MIP-based heuristics for multi-item capacitated lot-sizing problem with setup times and shortage costs (original) (raw)
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American Journal of Operations Research
Our research focuses on the development of two cooperative approaches for resolution of the multi-item capacitated lot-sizing problems with time windows and setup times (MICLSP-TW-ST). In this paper we combine variable neighborhood search and accurate mixed integer programming (VNS-MIP) to solve MICLSP-TW-ST. It concerns so a particularly important and difficult problem in production planning. This problem is NP-hard in the strong sense. Moreover, it is very difficult to solve with an exact method; it is for that reason we have made use of the approximate methods. We improved the variable neighborhood search (VNS) algorithm, which is efficient for solving hard combinatorial optimization problems. This problem can be viewed as an optimization problem with mixed variables (binary variables and real variables). The new VNS algorithm was tested against 540 benchmark problems. The performance of most of our approaches was satisfactory and performed better than the algorithms already proposed in the literature.
The multi-item capacitated lot-sizing problem with safety stocks and demand shortage costs
Computers & Operations Research, 2009
We address a multi-item capacitated lot-sizing problem with setup times, safety stock and demand shortages. Demand cannot be backlogged, but can be totally or partially lost. Safety stock is an objective to reach rather than an industrial constraint to respect. The problem is np-hard. We propose a Lagrangian relaxation of the resource capacity constraints. We develop a dynamic programming algorithm to solve the induced sub-problems. An upper bound is also proposed using a Lagrangian heuristic with several smoothing algorithms. Some experimental results showing the effectiveness of the approach are reported.
Metaheuristics for the multi-item capacitated lot-sizing problem with time Windows and setup times
2011
In this paper, we address to the multi-item capacitated lot-sizing problem with production time windows and setup times under the non-customer specific case. This problem is known to be NP-hard. Two cooperative approaches are proposed for solving this problem by combining mathematical programming and metaheuristics based on a decomposition scheme. The algorithms use simultaneously the mathematical programming and heuristic procedures such that the local Search algorithm and Variable Neighborhood descent algorithm. The computational experiments show the effectiveness of our proposed algorithms according to the approaches already presented in the litterature.
Journal of the Operational Research Society, 2006
We address the multi-item, capacitated lot-sizing problem (CLSP) encountered in environments where demand is dynamic and to be met on time. Items compete for a limited capacity resource, which requires a setup for each lot of items to be produced causing unproductive time but no direct costs. The problem belongs to a class of problems that are difficult to solve. Even the feasibility problem becomes combinatorial when setup times are considered. This difficulty in reaching optimality and the practical relevance of CLSP make it important to design and analyse heuristics to find good solutions that can be implemented in practice. We consider certain mixed integer programming formulations of the problem and develop heuristics including a curtailed branch and bound, for rounding the setup variables in the LP solution of the tighter formulations. We report our computational results for a class of instances taken from literature.
A heuristic solution of multi-item single level capacitated dynamic lot-sizing problem
Journal of Mechanical Engineering, 2008
The multi-item single level capacitated dynamic lot-sizing problem consists of scheduling N items over a horizon of T periods. The objective is to minimize the sum of setup and inventory holding costs over the horizon subject to a constraint on total capacity in each period. No backlogging is allowed. Only one machine is available with a fixed capacity in each period. In case of a single item production, an optimal solution algorithm exists. But for multi-item problems, optimal solution algorithms are not available. It has been proved that even the two-item problem with constant capacity is NP (nondeterministic polynomial)-hard. That is, it is in a class of problems that are extremely difficult to solve in a reasonable amount of time. This has called for searching good heuristic solutions. For a multi-item problem, it would be more realistic to consider an upper limit on the lot-size per setup for each item and this could be a very important parameter from practical point of view. T...
