In these weeks, a lot of supply planners are grappling with the uncertainty of potential tariffs. The fundamental question: Should we stock up before prices go up? Without the right tool, this can be a daunting task.
You work at SupDS, a company that specializes in supply chain solutions. Your client usually imports a product but can also source the product locally, albeit at 8% higher costs. The imports are potentially the target of new tariffs that may or may not come. The client estimates a 2/3 chance that new tariffs will be imposed and is uncertain whether these may be 5%, 10%, or 15%. If tariffs come, all three levels appear equally likely.
You are to provide the amounts of how much to source locally and/or internationally in this planning cycle while looking three planning cycles ahead. The lead times for new shipments are 2 planning cycles.
Particularly, the expected demands for periods 0 (the current), 1, 2, and 3 are 100 thousand each, with a 10% standard deviation (normally distributed). At the beginning of period 0, the client has 10 thousand units in stock and will receive a shipment of 90 thousand units momentarily (at the beginning of period 0). Another 90 thousand units that are already sourced will arrive at the beginning of period 1. These internationally sourced units cost $1.00 each.
If new tariffs will be imposed, this will be known at the beginning of period 1, which means you can decide whether to source locally or internationally with that knowledge in the next period. At this point in time, you have to decide what orders to put in now for shipments that will arrive at the beginning of period 2.
The client's costs result from any unmet demand at $1.50 per unit, the sourcing costs at $1.00 internationally plus potential tariffs or $1.08 locally (this is the aforementioned 8% extra for local sourcing), and inventory costs of 4 cents per unit, which incur if an item is held from one period to the next.
What order(s) do we put into the system?
If you have found a good recommendation to minimize expected costs, please consider the risk as well. Particularly, look at the conditional value at a risk of 10%.
With the help of InsideOpt Seeker, we quickly arrive at this recommendation: Put in an order for 133,187 units from the international vendor now to arrive at the beginning of period 2. In the next period, we will source an additional 63,902 units to arrive at the beginning of period 3, whereby we will decide whether to source these internationally or locally, whichever will be cheaper.
With this plan, we expect average costs of $419,347 (marginally higher than $418,386 which we could achieve at higher risk) and a CVaR-10% of $462,535 (down from $465,368 at lower expected costs).
The Seeker model is given below. As you can see, Seeker works at a resolution of 10,000 scenarios here and gives you three different options after the allotted 90 seconds: the order levels to minimize expected costs (you would order ~113 thousand units now and ~77 thousand units later), the levels to minimize CVaR-10% (order ~188.5 thousand units now and ~16 thousand later), and the aforementioned compromise between mean and risk (order ~133 thousand now and ~64 thousand later).
All that in less than 90 straightforward lines of code. What tools are you using to make decisions under uncertainty?
env = skr.Env("license.sio", processID=pID, runID=uID, stochastic=True)
env.set_stochastic_parameters(int(1e4), 0.85)
# constants
zero = env.convert(0)
one = env.convert(1)
# stochastic data
demand = [env.normal(100, 10, 0, 200) for _ in range(4)]
tariffs = [[zero, env.bernoulli(2 / 3) * env.categorical_distribution([1 / 3, 1 / 3, 1 / 3], [0.05, 0.10, 0.15])],
[zero, zero]]
existing_lead_times = [0, 1]
new_lead_times = [[2, 3],
[2, 3]]
inbound_costs = env.convert([1, 1.08])
# decisions
gene_order_amount = [[env.continuous(0, 300), env.continuous(0, 300)],
[env.continuous(0, 300), env.continuous(0, 300)]]
# derive KPIs
in_stock = [env.convert(10)]
unsold = []
lost_sales = zero
inventory = zero
# infer what sourcing method is cheaper to use for period 1
order_amount = [[a for a in b] for b in gene_order_amount]
cheaper = (inbound_costs[0]+tariffs[0][1]) > (inbound_costs[1]+tariffs[1][1])
order_amount[0][1] = cheaper.not_() * gene_order_amount[0][1]
order_amount[1][1] = cheaper * (gene_order_amount[0][1] + gene_order_amount[1][1])
# simulate outcomes
for p in range(4):
additional = env.sum([order_amount[k][i]*(new_lead_times[k][i]==p) for k in range(2) for i in range(2)] +
[env.convert(90) * (existing_lead_times[k]==p) for k in range(2)])
available_to_sell = in_stock[p] + additional
diff = demand[p]-available_to_sell
in_stock.append(env.max_0(-diff))
inventory = inventory + 400/10000 * in_stock[-1]
lost_sales = lost_sales + 1.5 * env.max_0(diff)
inbound = 190 + env.sum([order_amount[k][i]*(inbound_costs[k]+0.1*tariffs[k][i]) for i in range(2) for k in range(2)])
exp_inventory = env.aggregate_mean(inventory)
exp_lost = env.aggregate_mean(lost_sales)
exp_inbound = env.aggregate_mean(inbound)
total_costs = exp_inventory + exp_lost + exp_inbound
cvar = env.aggregate_cvar(inventory+lost_sales+inbound, 0.10, True)
exp_in_stock = [in_stock[0]] + [env.aggregate_mean(a) for a in in_stock[1:]]
order_amount[0][1] = env.aggregate_mean(order_amount[0][1])
order_amount[1][1] = env.aggregate_mean(order_amount[1][1])
# optimize
env.minimize(cvar, 30)
cvar_exc = cvar.get_value()
costs_ok = total_costs.get_value()
env.minimize(total_costs, 30)
cvar_ok = cvar.get_value()
costs_exc = total_costs.get_value()
env.multi_objective([cvar,total_costs], [cvar_ok, costs_ok], [cvar_exc, costs_exc], [False, False], 30)
# report
print("costs", total_costs.get_value())
print("cvar", cvar.get_value())
print("a prior order", [[round(a.get_value(),3) for a in gene_order_amount[k]] for k in range(2)])
print("a posteriori orders", [[round(a.get_value(),3) for a in order_amount[k]] for k in range(2)])
print([a.get_value() for a in exp_in_stock])
print(env.get_number_evaluations(), "evals")
env.end()