Bayesian decision flow on supply chain

[hyunjimoon]

Estimation for inventory model takes 13 hours, so I need a simpler model for Bayesian decision workflow demonstration where posterior predictive (test functions) is supply chain profit. For this, we should build vensim model for https://twiecki.io/blog/2019/01/14/supply_chain/. Given this input, uncertainty propagation plot and value is the output.

goal

with be the test function from https://github.com/Data4DM/stanify/blob/main/stanify/calibrator/draws_data_mapper.py#L113

def objective(orders, supplier_yield=supplier_yield_post_pred,
              demand_samples=demand_samples, max_order_size=MAX_ORDER_SIZE):
    orders = np.asarray(orders)
    losses = []
    
    # Negative orders are impossible, indicated by np.inf
    if np.any(orders < 0):
        return np.inf
    # Ordering more than the supplier can ship is also impossible
    if np.any(orders > MAX_ORDER_SIZE):
        return np.inf
    
    # Iterate over post pred samples provided in supplier_yield
    for i, supplier_yield_sample in supplier_yield.iterrows():
        full_yield, price_per_item = calc_yield_and_price(
            orders,
            supplier_yield=supplier_yield_sample
        )
        
        # evaluate loss over each sample with one sample from the demand distribution
        loss_i = loss(full_yield, demand_samples[i], price_per_item)
        
        losses.append(loss_i)
        
    return np.asarray(losses)

structure (stock-flow variable)

three suppliers with different yields

decision rules

def loss(in_stock, demand, buy_price, sales_price=SALES_PRICE, holding_cost=HOLDING_COST):
    # How much do we earn per launch
    margin = sales_price - buy_price
    # Do we have more in stock than demanded?
    if in_stock > demand:
        total_profit = demand * margin
        # everything left over after demand was met goes into holding
        total_holding_cost = (in_stock - demand) * holding_cost
        reward = total_profit - total_holding_cost
    else:
        # Can only sell what we have in stock, no storage required
        reward = in_stock * margin
    
    # Usually we minimize, so invert
    return -reward

def calc_yield_and_price(orders, 
                         supplier_yield=np.array([.9, .5, .8]),
                         prices=PRICES
                        ):
    orders = np.asarray(orders)
    
    full_yield = np.sum(supplier_yield * orders)
    price_per_item = np.sum(orders * prices) / np.sum(orders)
    
    return full_yield, price_per_item

calc_yield_and_price([100, 60, 60])