Multi-period single-item lot sizing problem under stochastic environment has been tackled by few researchers and remains in need of further studies. It is mathematically intractable due to its complex structure. In this paper, an optimum lot-sizing policy based on minimum total relevant cost under price and demand uncertainties was studied by using various artificial neural networks trained with heuristic-based learning approaches; genetic algorithm (GA) and bee algorithm (BA). These combined approaches have been examined with three domain-specific costing heuristics comprising revised silver meal (RSM), revised least unit cost (RLUC), cost benefit (CB). It is concluded that the feed-forward neural network (FF-NN) model trained with BA outperforms the other models with better prediction results. In addition, RLUC is found the best operating domain-specific heuristic to calculate the total cost incurring of the lot-sizing problem. Hence, the best paired heuristics to help decision makers are suggested as RLUC and FF-NN trained with BA.
Lot-sizing problems have been studied with various respects for a long time whilst keeping the emphasis on modelling and optimisation of deterministic versions, which are known with the NP-Hard nature [1], [2] and [3] and usually handled with heuristic methods in-line with Wagner–Whitin (WW) approach [4], [5] and [6]. On the other hand, the real world versions of these problems are not as static and deterministic as modelled and handled in these ways, but, are rather dynamic and subject to probabilistic processes. That makes the problem type hard to model in easily solvable mathematical structures due to the complexity and uncertainty issues.
The stochastic dynamic lot-sizing (SDLS) problem can be formulated, in analytical or simulation models, either by assuming a penalty cost for each stock out and unsatisfied demand or by minimising the ordering and inventory costs subject to satisfying some customer service-level criterion. The analytical modelling approach is most frequently encountered in particular stochastic programming, where these models tackle only one type of uncertainty and assume a simple production system structure. Exact analytical solutions can only be developed, when the model is adequately simple. Further numbers of uncertain inputs/parameters escalate the complexity of the problems to an un-handlable state with analytical models. Due to the limitations given rise by stochastic/uncertain nature of controlling parameters in dynamic lot sizing problem (DLSP), heuristic approaches are preferred, rather than analytical models, in the solving larger-scale DLSP instances. Companies mostly work on a rolling horizon basis to form production plans consistent with new information on demand and prices which are usually uncertain and may only be known- sometimes partially over the forecast window. Since lot-sizing problem under uncertain demand and price conditions is so complex and mathematically intractable, generally, simulation techniques are used for obtaining good and feasible solutions. Simulation results have been accepted in finding total relevant cost as a real result. To reach the real total relevant cost, stochastic lot-sizing decision process under uncertain demand and price simultaneously using simulation was modelled by Manikas et al. [7] and Şenyiğit and Erol [8]. In this research, both price and demands are considered uncertain and assumed to be stochastic. On the other hand, among the heuristic approaches, artificial neural networks become very useful popular in modelling such ill-structured and/or highly complex problems, therefore stands promising to tackle SDLS problem. In fact, artificial neural networks with/without other metaheuristic approaches such as genetic algorithm have been interested in by recent research on solving various combinatorial optimization problems [3], [5] and [9].
This paper reports the attempts of solving SDLS problems with using a variety of artificial neural networks (ANN) trained with metaheuristic algorithms, namely genetic algorithms and bees algorithm, using Taguchi experimental design patterns in experimentation. To the best of authors’ knowledge, Taguchi design patterns have not been used to compare the performance of domain-specific heuristics. Furthermore, ANN trained with Bee algorithms have never been used in solving lot sizing problems. The data used for training and testing purposes is gathered from the simulation model of Şenyiğit and Erol [8] instead of an analytical solution. In the rest of the paper, the background of SDLS problem is introduced in the second section, while the novel approaches employed are revealed in section three and four. The experimental study is provided in section five and conclusions are indicated in section six.
This paper reports an investigation for solving the problem of multiple period single-item SDLS with uncertain and variable demand and price, where holding cost assumed independent of purchasing cost. Since SDLS problem is analytically intractable, heuristics embedded in FF-NN approaches are used to model and solve the problem. We have made an application dealing with multiple period single-item lot sizing problem with lost sale and rolling horizon using FF-NN models trained with BP, GA and BA. The significant factors and their levels identifying the problem and its degree of freedom have been considered as system inputs for RLUC, RSM, and CB cost calculation methods. After a TDOE-based ANOVA, RLUC is found the best of three operating methods with simulation. BA has been found the best of 3 learning heuristic algorithms used to train FF-NN models for lot-sizing problems first time in the literature.
