Logistics & Supply Chain
7 optimization problems
From One Node to Another — How Do I Compute the Shortest Path on a Weighted Graph?
For SMBs that need to compute the fastest or shortest route between two points: 10-50-vehicle field-service teams (plumbing, electrical, appliance repair), urban courier/parcel operations, or dispatch centres coordinating emergency response. Every day brings hundreds of 'how do I get from A to B fastest right now' questions; the answer shifts with traffic, road closures and vehicle type. A wrong route costs the technician one or two jobs missed for the day, the courier a late delivery, and the firm a customer. Manual or by-eye routing typically leaves 20-60 wasted minutes per vehicle per day on the table compared with a network-aware route calculation.
Multiple Plants, Multiple Customers — How Much Does Each Plant Ship to Each Customer to Minimise Total Freight?
For food, packaging or textile producers shipping weekly from 3-8 plants or regional warehouses to 20-100 customers. The weekly decision is: which plant ships how much to which customer, given fixed plant capacities, stated customer demands, and a different per-unit cost (distance + vehicle + contract terms) for each plant-customer pair. The goal is the lowest total freight bill across the network. A 'nearest plant' or 'we've always done it this way' habit typically leaves 10-20% extra fuel and vehicle cost on the table compared with a systematic allocation.
One Vehicle, Many Stops — In What Order Should I Visit Them All to Minimize Total Distance?
You run a field technician visiting 8-15 customers a day (HVAC, lift servicing, white-goods repair), a single-vehicle supplier tour by a sales rep, or a PCB drilling machine sequencing 500-5,000 holes. All of them face the same core call: given N points, in what order should a single vehicle or head visit each one and return to the start. Get the order wrong and a field service vehicle burns 80-200 TRY/day extra in fuel and driver hours, a PCB line takes 15-30% longer per part, and the last customer of the day misses their delivery window. At 50 stops, a hand-built sequence runs 20-40% above the true minimum; as the number of stops grows, the gap from intuitive ordering compounds.
Several Vehicles, Many Customers — Which Vehicle in Which Sequence, Capacity Not Exceeded, Total Distance Minimum?
A distributor or supplier delivering daily from one depot to 10-100 customers (food, beverage, water, B2B spare parts); fixed vehicle capacity (2-5 tonnes, 30 m³), known order quantities per customer, flexible delivery times. Every morning three questions: how many vehicles dispatch today, which vehicle visits which customers, in what sequence — capacity not exceeded, total distance minimised. A dispatcher handles 15-25 customers mentally; beyond that, route quality drops, customers in the same area split across two vehicles, and 1-2 extra vehicles hit the road each day. 10-25% of total distance and 1-2 vehicles per day depend on planning quality; fuel + driver cost is 30-50% of operating expense.
What Fits Into a Truck or Container, and In What Order Do You Load It?
Given a truck, container, or cargo vehicle of fixed dimensions, what placement of boxes (or pallets) with varying sizes, weights, and stacking rules gives the highest utilization rate? The mathematical name for this question is the three-dimensional bin packing problem (3D-BPP) or container loading problem (CLP). Methods that simultaneously solve volume-fit, weight limits, stacking rules, weight distribution (balance), and delivery sequence (multi-drop) have been studied since the 1990s. Even a 5% utilization improvement materially raises deliveries-per-vehicle for an SMB.
Where Should I Open the New Warehouse?
A distributor, e-commerce operator, or SMB manufacturer is planning to open 1–5 new warehouses, branches, or distribution centers over the next 2–5 years. The decision: which city or region, how many facilities, what size, and which existing warehouses transfer which customer or order volume to which new facility. A bad location means 5–10 years of high transport cost, late deliveries, and lost customers; a good location means $300K–1.5M annual savings over the same period. When the decision is made on gut feel (e.g. 'put it next to the factory, the workers live nearby'), it rarely lands on the optimum — because transport cost, rent, taxes, labor, and service time are constraints that must be balanced together.
Which Van to Which Customer, at What Time?
A local delivery fleet of 5–30 vans planning daily routes. Each customer has a delivery time window (a shop accepts deliveries between 09:00–12:00; a restaurant only before 14:00). The decision: which customer goes on which van, in which order, so every window holds, fuel and driver hours stay low, and no van runs over capacity. A dispatcher can hand-plan 30–50 stops; past that, plan quality drops — empty kilometers, late deliveries, second runs, and driver overtime.