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    The Capacitated Lot-Sizing Problem

    Prerequisites

    • Please look at Getting Started first for the most basic functions and the setup of OPTANO.Modeling

    The mathematical Model

    Sets: $$T= \text{the set of }t\text{ time steps}$$

    Parameters: \begin{array}{l} d_t& = \text{ demand in time step }t\newline p_t& = \text{ unit production cost in time step }t\newline f_t& = \text{ machine setup cost in time step }t\newline h_t& = \text{ inventory cost in time step }t\newline c_t& = \text{ production capacity in time step }t \end{array}

    Variables: $$ y_t = \begin{cases} 1, \text{ if we set up machines in time step }t\newline 0, \text{ else} \end{cases} $$

    \begin{array}{l} x_t \in \mathbb{R}^+ = \text{ production amount in time step }t \newline s_t \in \mathbb{R}^+ = \text{ inventory amount in time step }t \end{array}

    Objective: $$min \sum\limits_{t=1}^T( p_t x_t + f_t y_t + h_t s_t )$$

    Restrictions:

    \begin{array}{l} s_{t-1} + x_t = d_t + s_t & \forall t=1,...,T & \text{(Production, inventory & demand balance)}\newline s_0 = 0,s_T= 0 & & \text{(Inventory is empty at the start and the end)}\newline x_t \le c_t y_t & \forall t=1,...,T & \text{(Capacity can not be exceeded)} \end{array}

    The Capacitated Lot-Sizing Problem

    • Step 1: Create Business objects for your Model
    • Step 2: Create your Model Class
    • Step 3: Retrieve the Solution of your Model
    • Step 4: Visualize your model (optional)
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