| Production planning problem is about how to arrange the product yield and produc-tion time so that customers’ demand can be meet. That is to say, production planning,is direct impacting the ability of the product to adapt for the market. However, in therealistic production planning, the customers’ demand often have randomness due to themeasure errors and data noise. In this thesis, we employ a theoretical tool that deal withrandomness to study the production planning problem.We present two classes of production planning models–the probability productionplanning model with separate service-level constraints and the value-at-risk productionplanning model with joint service-level constraint. When demand variables are mutuallyindependent discrete and continuous ones, the models can be transformed into their equiv-alent integer programming and mixed-integer programming problems with deterministicconstraints, respectively. So we suggest the branch-and-bound method and the branch-and-bound method based on approximation method to solve the equivalent programmingproblems. Finally, some numerical experiments are performed to demonstrate the newmodeling idea and the efciency of the proposed solution methods.The main contribution of this thesis contains the following four aspects:(i) We present two classes of production planning models–the probability production plan-ning model with separate service-level constraints and the value-at-risk production plan-ning model with joint service-level constraint;(ii) In the case that demands are discrete and continuous variables, the methods of theoriginal problems being turned into their equivalent deterministic ones are proposed;(iii) Considering this two cases, we use the branch and bound algorithm and the branchand bound algorithm based on approximation method,respectively, to solve the equivlentproblems;(iv) numerical examples are provided to illustrate the modeling ideas and the efectivenessof the proposed approachs. |
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