Stochastic and fuzzy flexible aggregate production planning to manage plan stability
Aggregate production planning generally deals with configuration of an aggregate plan in advance of 6 to 18 periods (e.g. months) to give the organizations an idea about the amount of invested money, utilized capacity, required inventory and any other procurement activities need to be done before the actual times arrives. Inherent uncertainties faced by the planners (caused by unreliable estimates of demand, cost or production processes) could make the production planning a challenging task. That is, the production planners not only have to deal with the available parameters’ uncertainties (Demand, cost, etc.), but also, new information which become available with the pass of time, sometimes requires several re-planning activities for the future periods. Stochastic and Fuzzy planning are among the popular techniques to deal with the uncertainties in optimization models. While the stochastic/fuzzy programming techniques provide a more realistic representation of future estimations, the production plans need to be also revised from one planning period to another as time rolls and new information become available (a.k.a. rolling horizon planning). However, frequent re-planning activities and changes in the production plans could result in a state of plan instability causing plan related "nervousness" in manufacturing firms, which could undermine manager’s confidence in the system, depriving it of the support needed for successful operations. It could also result in disruptions in the production and delivery systems, which could result in inaccurate personnel scheduling, machine loading, and unnecessary supplier orders (Pujawan and control 2004). Frozen horizon along with other solution approaches attempt to provide insights on how to mitigate nervousness, however, most of the existing approaches do not consider the flexibility aspect in production plans. Flexible Requirements Profile (FRP) and bi-objective optimization are alternative stabilizing approaches which are the focus of this research. In FRP, flexible bounds are enforced on production plans to maintain the desired degree of flexibility. Instead of 0% flexibility in the case of a frozen period or 100% flexibility in the case of plan to order, FRP model considers different flexibility levels. For the bi-objective optimization approach, the production planning problem can also be formulated with two objectives, where one trades-off between the traditional cost objective and the plan stability objective. The aim of this research is to address several flexible production planning related open research questions. While deterministic FRP-APP and Bi-Objective APP models have been developed (Demirel 2014) and compared to a traditional deterministic APP model, 1) the deterministic FRP-APP and Bi-objective APP models have not been compared with APP techniques such as Stochastic APP and Fuzzy APP models that are meant to handle uncertainties, and 2) there has not been an attempt to develop Stochastic and Fuzzy FRP-APP and Stochastic and Fuzzy Bi-Objective APP models to deal with planning system uncertainties and 3) also, while FRP-APP was tested with two industry-based case studies and Bi-Objective APP was tested on one industry-based case study, more validation is needed under different industrial scenarios to conclude about the performance of the FRP-based models. Therefore, our main research objectives here are: 1) to compare FRP-APP with Stochastic and Fuzzy APP in terms of both plan cost and stability, 2) to develop and compare new "hybrid" Stochastic and Fuzzy FRP-APP models to combine the strengths of stochastic and fuzzy models, which represent input uncertainties more realistically, and FRP models that have better control over plan variability, 3) to develop and compare new Stochastic and Fuzzy Bi-objective APP models as alternate techniques to trade off the traditional cost objective with the stability objective formally following a multi-objective decision making framework, and 4) to conduct extensive testing of the proposed FRP-based and Bi-objective models under various industry scenarios. Since there are multiple ways to approach stochastic and fuzzy production planning models, for both Stochastic and Fuzzy FRP-APP as well as the Bi-objective Stochastic and Fuzzy APP models that are developed here, we used four of the well-known techniques (two on the stochastic and two on the fuzzy programming) to analyze the effect of specific stochastic and fuzzy approaches on the model performance. More specifically, for the stochastic models, we utilized the Chance-Constraint (CC) and Robust-Stochastic (RS) approaches and for the fuzzy models, we utilized Fuzzy Max-Min (MM) and Fuzzy Ranking (R) approaches. Hence, we will propose in this dissertation eight new APP models, namely: Stochastic CC-FRP-APP, Stochastic RS-FRP-APP, Stochastic CC-BO-APP, Stochastic RS-BO-APP, Fuzzy MM-FRP-APP, Fuzzy R-FRP-APP, Fuzzy MM-BO-APP, and Fuzzy R-BO-APP. For each of these models, the effect of industry cost structure, demand structure, flexible limits, and the modeling approaches are analyzed using a comprehensive design of experiments analysis to identify influential factors on plan cost and stability. The results indicate that, for most of the industries tested, the Fuzzy FRP-APP models improve on stability while yielding close cost performance as compared to the Fuzzy APP models. Fuzzy FRP-APP and (non-fuzzy) FRP-APP models show similar performances especially when the Fuzzy R-FRP-APP formulation is used. It is found that lower levels of flexibility limits control stability better as expected, but in general depending on the industry setting and the demand scenario, the cost and stability of the FRP-based models need to be carefully analyzed to choose an ideal flex-limit for practical applications. The results for the stochastic case show that when Stochastic APP is compared with the FRP-APP, a scenario-based modeling could adversely affect its stability performance. While maintaining the same cost preference as compared to the FRP-APP, the CC-APP, shows more control on the stability of the plans compared to the FRP-APP. The incorporation of the stochastic uncertainty into the FRP-APP formulation, however, can retrieve its better stability performance with improved cost performance as compared to its Stochastic APP counterpart. As a result, Stochastic FRP-APP can be considered as a reliable planning approach to take care of input uncertainty and stability issues at the same time. The stability improvements are more visible using Stochastic RS-FRP-APP with more strict flex-limits. Similar to the fuzzy models, for the stochastic case, a careful selection of flex-limits can further highlight the comparative stability improvement of the Stochastic FRP-APP models as compared to the Stochastic APP planning formulations. The Bi-objective Stochastic/Fuzzy APP model results indicate that defining the stability as a second objective in the Fuzzy/Stochastic APP formulation could result in more stable plans. In addition, the general observation from different Industry Cases indicates the cost and stability tradeoff performance of the Fuzzy Bi-objective APP are more promising as compared to the Fuzzy FRP-APP, while under stochastic formulations, the Stochastic Bi-objective APP and the Stochastic FRP-APP show more competitive cost and stability performances. This emphasizes the importance of a more careful selection of the specific stochastic/fuzzy technique (i.e. CC vs. RS / MM vs. R) and the weights for the cost and stability objectives in the Bi-objective APP formulation. The overall results indicate that the proposed Stochastic and Fuzzy FRP-APP and the Stochastic and Fuzzy Bi-objective APP techniques show good potential in terms of stability and cost performance. They also provide more control to a planner to manage plan stability concerns, while representing input data uncertainties more realistically at the same time. For a given industry, these planning techniques require sensitivity analysis with respect to the flexibility limits and objective weight selection, depending on the technique deployed.