the decisions behind the plans.

Routes, schedules, allocations, stock and prices. Each problem type below shows the question planners ask and why it is hard. It also shows how kint solves it to a plan with a stated gap.

see the problem types show us one decision

01 · familyroutes and allocationvehicle routing · resource allocation 02 · familyschedulingproduction scheduling · workforce scheduling 03 · familystock and priceinventory optimization · pricing and bidding

the resulta plan with its gapbinding limit · sensitivity · bound and gap · record

Why types matter

Most weekly planning decisions take one of a few mathematical shapes. Recognise the shape and the method follows. With the right method, the solver reports how close the plan is to the best one possible.

Problem types

three families, six problems.

Each page explains one problem in plain language first and in mathematical terms second.

01 · family

routes and allocation

Who or what goes where. Vehicles to stops, crews to regions, assets to tasks.

NP-hardvehicle routingWhich vehicle serves which stop, in which order, so every delivery lands in its window with the fewest kilometres?MIP · CP · Metaheuristicsread →NP-hardresource allocationTwo crews dropped out after the storm. How do the remaining crews cover every region with the least travel and no gap in emergency cover?LP · MIP · Multi-periodread →

02 · family

scheduling

What happens when, and in which order. Jobs on machines, people on shifts.

NP-hardproduction schedulingWhich job runs on which machine, in which order, so the due dates hold with the fewest changeovers?CP · MIP · Hybridread →NP-hardworkforce schedulingWho works which shift next month, so every position has a qualified person and every rest period holds?MIP · CP · ML demand forecastingread →

03 · family

stock and price

How much to hold and what to ask. Inventory across a network, prices and bids across markets.

NP-hardinventory optimizationHow much of each item belongs in which warehouse, so the service level holds with the least capital tied up?MIP · Stochastic · ML forecastingread →NP-hardpricing and biddingWhich prices or bids, across products, channels or markets, give the best margin within the rules we have to keep?MIP · QP · ML elasticityread →

At a glance

methods, flagships, industries.

Which methods each problem calls for, how hard it is in theory, which kint flagship takes it on, and where it shows up.

Optimization problem types at a glance
Problem	Methods	Complexity	Flagships	Used in
vehicle routing	MIP · CP · Metaheuristics · Warm start	NP-hard	manifest horizon	logistics and supply chain energy and utilities +2 more
production scheduling	CP · MIP · Hybrid	NP-hard	takt	logistics and supply chain manufacturing
resource allocation	LP · MIP · Multi-period · Rolling horizon	NP-hard when integer, polynomial when continuous	manifest merit	logistics and supply chain energy and utilities +3 more
inventory optimization	MIP · Stochastic · ML forecasting	NP-hard (multi-echelon)	horizon	logistics and supply chain manufacturing +1 more
pricing and bidding	MIP · QP · ML elasticity	NP-hard when discrete, convex when continuous	merit horizon	energy and utilities retail and e-commerce
workforce scheduling	MIP · CP · ML demand forecasting	NP-hard	manifest takt	logistics and supply chain energy and utilities +4 more

real decisions mix shapes.

A port's berth plan is allocation and scheduling at once. Bring one recurring decision: kint's decision agent writes the rules down with the planners, and the model takes whatever shape the rules require.

show us one decision

Methods: LP · MIP · CP · QP · blackbox
Results: Plan, binding limit, sensitivity, bound and gap, record
Read next: how it works · glossary · comparisons
Contact: hello@kint.pro