An efficient optimal algorithm for the quantity discount problem in material requirement planning

Mirmohammadi, S. Hamid; Shadrokh, Shahram; Kianfar, Farhad

doi:10.1016/j.cor.2008.05.003

Cited by 28 publications

(9 citation statements)

References 9 publications

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“…Benton (1991), Munson and Rosenblatt (1998), and Munson and Jackson (2015) have analyzed the most relevant quantity discount scenarios from both the buyer's and seller's perspectives. In the recent decades, this practice has been studied mostly from a quantitative perspective in many different application contexts (dairy, chemical industry, project's resource investment, telecommunication systems) and considering many complicating factors such as multiple periods, multiple sites, inventory costs, buyers coalition, budgetary limitations and so on (see, e.g., McConnel and Galligan, 2004, van de Klundert et al, 2005, Mirmohammadi et al, 2009, Munson and Hu, 2010, Krichen et al, 2011, Jolai et al, 2013. Among the different existing policies (incremental discount, fixed fees, truckload discount), the total quantity discount (TQD) represents the most popular form applied so far and studied in the literature since it correctly models many multiproduct procurement settings where the purchase is completed at a single point in time, without any auctions or rebate mechanisms (Crama et al, 2004, Shahsavar et al, 2016.…”

Section: Literature Reviewmentioning

confidence: 99%

New solution approaches for the capacitated supplier selection problem with total quantity discount and activation costs under demand uncertainty

Manerba

Perboli

2019

Computers & Operations Research

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The Capacitated Supplier Selection problem with Total Quantity Discount policy and Activation Costs is a procurement problem where a company needs to purchase a certain quantity of different products from a set of potential suppliers offering discounts based on the total quantity purchased. The buyer company wants to minimize the total expenditure that satisfies its own products demand, also considering the fixed costs needed to activate the business activities with the selected suppliers. We study the problem on a long-term perspective and thus consider the product demand as non-deterministic. Recent works have shown the importance of explicitly incorporate demand uncertainty in this economic setting, along with the evidence about the computational burden of solving the relative Stochastic Programming models for a sufficiently large number of scenarios. In this work, we propose different solution strategies (several variants of a Progressive Hedging based heuristic approach as well as a Benders algorithm) to efficiently cope with these models by taking advantage of the particular structure of the stochastic problem. The results obtained on benchmark instances show how the proposed methods outperform the existing ones and the state-of-the-art solvers in terms of efficiency and solution quality.

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Section: Literature Reviewmentioning

confidence: 99%

New solution approaches for the capacitated supplier selection problem with total quantity discount and activation costs under demand uncertainty

Manerba

Perboli

2019

Computers & Operations Research

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“…This paper is outlined as follows. In Sections 2 and 3, (1) we investigate the research background of this problem, (2) we propose dynamic multiobjective optimization based on development prediction, and (3) we propose an evolutionary algorithm combined with dynamic strategy (RS/AS) to solve dynamic multiobjective optimization problem. In Section 4, we investigate two cases to clearly demonstrate the experimental process and to prove the effectiveness of the method.…”

Section: Introductionmentioning

confidence: 99%

The Optimal Supply Decision Based on Dynamic Multiobjective Optimization and Prediction

Cheng

Zhou

et al. 2022

Journal of Function Spaces

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Different material supply-related decisions intensively affect the efficiency of manufacturers. To obtain a suitable supply-related protocol, this study proposes a supply selection model which considers both manufacturers’ development orientation and material ordering. In contrast to traditional approaches that rely on expert opinions, the proposed approach in this study allows the time series analysis (ARIMA) to forecast the trend in manufacturers’ development during the execution of the plan. Based on the predicted trend, taking the minimum of total material management cost as the objective function, the control function and optimization conditions are constructed to select the appropriate protocol. The dynamic prediction protocol is obtained by considering the variation in production and material costs by an evolutionary algorithm. The model enables users to determine material supply protocol in continuous time and autonomously adapt to changes in the manufacturers’ production goals within a lower convergence time.

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“…Moreover, no polynomial-time approximation algorithm with a constant worst-case ratio exists for the TQD problem (unless the complexity class P is equal to the complexity class N P ). More information on many variations on the TQD can be found in the literature (Goossens et al, 2007;Mirmohammadi et al, 2009;Munson and Hu, 2010;Krichen et al, 2011).…”

Section: Related Researchmentioning

confidence: 99%

Exact and heuristic approaches to solve the Internet shopping optimization problem with delivery costs

López-Locés

Musiał

Pecero

et al. 2016

International Journal of Applied Mathematics and Computer Science

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Internet shopping has been one of the most common online activities, carried out by millions of users every day. As the number of available offers grows, the difficulty in getting the best one among all the shops increases as well. In this paper we propose an integer linear programming (ILP) model and two heuristic solutions, the MinMin algorithm and the cellular processing algorithm, to tackle the Internet shopping optimization problem with delivery costs. The obtained results improve those achieved by the state-of-the-art heuristics, and for small real case scenarios ILP delivers exact solutions in a reasonable amount of time.

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An efficient optimal algorithm for the quantity discount problem in material requirement planning

Cited by 28 publications

References 9 publications

New solution approaches for the capacitated supplier selection problem with total quantity discount and activation costs under demand uncertainty

New solution approaches for the capacitated supplier selection problem with total quantity discount and activation costs under demand uncertainty

The Optimal Supply Decision Based on Dynamic Multiobjective Optimization and Prediction

Exact and heuristic approaches to solve the Internet shopping optimization problem with delivery costs

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