The EOQ with backlogging derived without derivatives

Grubbström, Robert W.; Sencer, Asli

doi:10.1016/s0925-5273(98)00015-2

Cited by 172 publications

(100 citation statements)

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“…The risk of shortages is currently a common assumption for most researchers dealing with Lot sizing models. Grubbström and Erdem (1999) derived the EOQ formula including backlogging without reference to the use of derivatives, neither for necessary conditions nor for second-order sufficient conditions, as is basically illustrated by Eq. (3).…”

Section: C T I D C T I D C T I Kmentioning

confidence: 99%

A century of evolution from Harris׳s basic lot size model: Survey and research agenda

Andriolo

Battini

Grubbström

et al. 2014

International Journal of Production Economics

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169

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Determining the economic lot size has always represented one of the most important issues in production planning. This problem has long attracted the attention of researchers, and several models have been developed to meet requirements at minimum cost. In this paper we explore and discuss the evolution of these models during one hundred years of history, starting from the basic model developed by Harris in 1913, up to today. Following Harris's work, a number of researchers have devised extensions that incorporate additional considerations. The evolution of EOQ theory strongly reflects the development of industrial systems over the past century. Here we outline all the research areas faced in the past by conducting a holistic analysis of 219 selected journal papers and trying to give a comprehensive view of past work on the EOQ problem. Finally, a new research agenda is proposed and discussed.

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Section: C T I D C T I D C T I Kmentioning

confidence: 99%

A century of evolution from Harris׳s basic lot size model: Survey and research agenda

Andriolo

Battini

Grubbström

et al. 2014

International Journal of Production Economics

Self Cite

169

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“…Wu & Ouyang (2003) determined the optimal replenishment policy for the integrated singlevendor single-buyer inventory system with shortage algebraically. This approach was developed by Grubbström & Erdem (1999) who showed that the formula for the EOQ with backlogging could be derived algebraically without reference to derivatives. Wu & Ouyang's (2003) integrated vendor-buyer total cost per year is given by…”

Section: Vendor-buyer Coordinationmentioning

confidence: 99%

“…Cárdenas-Barrón (2007) extended the work of Khouja's (2003b) three-stage supply chain by presenting an n-stage-multi-customer supply chain inventory model. He solve the cost function applying the algebraically (Grubbström & Erdem, 1999). Cárdenas-Barrón (2007) selects the equal cycle time coordination mechanism for two reasons: the first one is that this Mechanism is the most simple and the second one is because our main purpose is to develop a useful supply chain model that can be taught without the use of calculus.…”

Section: Stochastic Modelsmentioning

confidence: 99%

Quantitative Models for Centralised Supply Chain Coordination

Jaber¹,

Zolfaghari²

2008

Supply Chain

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IntroductionA supply chain is defined as a network of facilities and distribution options that perform the functions of procurement of materials, transformation of these materials into intermediate and finished products, and the distribution of these finished products to customers. Managing such functions along the whole chain; that is, from the supplier's supplier to the customer's customer; requires a great deal of coordination among the players in the chain. The effectiveness of coordination in supply chains could be measured in two ways: reduction in total supply chain costs and enhanced coordination services provided to the end customer ⎯ and to all players in the supply chain. Inventory is the highest cost in a supply chain accounting for almost 50% of the total logistics costs. Integrating order quantities models among players in a supply chain is a method of achieving coordination. For coordination to be successful, incentive schemes must be adopted. The literature on supply chain coordination have proposed several incentive schemes for coordination; such as quantity discounts, permissible delay in payments, price discounts, volume discount, common replenishment periods. The available quantitative models in supply chain coordination consider up to four levels (i.e., tier-1 supplier, tier-2 supplier, manufacturer, and buyer), with the majority of studies investigating a two-level supply chain with varying assumptions (e.g., multiple buyers, stochastic demand, imperfect quality, etc). Coordination decisions in supply chains are either centralized or decentralized decision-making processes. A centralized decision making process assumes a unique decision-maker (a team) managing the whole supply chain with an objective to minimize (maximize) the total supply chain cost (profit), whereas a decentralized decision-making process involves multiple decision-makers who have conflicting objectives. This chapter will review the literature for quantitative models for centralised supply chain coordination that emphasize inventory management for the period from 1990 to end of 2007. In this chapter, we will classify the models on the basis of incentive schemes, supply chain levels, and assumptions. This chapter will also provide a map indicative of the limitations of the available studies and steer readers to future directions along this line of research. Centralised supply chain coordinationA typical supply chain consists of multistage business entities where raw materials and components are pushed forward from the supplier's supplier to the customer's customer. During this forward push, value is gradually added at each entity in the supply chain transforming raw materials and components to take their final form as finished products at the customer's end, the buyer. These business entities may be owned by the same organization or by several organizations. Goyal & Gupta (1989) suggested that coordination could be achieved by integrating lotsizing models. However, coordinating orders among players in a supply chain might...

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“…Grubbstrom and Erdem [1] stated that algebraic methods can be applied as an alternative approach to teach inventory models to practitioners who are not familiar with calculus. There are several papers that have used algebraic methods to solve the optimal solution for inventory systems.…”

Section: Introductionmentioning

confidence: 99%

Note on “An Easy Method to Derive EOQ and EPQ Inventory Models with Backorders”

Lin¹,

Tuan²,

Julian³

2017

AAN

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Cárdenas-Barrón (2010) applied algebraic methods to EOQ and EPQ models without referring to differential equations, allowing researchers without backgrounds in calculus to understand inventory models with ease. In this note, we point out that the derivation for EPQ model can be obtained by a transformation of the EOQ model and then we provide a further simplification of his approach such that future practitioners can realize his important findings and apply algebraic methods in their own research.Keywords: Algebraic method, Cauchy-Bunyakovsky-Schwarz (CBS) inequality, arithmeticgeometric mean (AGM) inequality. IntroductionGrubbstrom

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The EOQ with backlogging derived without derivatives

Cited by 172 publications

References 1 publication

A century of evolution from Harris׳s basic lot size model: Survey and research agenda

A century of evolution from Harris׳s basic lot size model: Survey and research agenda

Quantitative Models for Centralised Supply Chain Coordination

Note on “An Easy Method to Derive EOQ and EPQ Inventory Models with Backorders”

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