Manufacturing
11 optimization problems
A New Part Order Arrives — How Do I Get the Optimal Operation Sequence + Machine Choice + Setup?
If you are an SMB CNC manufacturer, tooling shop or engineering workshop producing 50-500 different parts, every new order puts the same decision in front of you: you take the customer's CAD model and have to work out on which machine, in which order, with which tool and fixture, and in how many setups the part will be made. If you simply write down the first feasible sequence that comes to mind, setup time grows 3-5x and parts that miss tolerance are reworked; finding the right sequence means comparing several alternative routings for the same part. When the decision lives only in one engineer's head, the similar-part memory walks out of the door when that engineer leaves, and routings of older parts are not refreshed when a new machine is bought. This page is for production-engineering teams who want to make the operation sequence and the machine assignment written and comparable as the bridge from design to make.
Backward from the Customer Order — Which Raw Material, When, and How Much Should I Order?
For mid-size manufacturing SMBs running 50-500 end items and 200-2,000 raw materials and sub-components (automotive Tier-2, white-goods component shops, furniture and assembly, machinery). With each product's parts list (BOM) and each part's procurement or production lead time on file, the question is: a customer orders 200 units of product X with a fixed delivery week — which raw materials in what quantity must be ordered which week, and which sub-parts must enter assembly when? Material requirements planning (academic name MRP) answers this question backwards from the delivery date and is the core logic underneath every ERP. Done on paper or by 'my supplier always takes 3 weeks' rules of thumb, you either run out and stop the line, or burn cash on excess stock.
Five Suppliers Quote the Same Part — How Much Do I Buy from Each?
You run a manufacturer with 20-200 staff and buy the same raw material or component from 4-8 different suppliers. Each supplier differs on price, quality, lead time, capacity, payment terms, and financial stability; deciding who stays on the approved list and how much of each order goes to whom are two separate calls. A wrong pick can trigger a months-long quality crisis or stop the line when a single supplier fails; the 'cheapest bid wins' approach hides quality, late-delivery, and compliance costs and ends up 15-40% more expensive. Scoring 5-15 bids across 8-12 criteria by hand in a spreadsheet becomes inconsistent fast.
How Do I Balance Production Rate, Inventory, Overtime and Subcontracting Over the Next 12 Months?
You run a mid-size manufacturer with 10-50M TRY monthly revenue, 5-30 product families and 30-200 workers; sales hands you a one-year demand forecast where peaks and troughs vary sharply month to month. Each month for each product family you must make five interlocking calls at once: run at a steady rate and build inventory, hire and fire workers, cover peaks with overtime, subcontract to sub-tier manufacturers, or push orders into next month. Get the mix wrong and average inventory bloats 20-40%, overtime breaks the 270 hours per year legal cap, last-minute subcontracting closes 20-40% above market price, and late deliveries lose customers. Splitting these five decisions across sales, production and HR with three separate intuitions burns 4-25M TRY of operating margin each year.
How Many Items Do I Sample From an Incoming Lot, and How Many Defects Do I Allow — Inspection Cost vs Customer Complaint Trade-off?
If you run incoming inspection at an automotive tier-1 supplier, the entry-control desk of an export textile mill, or quality control at a food or pharmaceutical plant, weekly lots of 100-5,000 parts arrive from your suppliers; testing each lot 100% is expensive, sometimes destructive, or delays production. For every lot you have to decide two numbers: how many parts to sample at random, and how many defects to allow before rejecting the whole lot. Too few samples plus a loose limit lets bad lots through and into customer complaints; too many samples plus a tight limit rejects good lots, picks unnecessary fights with the supplier, and delays deliveries. No matter how numeric the quality target in the contract looks, balancing those two risks by intuition gradually erodes both your quality memory and your cost control.
How Many Orders Per Year, How Much Per Order — So Setup + Holding Cost Is Minimum?
For a mid-size wholesaler with 5-50M TRY revenue, an SMB manufacturer buying packaging or raw materials, or a warehouse/purchasing lead managing 50-500 SKUs, two decisions repeat on every SKU: how large should each order be, and how often. Order too large and capital sits in the warehouse, storage fills up, spoilage + obsolescence + financing costs rise; order too small and per-order transport + customs + processing fees crush the unit cost as order frequency explodes. The practical 'buy one month's stock' or 'fill the truck' rule typically deviates 20-50% from the optimum — about 10-25% extra in total annual cost. The right balance per SKU comes from annual demand, fixed cost per order, capital-tying rate (25-45% per year in Turkey over the last 5 years), and unit storage cost; supplier volume discounts require a tier-by-tier comparison. On 200M TRY of annual purchases, doing this right is worth 300K-2M TRY of operating margin per year.
How Much of Each Product Should I Make for the Most Profit?
You run a 5-50-worker shop making 3-15 products. The same raw material, the same machines and the same workers are shared across products. Each week sales says 'we can sell 200 more of this', production says 'but that machine is full', accounting says 'product A has the highest margin, push that one'. Each product has a different margin, a different machine-hour consumption, a different raw-material usage and a different demand ceiling. Decide by gut and you usually load the product with the highest sale price — yet the product that **eats the least bottleneck-machine hour** can be more profitable. Take this call by intuition and 10-25% of the monthly margin you could earn from the same capacity stays on the table.
How Much Should I Produce In One Batch, and When Do I Start Again?
One of the basic questions a manufacturer faces: there is demand data for some period, every new production batch carries a setup cost (mold change, line setup, calibration), and what gets produced but not sold immediately incurs inventory cost (warehouse, capital tied up, obsolescence). The schedule of how much to produce each week must be planned in advance; the mathematical name for this is the Lot Sizing Problem. The single-product, deterministic-demand, uncapacitated variant was solved by Wagner and Whitin in 1958 via dynamic programming. Multi-product, capacitated, multi-stage variants grew into MRP, Capacitated Lot Sizing (CLSP), and Economic Lot Scheduling (ELSP).
Which Equipment Should I Service, and How Often?
Setting the preventive maintenance schedule for a production line with 5–30 major pieces of equipment, a fleet of 10–100 vehicles, or a facility with 50–300 machines/assets (hotel, hospital, factory, mall). Each asset has a different failure tendency, usage intensity, maintenance duration, and downtime cost. The decision: which asset, when, with which crew, in which sequence, so that unplanned failures are minimal, planned downtime is short, and the maintenance workload stays balanced. Manual planning works up to 20–30 assets; above that, either too-early maintenance wastes parts and labor, or too-late maintenance triggers failures and lost production.
Which Job to Which Machine, in What Order?
A CNC shop with 5–20 machines, processing 50–200 work orders per month. Each job runs on one or several machines; tool or fixture changeovers take 15–90 minutes and the time depends on the previous job (for example, an aluminum-to-steel switch can take 75 min while steel-to-steel takes 20 min). The decision: which job goes on which machine in which order, so delivery dates are met and total setup time stays low. A foreman can hold roughly 30 jobs in their head; past that the plan quality drops — overtime, late-delivery penalties, lost customers.
Which Task to Which Station — Hit the Takt, Keep the Headcount Low
For small and mid-sized manufacturers running an assembly line with 10-30 stations and 100-1,000 units per hour (automotive supplier, white goods, food packaging). The decision is this: each of the 30-200 elementary tasks on the product — screwing, fitting, welding, inspection, labelling — has to be assigned to one specific station. If a worker has too few tasks they stand idle; if too many, the line backs up and hourly output drops. Trial-and-error with a stopwatch and a spreadsheet cannot simultaneously satisfy task-order, ergonomic and must-not-pair rules.