A compilation of OR tools for the Stochastic-Dynamic perishable Inventory Routing Problem (pIRP).

• Physical State ($R_t$):

  state:  Current available inventory: (dict)  Inventory of product k \in K of age o \in O_k. 
  Since the state is the inventory before the decision is taken, there is no age 0 inventory.
          
  When backlogs are activated, will appear under age 'B'   
  

• Other deterministic info ($Z_t$):

  p: Prices: (dict) Price of product k \in K at supplier i \in M
  
  h: Holding cost: (dict) Holding cost of product k \in K
  
  historical_data: (dict) Historical log of information
  

• Belief State ($B_t$):

  sample_paths: Simulated sample paths (optional)
  
  q: Available quantities: (dict) Forecasted available quantity of product k \in K at supplier i \in M
  
  d: Demand: (Dict) Forecasted demand of product k \in K
  

The action can be seen as a three level-decision. These are the three layers:

1. Routes to visit the selected suppliers

2. Quantities to purchase from each supplier

3. Demand compliance plan, dispatch decision

4. (Optional) Backlogs compliance

Accordingly, the action will be a list composed as follows:

$$ X = [\text{routes, purchase, demand compliance, backlogs compliance}] $$

    routes: (list) list of lists, each with the nodes visited on the route (including departure and arriving to the depot)

    purchase: (dict) Units to purchase of product k \in K at supplier i \in M

    demand_compliance: (dict) Units of product k in K of age o \in O_k used to satisfy the demand

    backlogs_compliance: (dict) Units of product k in K of age o \in O_k used to satisfy the backlogs

The realized values of the parameters of the environment (prices, available quantities, demand and holding costs). This are the real observed values used on the transition function.

    p: Prices: (dict) Realized price of product k \in K at supplier i \in M

    q: Available quantities: (dict) Realized available quantity of product k \in K at supplier i \in M
    
    d: Demand: (Dict) Realized demand of product k \in K

    h: Holding cost: (dict) Realized holding cost of product k \in K

The transition function takes as input the current state, the action and the stochastic realization and returns the next state. I.e., updating the inventories, the forecasted parameters, the historical values and the sample paths.

$$ S_M^X(S_t, X_t, W_t)=S_{t+1} $$

The cost function computes the following costs of a given action:

1. Routing cost
2. Purchasing cost
3. Holding cost
4. Backorders cost