「紅色接單、黑色出貨」之數理分析及其延伸－－模式參數可變下之數學規劃模型

Generalized Theoretical Analysis on “Taking Loss at the Ordering Time and Making Profit at the Delivery Time” -- Programming Models with Changeable Parameters

企業能力可能因為投資而擴展，也會隨著時間動態改變，這使得企業敢低價搶單，實現「接單時虧損，交貨時獲利」的目標；雖然在實務上，此現象確實存在（特別是在競爭劇烈、經營環境變動快速的高科技產業），但仍缺乏足以解釋此實務現象的理論架構，以及量化的數學模式。本研究運用「多目標決策」方法中的「多準則多資源水準限制下之線性規劃模型」(multiple criteria and multiple constraint levels linear programming models; MC2LP model)，研究當企業的經營參數（包括產品單位利潤與可用資源水準）可隨資本投資與時間變動時，如何設計有效的量化模式來分析及尋找最佳的決策，使「接單時虧 損，交貨時獲利」變成可行的、有效的競爭策略。

Not all of the products or services proven to be successful finally in the markets are promising to make profit, even expecting to be loss, in the initial stage for the product or service be created. Eventually, due to the dynamic change of productive conditions and/or marketing environment, these products or service reap profits for corporate. This explains why do some companies rather take loss at the ordering time, because they have the confidence that they can make profit at the delivery time due to the dynamic change of production system parameters, including profit rate, cost rate and resource consumption efficiency, etc. Even time delay cannot bring change, the production system conditions can be changed by capital investment. In other words, as time of entering market drifts, the efficiency of production and market system improve and then providing the possibility to cut down the production cost. Accordingly, enterprises can promise their customers a competitive price to take the order and, later, produce the products at the optimal timing and production conditions. Above phenomenon exists especially in high-tech industries which compete violently and whose environment change quickly. Nevertheless, aforementioned phenomenon cannot be explained by traditional product planning model or product mix model, since, in these models, parameters such as the unit profit in objective function, the resource consumption rate and the resource available level are given in advance and cannot be changed during the solving process. To cope with this restriction, sensitivity analysis can be adopted. However, sensitivity analysis for model parameters restrains researcher from exploring the overall solution space, which is changed with variation of the parameter set, and limits the capability of designing the optimal strategy. For breaking through the limitation of the traditional model, changeable parameter production planning models are proposed to solve the above problems. The purpose of this thesis is to take the coefficients of production planning model as changeable values, which can be varied by environmental factors, but not fixed values as in the traditional model. Accordingly, the characteristics of the changeable parameter space of the model can be derived. We applies mathematical models of multiple criteria decision making – multiple criteria and multiple constraint levels linear programming (MC2LP) models, and extended techniques Seiford and Yu, 1979) to explore that when the management parameters (including profit and available resources) can be changed with capital investment and time, how to design an effective model to identify the best solution as to make “taking loss at the ordering time and making profit at the time of delivery” an effective competitive business strategies. From the application perspective, this paper provides an effective and efficient approach for analyzing, interpreting and programming usable production strategies in dynamic environment. Some further research directions can be derived including: (i) considering practical constraints in the model, (ii) dealing the uncertainty and fuzziness of parameter change, (iii) developing contingence plan (Li, Shi and Yu, 1990) to cope with different situations, (iv) discussing the dual problem of the proposed model and its meaning, and (v) applying the proposed model in other application fields.