighted AM-GM inequality) and Jensen’s inequality. Instead of using calculus, the substitution method or the Lagrange multiplier method, the maximum utility and global maximizer for the case of the Cobb-Douglas and CES utility functions are derived in a direct way. The new method does not require checking first and second order conditions, which the substitution method and the Lagrange multiplier method normally require

Existence of EOQ and its evaluation: some cases of stock blow down dynamics depending on its level

The EOQ mathematical models usually deal with the problem of a wholesaler who has to manage a goods restocking policy, settling his best amount of goods to be procured. Best means capable of minimizing all the costs concerning the trade of the stored goods. The relevant seminal contributions are due to Harris, and Wilson, who analyzed an easy scenario with a certain demand uniform all over the time so that its instantaneous change rate is fixed, with stocking charges not dependent on time. In such a field, our own contribution consists of establishing sufficient conditions on the well posedness to the minimum cost problem and relationships providing either closed form solutions or, alternatively, quadrature formulae, without ex ante approximations. All this allows a numerical solution to the transcendental (or algebraical of high degree) equation solving to the most economical batch. In short, such our paper is concerning the special family of EOQ mathematical models with different deterministic time-dependent demands

Mathematical properties of EOQ models with special cost structure

An existence-uniqueness theorem is proved about a minimum cost order for a class of inventory models whose holding costs grow according to a stock level power law. The outcomes of G. Mingari Scarpello, D. Ritelli, EOQ when holding costs grow with the stock level: well-posedness and solutions, Advanced Modeling and Optimization, 10 (2) (2008) 233-240. are then extended to different environments: i.e. when the holding costs change during time generalizing a model available in H.J. Weiss, Economic Order Quantity Models with Nonlinear Holding Costs, European Journal of Operational Research 9 (1) (1982) 56-60., or with invariable holding costs but adopting a backordering strategy. Application cases are provided assuming several functional behaviors of demand versus the stock level

Optimal economic order quantity for buyer–distributor–vendor supply chain with backlogging derived without derivatives

[[abstract]]In this article, we first complement an inappropriate mathematical error on the total cost in the previously published paper by Chung and Wee [2007, ‘Optimal the Economic Lot Size of a Three-stage Supply Chain With Backlogging Derived Without Derivatives’, European Journal of Operational Research, 183, 933–943] related to buyer–distributor–vendor three-stage supply chain with backlogging derived without derivatives. Then, an arithmetic–geometric inequality method is proposed not only to simplify the algebraic method of completing prefect squares, but also to complement their shortcomings. In addition, we provide a closed-form solution to integral number of deliveries for the distributor and the vendor without using complex derivatives. Furthermore, our method can solve many cases in which their method cannot, because they did not consider that a squared root of a negative number does not exist. Finally, we use some numerical examples to show that our proposed optimal solution is cheaper to operate than theirs.[[incitationindex]]SCI[[booktype]]紙本[[booktype]]電子

A State of art on economic production quantity models

Economic ordering quantity is a commonly accepted inventory management model. Its variant economic production quantity (EPQ) model is also a widely researched inventory model. The number of researchers had developed the EPQ model by considering different parameters, such as shortage, backorder, setup cost, deterioration, constant or linear or power form of the demand, rework, scrap, inspection, machine breakdown, etc. The objective of this paper is to review the literature, identify the gap in literature, develop and expand the knowledge base regarding EPQ models. This state of art paper would act as a guideline for researchers. The wide spectrum of the subject provides interesting future research problems