Pesquisa Operacional
This research addresses a lot sizing and scheduling problem inspired by a real-world production environment where the customers make advanced orders and the industry need to decide which orders will be accepted with the aim of maximizing the profit respecting the production capacity constraints. Orders are composed of different types of items which must be delivered within a given time interval and, moreover, such orders cannot be split. A mixed integer programming (MIP) model is proposed to represent the problem and a MIP-based heuristic is also proposed to deliver good solutions at an acceptable computational time. The heuristic is composed of three phases (construction, deterministic improvement and stochastic improvement phases) and combines relax-and-fix, fix-and-optimize, and iterative MIP based neighborhood search procedures. Computational tests are presented in order to study the efficiency of the proposed approaches.
An optimization framework for solving capacitated multi-level lot-sizing problems with backlogging
European Journal of Operational Research, 2011
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. manuscript no. (Please, provide the mansucript number!) capacitated single level multi-item lot-sizing problem with backlogging. examined the uncapacitated single item lot-sizing problem with backlogging and start-up costs, when Wagner-Whitin costs are assumed. Cheng et al. (2001) formulated single-level lot-sizing problems with provisions for backorders using a fixed-charge transportation model and proposed a heuristic solution method. Ganas and Papachristos (2005) proposed a polynomial-time algorithm for the single-item lot-sizing problem with backlogging. Song and Chan (2005) proposed a dynamic programming algorithm for solving a single-item lot-sizing problem with backlogging on a single machine at a finite production rate. Mathieu (2006) proposed two extended linear programming (LP) reformulations of single-item lot-sizing problems with backlogging and constant capacities. In a recent study, Küçükyavuz and Pochet (2009) provided the full description of the convex hull for the single-level uncapacitated problem with backlogging. Wu and Shi (2009b) proposed a heuristic that combines domain knowledge from the different strategies of relax-and-fix effectively for the capacitated multi-level lot sizing problem with the consideration of backlogging. We refer the interested reader to Pochet and Wolsey (2006) for a detailed general review of different lot-sizing problems. We note that the term backlog is used interchangeably with backorder in the lot-sizing literature, referring to any demand that is not satisfied on time but in a later time period, no matter what type of manufacturing environment. In our context, we consider a model that is flexible enough to apply to both MTO (Make-To-Order) and MTS (Make-To-Stock) environments when production is planned based on fixed demands or forecasts. The past research has also considered other classes of lot sizing problems. For example, Thizy and van Wassenhove (1985) designed a Lagrangian relaxation (LR) approach, in which capacity constraints are relaxed, in an attempt to decompose the problem into N uncapacitated single item lot-sizing subproblems, solvable by the Wagner-Whitin algorithm. Trigeiro (1987) developed a similar approach for solving the deterministic, multi-item, single-operation lot-sizing problem. Trigeiro et al. (1989) also proposed LR based methods for large-scale lot-sizing problems. Kuik and Salomon (1990) evaluated a simulated annealing heuristic for solving multi-level lot-sizing problem. Pochet and Wolsey (1991) applied strong cutting planes
International Journal of Production Economics, 2009
This paper presents a novel mathematical programming approach to the singlemachine capacitated lot-sizing and scheduling problem with sequence-dependent setup times and setup costs. The approach is partly based on the earlier work of Haase and Kimms which determines during pre-processing all item sequences that can appear in given time periods in optimal solutions. We introduce a new mixed-integer programming model in which binary variables indicate whether individual items are produced in a period, and parameters for this program are generated by a heuristic procedure in order to establish a tight formulation. Our model allows us to solve in reasonable time instances where the product of the number of items and number of time periods is at most 60-70. Compared to known optimal solution methods, it solves significantly larger problems, often with orders of magnitude speedup.
This paper presents a novel mathematical programming approach to the singlemachine capacitated lot-sizing and scheduling problem with sequence-dependent setup times and setup costs. The approach is partly based on the earlier work of Haase and Kimms (2000) which determines during pre-processing all item sequences that can appear in given time periods in optimal solutions. We introduce a new mixed-integer programming model in which binary variables indicate whether individual items are produced in a period, and parameters for this program are generated by a heuristic procedure in order to establish a tight formulation. Our model allows us to solve in reasonable time instances where the product of the number of items and number of time periods is at most 60-70. Compared to known optimal solution methods, it solves significantly larger problems, often with orders of magnitude speedup.