Demand Forecasting,Lot-sizing And Scheduling In The Multistage Production System With Dynamic Information Updates

Customer orientation makes manufacturing switch back and forth among different products,and product complexity makes such switching rather difficult.Hence,lot-sizing and scheduling（LSS）becomes critical and challenging in such manufacturing systems.LSS is to determine the optimal production batches and quantities,machine assignment（in case of multiple machines）and production sequence to fulfill the demand with minimal costs of production and inventory.Lot-sizing and scheduling（LSS）is critical due to its profound impact on the productivity of the manufacturing system.However,most approaches to LSS problem use hierarchical planning method to obtain solutions,namely,considering separately the problem at mid-term（lot-sizing）and short-term（scheduling）level.Although hierarchical planning helps to reduce the complexity of the solution process,however,due to inter-dependence between mid-term and short-term planning levels,it usually leads to sub-optimal solutions to original LSS problem.In fact,these planning and scheduling decisions should be made simultaneously in order to obtain global optimal solutions（Stadtler,2005）.In manufacturing firms,production planning and scheduling usually starts from demand forecasting.Thus,accurate demand forecasting is crucial for production planning and scheduling.Often,the manufacturing managers need demand information from the component item level to multiple product family level,which forms a hierarchical time series.Furthermore,in many cases,demands evolve over time as new information becomes available;therefore it must be incorporated into the production plan.In the literature,the LSS problem with deterministic demands over the planning horizon receives considerable attention（see,e.g.,Almeder et al.2015;Seeanner and Meyr 2013）.However,to the best of our knowledge,the integrated LSS problem with demand information updating has yet been studied.In this thesis,we consider the mid-term demand forecasting,production planning and scheduling problems.This problem is the most significant in manufacturing firms as it plays a critical role in improving both the tactical and operational efficiency,and enables the firms to compete in the market successfully.The thesis is organized as follows.Chapter 1 and 2 briefly discuss the background and challenges of lot-sizing and scheduling problems.Firstly,we discourse the relationship between supply chain planning matrix with advanced planning systems（APS）.We then highlight the interrelationship among different planning levels.Finally,we describe the importance of integration of different planning levels and discuss the five classical single-level integrated lot-sizing and scheduling problems.The literature related to lot-sizing and scheduling is summarized and discussed in Chapter 3.We divide the literature review into two sections as follows:（i）forecasting under correlated demand,and（ii）lot sizing and scheduling problems with highlighted gap in the literature.In Chapter 4,we first address the hierarchical forecasting problem and examine the performance of classical hierarchical forecasting approaches under the cross-correlated data series.The computational results reveal that the top-down approach performs better when data have high positive correlation compared to high negative correlation.We also propose a new hybrid approach,and consider the updated demand information using the MMFE（Martingale Model for Forecast Evolution）by assuming that demand of the final product follows an AR（1）process.The most commonly used forecasting approaches are Top-down（TD）and bottom-up（BU）forecasting approaches.However,the literature is unclear about the conditions in which one method is superior to the other.The combination of the two methods may improve the forecast accuracy when the performance of one method is not significantly better than the other one（DeLurgio,1998;Hyndman et al.,2011;Pennings,Dalen,and Dalen,2017）.We develop a new hybrid approach（HA）with step-size aggregation for hierarchical time series forecasting,which performs better compared to either the top-down approach or the bottom-up approach as shown in the computational experiments.The new approach is a weighted average of the two classical approaches with the weights being optimally determined for all the series at each level of the hierarchy to minimize the variance of the forecasting errors of the approach.With the objective of minimizing the variance of the forecast errors of HA,we build a nonlinear programming model to compute the weights of BU and TD.The resulting weights depend on the variances and covariances of the forecasting errors.However,the independent selection of weights for all the series at each level of the hierarchy makes the HA inconsistent while aggregating suitably across the hierarchy.To deal with this issue,we propose a step-size aggregate factor which indicates the relationship between forecasts of the two consecutive levels of the hierarchy.The key advantage of the proposed HA is that it captures the structure of the hierarchy inherently due to the combination of the hierarchical approaches instead of independent forecasting all the series at each level of the hierarchy.We demonstrate the performance of hierarchical forecasting approaches by using the monthly data of the Industrial category of M3-Competition data.Finally,we study the problem of forecast evolution over time across the planning horizon.We employ the MMFE to model the evolving demand over time with demand information updating by assuming that the demand of each final product follows lag 1 auto-regressive AR（1）process.In Chapter 5,we consider a multilevel multistage integrated LSS problem with demand evolution,where the independent demand forecasting of the end products is based on the historical data and evolves over the time along the planning horizon as new information become available.The demand for components in other production stages depends on the production of its downstream stage.The products manufactured with limited production capacity and backorders are not allowed.Due to the variety of products,the bottleneck stages may shift during manufacturing process,and sequence-dependent setups incur time or costs.The products also incur an inventory holding cost if they are held in warehouses before delivered to customers.The objective is to find the production batches,quantities and production sequences at different production stages to minimize the total costs of production and inventory.Obviously,this problem is NP-hard since the NP-hard problem F F s||C_maxis a special case of this problem.We model this multilevel multistage lot-sizing and scheduling（LSS）problem as mixed-integer programs（MIP）,denoted as MMSLSP（multilevel multistage simultaneous lot-sizing and scheduling problem）,and as MMSLSP-SCC（model with shortfall based chance constraints）,respectively,using a hybrid period approach（i.e.,combining micro and macro-periods）where updated demand information is incorporated in the model based on the rolling horizon.The solution approaches and the computational experiments for lot-sizing and scheduling problem are studied in Chapter 6.Three heuristic algorithms based on the relax-and-fix method within a rolling horizon framework are developed to solve the models.The performance of the heuristic algorithms are tested using computational experiments with both small and large-scale problem instances.The results of the computational experiments show that heuristic 1 and 3 perform better than Heuristic 2 for all the problem instances.In particular,for the large-sized instances,heuristic 1 produces good quality solutions compared to heuristic 2 and3 because heuristic 2 and 3 are unable to provide feasible solutions in many cases with assembly and general product structure.The conclusions and future research directions are discussed in the chapter 7.The computational results show that the proposed hybrid approach for hierarchical forecasting performs better compared to the existing hierarchical forecasting approaches.To model the forecast updates,MMFE is employed,and based on the rolling horizon it is integrated into the proposed lot-sizing and scheduling models.Heuristic 1is the most efficient and effective for all the testing instances among the three heuristic algorithms.As for the future research:first,more sophisticated forecasting approaches are still needed for hierarchical forecasting in order to produce smaller forecast errors compared to the existing methods;second,it is necessary to develop better mathematical models for lot-sizing and scheduling problems by incorporating practical constraints in manufacturing such as limited work-in-process（WIP）inventory,certain inventory level after the planning horizon,and effective and efficient solution approaches for solving such optimization models.