3,740 research outputs found
A note on "The Economic Lot Sizing Problem with Inventory Bounds"
In a recent paper, Liu (2008) considers the lot-sizing problem with lower and upper bounds on the inventory levels. He proposes an O(n^2) algorithm for the general problem, and an O(n) algorithm for the special case with non-speculative motives. We show that neither of the algorithms provides an optimal solution in general. Furthermore, we propose a fix for the former algorithm that maintains the O(n^2) complexity
A heuristic approach for big bucket multi-level production planning problems
Multi-level production planning problems in which multiple items compete for the same resources frequently occur in practice, yet remain daunting in their difficulty to solve. In this paper, we propose a heuristic framework that can generate high quality feasible solutions quickly for various kinds of lot-sizing problems. In addition, unlike many other heuristics, it generates high quality lower bounds using strong formulations, and its simple scheme allows it to be easily implemented in the Xpress-Mosel modeling language. Extensive computational results from widely used test sets that include a variety of problems demonstrate the efficiency of the heuristic, particularly for challenging problems
Four equivalent lot-sizing models
We study the following lot-sizing models that recently appeared in the literature: a lot-sizing model with aremanufacturing option, a lot-sizing model with production time windows, and a lot-sizing model with cumulativecapacities. We show the equivalence of these models with a classical model: the lot-sizing model with inventory bounds.lot-sizing;equivalent models
A computational analysis of lower bounds for big bucket production planning problems
In this paper, we analyze a variety of approaches to obtain lower bounds for multi-level production planning problems with big bucket capacities, i.e., problems in which multiple items compete for the same resources. We give an extensive survey of both known and new methods, and also establish relationships between some of these methods that, to our knowledge, have not been presented before. As will be highlighted, understanding the substructures of difficult problems provide crucial insights on why these problems are hard to solve, and this is addressed by a thorough analysis in the paper. We conclude with computational results on a variety of widely used test sets, and a discussion of future research
An optimization framework for solving capacitated multi-level lot-sizing problems with backlogging
This paper proposes two new mixed integer programming models for capacitated multi-level lot-sizing problems with backlogging, whose linear programming relaxations provide good lower bounds on the optimal solution value. We show that both of these strong formulations yield the same lower bounds. In addition to these theoretical results, we propose a new, effective optimization framework that achieves high quality solutions in reasonable computational time. Computational results show that the proposed optimization framework is superior to other well-known approaches on several important performance dimensions
Mixed integer programming in production planning with backlogging and setup carryover : modeling and algorithms
This paper proposes a mixed integer programming formulation for modeling the capacitated multi-level lot sizing problem with both backlogging and setup carryover. Based on the model formulation, a progressive time-oriented decomposition heuristic framework is then proposed, where improvement and construction heuristics are effectively combined, therefore efficiently avoiding the weaknesses associated with the one-time decisions made by other classical time-oriented decomposition algorithms. Computational results show that the proposed optimization framework provides competitive solutions within a reasonable time
Single item stochastic lot sizing problem considering capital flow and business overdraft
This paper introduces capital flow to the single item stochastic lot sizing
problem. A retailer can leverage business overdraft to deal with unexpected
capital shortage, but needs to pay interest if its available balance goes below
zero. A stochastic dynamic programming model maximizing expected final capital
increment is formulated to solve the problem to optimality. We then investigate
the performance of four controlling policies: (), (), () and
(, , ); for these policies, we adopt simulation-genetic
algorithm to obtain approximate values of the controlling parameters. Finally,
a simulation-optimization heuristic is also employed to solve this problem.
Computational comparisons among these approaches show that policy and
policy provide performance close to that of optimal
solutions obtained by stochastic dynamic programming, while
simulation-optimization heuristic offers advantages in terms of computational
efficiency. Our numerical tests also show that capital availability as well as
business overdraft interest rate can substantially affect the retailer's
optimal lot sizing decisions.Comment: 18 pages, 3 figure
The linear dynamic lot size problem with minimum order quantities
This paper continues the analysis of a special uncapacitated single item lot sizing problem where a minimum order quantity restriction, instead of the setup cost, guarantees a certain level of production lots. A detailed analysis of the model and an investigation of the particularities of the cumulative demand structure allowed us to develop a solution algorithm based on the concept of minimal sub-problems. We present an optimal solution to a minimal sub-problem in an explicit form and prove that it serves as a construction block for the optimal solution of the initial problem. The computational tests and the comparison with the published algorithm confirm the efficiency of the solution algorithm developed here. --lot sizing problem,minimum order quantity,dynamic programming
Improved Lower Bounds For The Capacitated Lot Sizing Problem With Set Up Times
We present new lower bounds for the Capacitated Lot Sizing Problem with Set Up Times. We improve the lower bound obtained by the textbook Dantzig-Wolfe decomposition where the capacity constraints are the linking constraints. In our approach, Dantzig-Wolfe decomposition is applied to the network reformulation of the problem. The demand constraints are the linking constraints and the problem decomposes into subproblems per period containing the capacity and set up constraints. We propose a customized branch-and-bound algorithm for solving the subproblem based on its similarities with the Linear Multiple Choice Knapsack Problem. Further we present a Lagrange Relaxation algorithm for finding this lower bound. To the best of our knowledge, this is the first time that computational results are presented for this decomposition and a comparison of our lower bound to other lower bounds proposed in the literature indicates its high quality.Lagrange relaxation;Dantzig-Wolfe decomposition;capacitated lot sizing;lower bounds
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