خلاصة:
This paper investigated the problem of simultaneous determination of lot-sizing and production scheduling with earliness/tardiness penalties. In this problem, decisions about lot-sizing and scheduling are made so that the sum of holding, tardiness, and setup costs is minimized. There are n orders waiting to be processed on a machine. Each order has its own due date as well as tardiness and earliness cost being the same as holding cost .Each order is delivered only once. If the production is completed before or on the due date, delivery will be on the due date. Otherwise, the order will be delivered immediately after its production is completed. In spite of its wide applications, this problem has not yet been reported in the literature. A mathematical model was presented as solution methods for the problem. Two meta-heuristics, namely, Simulated Annealing and Ant Colony System meta-heuristic algorithms are presented for solving the problem. Also, lower bounds are obtained from solving the problem relaxation, and they are compared with the optimal solutions to estimate the goodness of two meta-heuristic algorithms. They are difficult benchmarks, widely used to measure the efficiency of metaheuristics with respect to both the quality of the solutions and the central. The results show that the Simulated Annealing recorded a lower solution time and average percentage deviation than did the Ant Colony System algorithm. The presented SA is capable to solve large instances that are mostly compatible with the real-world problems.
ملخص الجهاز:
Several papers on simultaneous lot-sizing and scheduling problems have developed models and methods to solve this problem (Clark and Clark (2000); Mahdieh, Bijari and Clark (2011); Mohammadi (2010); Mohammadi and Jafari (2011);Meyr (2013); Seeanner et al.
Almada-Lobo and James (2010) solved the single-machine CLSD (CLSD-SM) by integrating a big- bucket lot-sizing and scheduling model and a batching scheduling model to develop two neighborhood-based search algorithms.
Luis, Klabjan, and Bernardo (2014) proposed a two-dimensional framework for reviewing and classifying the different modelling approaches adopted for sequencing decisions in lot- sizing and scheduling problems.
Mehdizadeh,Hajipour, and Mohammadizadeh, studied a multi- item capacitated lot-sizing problem (MICLSP) with setup times, safety stock deficit costs, demand shortage costs – both backorder and lost sale states – and different manners of production.
Mirabi (2011) considered the assumption of tardiness penalty in the model for the simultaneous lot-sizing and scheduling problem and presented a mathematical model for it.
3. Problem definition The problem is must determine production lot sizes and their schedules to minimize the sum of sequence -dependent setup costs, earliness costs (holding cost) and tardiness costs.
3. 1 Assumptions Major assumptions for problems simultaneous scheduling and lot-sizing with earliness/tardiness penalties (called SLET) are as follows: (1) Each order contains one product.
7. Conclusions and future research The problem investigated in this paper is one of simultaneous lot-sizing and scheduling with earliness/tardiness penalties (SLET) along with the sequence-dependent setup time and cost.
The problem objective is to determine the production lot-sizes and their schedules in order to minimize the sum of the total setup, holding, and tardiness cost.