meio_general Module

Overview

For MEIO systems with arbitrary topology (not necessarily serial or tree systems), the meio_general module can optimize base-stock levels approximately using relatively brute-force approaches—either coordinate descent or enumeration. These heuristics tend to be quite slow and not particularly accurate, but they are sometimes the best methods available for complex systems that are not well solved in the literature.

Note

The terms “node” and “stage” are used interchangeably in the documentation.

Note

The notation and references (equations, sections, examples, etc.) used below refer to Snyder and Shen, Fundamentals of Supply Chain Theory (FoSCT), 2nd edition (2019).

See Also

For an overview of multi-echelon inventory optimization in Stockpyl, see the tutorial page for multi-echelon inventory optimization.

API Reference

meio_by_enumeration(network, base_stock_levels=None, truncation_lo=None, truncation_hi=None, discretization_step=None, discretization_num=None, groups=None, objective_function=None, sim_num_trials=10, sim_num_periods=1000, sim_rand_seed=None, progress_bar=True, print_solutions=False)[source]

Optimize the MEIO instance by enumerating the combinations of values of the base-stock levels. Evaluate each combination using the provided objective function, or simulation if not provided.

Parameters

  • network (SupplyChainNetwork) – The network to optimize.

  • base_stock_levels (dict, optional) – A dictionary indicating, for each node index, the base-stock levels to test in the enumeration. Example: {0: [0, 5, 10, 15], 1: [0, 2, 4, 6]}.

  • truncation_lo (float or dict, optional) – A float or dictionary indicating, for each node index, the low end of the truncation range for values to test for that node. If float, the same value is used for every node. If omitted, it is set automatically.

  • truncation_hi (float or dict, optional) – A dictionary indicating, for each node index, the high end of the truncation range for values levels to test for that node. If float, the same value is used for every node. If omitted, it is set automatically.

  • discretization_step (float or dict, optional) – A dictionary indicating, for each node index, the interval width to use for discretization of the values to test for that node. If float, the same value is used for every node. If omitted, it is set automatically.

  • discretization_num (int or dict, optional) – A dictionary indicating, for each node index, the number of intervals to use for discretization of the values to test for that node. If int, the same value is used for every node. If omitted, it is set automatically. Ignored if discretization_step is provided.

  • groups (list of sets, optional) – A list of sets, each of which contains indices of nodes that should have the same base-stock level. This speeds the optimization since the base-stock levels for the nodes in a given group do not have to be optimized individually. Any nodes not contained in any set in the list are optimized individually. If omitted, all nodes are optimized individually.

  • objective_function (function, optional) – The function to use to evaluate a given solution. The function must take a single argument, the dictionary of base-stock levels, and return a single output, the expected cost per period. If omitted, simulation will be used.

  • sim_num_trials (int, optional) – Number of trials to run in each simulation. Ignored if objective_function is provided.

  • sim_num_periods (int, optional) – Number of periods per trial in each simulation. Ignored if objective_function is provided.

  • sim_rand_seed (int, optional) – Rand seed to use for simulation. Ignored if objective_function is provided.

  • progress_bar (bool, optional) – Display a progress bar? Ignored if print_solutions is True.

  • print_solutions (bool, optional) – Print each solution and its cost?

Returns

  • best_S (dict) – Dict of best base-stock levels found.

  • best_cost (float) – Best cost found.

meio_by_coordinate_descent(network, initial_solution=None, search_lo=None, search_hi=None, groups=None, objective_function=None, sim_num_trials=10, sim_num_periods=1000, sim_rand_seed=None, tol=0.01, line_search_tol=0.0001, verbose=False)[source]

Optimize the MEIO instance by coordinate descent on the base-stock levels. Evaluate each solution using the provided objective function, or simulation if not provided.

Parameters

  • network (SupplyChainNetwork) – The network to optimize.

  • initial_solution (dict, optional) – The starting solution, as a dict. If omitted, initial solution will be set automatically.

  • search_lo (float or dict, optional) – A float or dictionary indicating, for each node index, the low end of the search range for that node. If float, the same value is used for every node. If omitted, it is set automatically.

  • search_hi (float or dict, optional) – A dictionary indicating, for each node index, the high end of the search range for that node. If float, the same value is used for every node. If omitted, it is set automatically.

  • groups (list of sets, optional) – A list of sets, each of which contains indices of nodes that should have the same base-stock level. This speeds the optimization since the base-stock levels for the nodes in a given group do not have to be optimized individually. Any nodes not contained in any set in the list are optimized individually. If omitted, all nodes are optimized individually.

  • objective_function (function, optional) – The function to use to evaluate a given solution. If omitted, simulation will be used.

  • sim_num_trials (int, optional) – Number of trials to run in each simulation. Ignored if objective_function is provided.

  • sim_num_periods (int, optional) – Number of periods per trial in each simulation. Ignored if objective_function is provided.

  • sim_rand_seed (int, optional) – Rand seed to use for simulation. Ignored if objective_function is provided.

  • tol (float, optional) – Algorithm terminates when iteration fails to improve objective function by more than tol.

  • line_search_tol (float, optional) – Tolerance to use for line search (golden section search) component of algorithm.

  • verbose (bool, optional) – Set to True to print messages at each iteration.

Returns

  • best_S (dict) – Dict of best base-stock levels found.

  • best_cost (float) – Best cost found.

truncate_and_discretize(node_indices, values=None, truncation_lo=None, truncation_hi=None, discretization_step=None, discretization_num=None)[source]

Determine truncated and discretized set of values for each node in network.

  • If values is provided, it is assumed to be a dictionary of truncated and discretized values, and it is returned without modification.

  • If truncation_lo, truncation_hi, and discretization_step or discretization_num are provided, these are used to determine the set of values.

  • truncation_lo, truncation_hi, discretization_step, and discretization_num may each either be a dictionary (with keys equal to node indices) or a singleton. If a singleton, the same value will be used for all nodes.

  • If any or all of truncation_lo, truncation_hi, discretization_step, and discretization_num are omitted, they will be set automatically:

    • truncation_lo is set to 0.

    • truncation_hi is set to 100.

    • discretization_step is set to 1 and discretization_num is set to (truncation_hi - truncation_lo) / discretization_step.

Parameters

  • node_indices (list) – List of indices of all nodes in the network.

  • values (dict, optional) – Dictionary in which keys are node indices and values are lists of truncated, discretized values; if provided, it is returned without modification.

  • truncation_lo (float or dict, optional) – A float or dictionary indicating, for each node index, the low end of the truncation range for values to test for that node. If float, the same value is used for every node. If omitted, it is set automatically.

  • truncation_hi (float or dict, optional) – A dictionary indicating, for each node index, the high end of the truncation range for values levels to test for that node. If float, the same value is used for every node. If omitted, it is set automatically.

  • discretization_step (float or dict, optional) – A dictionary indicating, for each node index, the interval width to use for discretization of the values to test for that node. If float, the same value is used for every node. If omitted, it is set automatically.

  • discretization_num (int or dict, optional) – A dictionary indicating, for each node index, the number of intervals to use for discretization of the values to test for that node. If int, the same value is used for every node. If omitted, it is set automatically. Ignored if discretization_step is provided.

Returns

truncated_discretized_values – Dictionary indicating a list of truncated, discretized values for each node index.

Return type

dict