Multi-Item Capacity Constrained Dynamic Lot-Sizing and Sequencing with Setup Time (original) (raw)
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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...
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.
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.
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.
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.
International Journal of Production Economics, 2000
This paper deals with lot sizing and scheduling for a single-stage, single-machine production system where setup costs and times are sequence dependent. A large-bucket mixed integer programming (MIP) model is formulated which considers only e$cient sequences. A tailor-made enumeration method of the branch-and-bound type solves problem instances optimally and e$ciently. The size of solvable cases ranges from 3 items and 15 periods to 10 items and 3 periods. Furthermore, it will become clear that rescheduling can neatly be done.
Joint lot sizing and scheduling of a multi-product multi-period supply chain
Independent Journal of Management & Production
The joint lot sizing and scheduling problem can be considered as an evolvement of the joint economic lot size problem which has drawn researchers’ interests for decades. The objective of this paper is to find the effect of a capacitated multi-period supply chain design parameters on joint lot sizing and scheduling decisions for different holding and penalty costs. The supply chain deals with two raw materials suppliers. The production facility produces two products which are shipped to customers through distribution centers. A mathematical model is developed to determine optimum quantities of purchased raw materials, production schedule (MPS), delivered quantities and raw material and products inventory for predetermined number of periods. The model is solved to maximize total supply chain profits. Results showed that at high capacity and low holding cost, the supply chain tends to produce only one product each period, for limited capacity and high value of holding cost, the supply ...
Multi-item lot-sizing with joint set-up costs
Mathematical Programming, 2009
We consider a multi-item lot-sizing problem with joint set-up costs and constant capacities. Apart from the usual per unit production and storage costs for each item, a set-up cost is incurred for each batch of production, where a batch consists of up to C units of any mix of the items. In addition, an upper bound on the number of batches may be imposed.
2010
In this work we introduce an innovative procedure to solve the capacitated lot sizing problem with backorders and setup times, called CLSP_BS. The procedure formulates CLSP_BS as a mixed integer programming (MIP) problem, reduces it to the structure of a bounded variable linear program; and then calculates some ratios of the coefficients to determine an approximate solution to the problem. This initial solution is further improved using an intelligent enumeration procedure. Adopting this procedure, we solve the NP hard MIP differently and easily, by mere calculation of a few ratios and without actually using any traditional solution approaches, viz. simplex, interior point method, etc.