IIE Transactions The capacitated lot sizing problem with overtime decisions and setup times (original) (raw)
Related papers
An Efficient Heuristic Algorithm for Capacitated Lot Sizing Problem with Overtime Decisions
Springer eBooks, 2012
Capacitated Lot Sizing Problem is a very important tactical level decision making problem that answers the questions of producing when and how many in dynamic demand environment. Solving Capacitated Lot Sizing Problem with Overtime decisions (CLSPO) and extensions derived from the fundamental structure optimally suffer from combinatorial nature of the problem. The aim of the study is to form a two-stage heuristic algorithm to solve related problem in polynomial time. In first part, characteristics of problem structure are presented. Dominance properties are presented to help algorithm obtain a bounded search area. Proposed algorithm directly utilizes such shortcoming. Performance of approach is tested by using different criteria. And finally, robustness test are applied to check how well algorithm performs against fluctuations in its data. Simulated annealing as improvement heuristic performs well for related problem. It is also observed that fluctuations of data directly affects performance outcome. Obtained results also reveal that performance of improvement heuristic highly depends on constructive heuristic. Algorithm is also applied to an industry case study to plan master production schedule with minimum costs.
1998
The capacitated lot sizing and loading problem (CLSLP) deals with the issue of determining the lot sizes of product families/end items and loading them on parallel facilities to satisfy dynamic demand over a given planning horizon. The capacity restrictions in the CLSLP are imposed by constraints specific to the production environment considered. When a lot size is positive in a specific period, it is loaded on a facility without exceeding the sum of the regular and overtime capacity limits. Each family may have a different process time on each facility and furthermore, it may be technologically feasible to load a family only on a subset of existing facilities. So, in the most general case, the loading problem may involve unrelated parallel facilities of different classes. Once loaded on a facility, a family may consume capacity during setup time. Inventory holding and overtime costs are minimized in the objective function. Setup costs can be included if setups incur costs other than lost production capacity. The CLSLP is relevant in many industrial applications and may be generalized to multi-stage production planning and loading models. The CLSLP is a synthesis of three different planning and loading problems, i.e., the capacitated lot sizing problem (CLSP) with overtime decisions and setup times, minimizing total tardiness on unrelated parallel processors, and, the class scheduling problem, each of which is NP in the feasibility and optimality problems. Consequently, we develop hybrid heuristics involving powerful search techniques such as simulated annealing (SA), tabu search (TS) and genetic algorithms (GA) to deal with the CLSLP. Results are compared with optimal solutions for 108 randomly generated small test problems. The procedures developed here are also compared against each other in 36 larger size problems.
Three Meta-heuristic Algorithms for the Single-item Capacitated Lot-sizing Problem
International Journal of Engineering
This paper proposes a mixed integer programming model for single-item capacitated lot-sizing problem with setup times, safety stock, demand shortages, outsourcing and inventory capacity. Due to the complexity of problem, three meta-heuristics algorithms named simulated annealing (SA), vibration damping optimization (VDO) and harmony search (HS) have been used to solve this model. Additionally, Taguchi method is conducted to calibrate the parameters of the meta-heuristics and select the optimal levels of the algorithm's performance influential factors. Computational results on a set of randomly generated instances show the efficiency of the HS against VDO and SA.
Journal of Operations Management, 1983
The problem considered in this paper deals with the sizing and timing of re~~en~shmentsfor an item facirzg a time-vurying, but known, pattern of requirements. Regular time and overtime (the latter at a cost premium) production options are available where there are production capacities that also can vary with time. The problem is to establish thepattern of repIen~shments so us to keep the total of setup, carrying and overtime premium costs as low as possible without any backlogging of demand and without violating any of the capacity constraints. A heuristic procedure, simple enough to implement mum&y, is developed and tested on a large representutive set of problems. The resulting performance is excellent, namely an average cost penalty of only 0.5%.
RAIRO - Operations Research, 2007
We address a multi-item capacitated lot-sizing problem with setup times that arises in real-world production planning contexts. 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 mixed integer programming heuristics based on a planning horizon decomposition strategy to find a feasible solution. The planning horizon is partitioned into several sub-horizons over which a freezing or a relaxation strategy is applied. Some experimental results showing the effectiveness of the approach on real-world instances are presented. A sensitivity analysis on the parameters of the heuristics is 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.
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.
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.