MIP models for production lot sizing problems with distribution costs and cargo arrangement

Molina, Flavio de Barros; Morábito, Reinaldo; Araújo, Silvio Alexandre de

doi:10.1057/jors.2016.12

Cited by 12 publications

(3 citation statements)

References 38 publications

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“…Molina et al (2009) develop a method consisting of a Lagrangian/surrogate heuristic to solve the problem presented in van Norden and van de Velde (2005) with backlogging and production time capacity constraints. Refer to Molina et al (2016) for extensions of the model originally proposed in van Norden and van de Velde (2005).…”

Section: Lot Sizing Problem With Capacity Reservation Contractmentioning

confidence: 99%

Batch replenishment planning under capacity reservation contract

Farhat¹

2019

4OR-Q J Oper Res

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Section: Lot Sizing Problem With Capacity Reservation Contractmentioning

confidence: 99%

Batch replenishment planning under capacity reservation contract

Farhat¹

2019

4OR-Q J Oper Res

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“…There is no setup cost, so items are bought according to shipping decisions. Molina et al [12] extend the work of Norden and Velde [13] and propose models for production lot sizing problems with distribution costs using unit load devices such as pallets and containers. Lot sizing decisions are subject to capacity constraints, and items must be packed for shipping at the very period they are produced.…”

Section: Introductionmentioning

confidence: 99%

The integrated uncapacitated lot sizing and bin packing problem

et al. 2021

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In the integrated uncapacitated lot sizing and bin packing problem, we have to couple lot sizing decisions of replenishment from single product suppliers with bin packing decisions in the delivery of client orders. A client order is composed of quantities of each product, and the quantities of such an order must be delivered all together no later than a given period. The quantities of an order must all be packed in the same bin, and may be delivered in advance if it is advantageous in terms of costs. We assume a large enough set of homogeneous bins available at each period. The costs involved are setup and inventory holding costs and the cost to use a bin as well. All costs are variable in the planning horizon, and the objective is to minimize the total cost incurred. We propose mixed integer linear programming formulations and a combinatorial relaxation where it is no longer necessary to keep track of the specific bin where each order is packed. An aggregate delivering capacity is computed instead. We also propose heuristics using different strategies to couple the lot sizing and the bin packing subproblems. Computational experiments on instances with different configurations showed that the proposed methods are efficient ways to obtain small optimality gaps in reduced computational times.

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“…Mathematical programming heuristics, Lagrangian relaxation heuristics, decomposition and aggregation heuristics, meta heuristics, problem-specific greedy heuristics, piecewise linear approximation methods are used to solve different lot sizing problems. Some works adopting those methods can be found in González-Ramírez et al (2011), Absi et al (2013), Toledo et al (2015), Rossi et al (2015), Molina et al (2016). Comprehensive reviews on lot sizing problem could be addressed in Maes and Van Wassenhove (1988), Karimi et al (2003), Brahimi et al (2006), Jans and Degraeve (2007), Buschkühl et al (2010), Brahimi et al (2017).…”

Section: Introductionmentioning

confidence: 99%

A cash‐constrained dynamic lot‐sizing problem with loss of goodwill and credit‐based loan

Zhen

Zhang

2019

Int Trans Operational Res

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We introduce capital flow constraints, loss of good will and loan to the lot sizing problem. Capital flow constraint is different from traditional capacity constraints: when a manufacturer launches production, its present capital should not be less than its present total production cost; otherwise, it must decrease production quantity or suspend production. Unsatisfied demand in one period may cause customer's demand to shrink in the next period considering loss of goodwill. Fixed loan can be adopted in the starting period for production. A mixed integer model for a deterministic single-item problem is constructed. Based on the analysis about the structure of optimal solutions, we approximate it to a traveling salesman problem, and divide it into sub-linear programming problems without integer variables. A forward recursive algorithm with heuristic adjustments is proposed to solve it. When unit variable production costs are equal and goodwill loss rate is zero, the algorithm can obtain optimal solutions. Under other situations, numerical comparisons with CPLEX 12.6.2 show our algorithm can reach optimal in most cases and has computation time advantage for large-size problems. Numerical tests also demonstrate that initial capital availability as well as loan interest rate can substantially affect the manufacturer's optimal lot sizing decisions.

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MIP models for production lot sizing problems with distribution costs and cargo arrangement

Cited by 12 publications

References 38 publications

Batch replenishment planning under capacity reservation contract

Batch replenishment planning under capacity reservation contract

The integrated uncapacitated lot sizing and bin packing problem

A cash‐constrained dynamic lot‐sizing problem with loss of goodwill and credit‐based loan

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