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From your plant to a priced, optimized decision.

This page is for planners, process engineers, and optimization leads. It covers what Mizahn models, how it values a plan, how it handles uncertainty, how it optimizes, and what it gives back.

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01The model

Your network as a resource-task network.

Mizahn represents your network as resources and tasks. Resources are what you have and move: feedstocks, intermediates, products, units, tanks, rail cars, and pipeline capacity. Tasks are what you do with them: crack, react, separate, store, ship.

A task can consume several resources and produce several at once, in linked ratios. That is how a cracker works, and it is how Mizahn plans. Co-products are first-class, so there is nothing to adjust by hand after the solve.

Tasks with many outputs
One operation makes a slate of products. Every output is planned, routed, and valued.
Linked yields
Yields depend on feed and operating mode, so changing one changes every co-product together.
Shared equipment
A unit can run different modes, grades, or campaigns, each with its own rates and yields.
Storage and logistics
Tanks, silos, rail cars, and pipelines are resources with capacities, not afterthoughts.

Fig. 01Co-product network, resource-task view

Illustrative

Co-product chemical network in resource-task form, with decision points (illustrative)Three feeds, ethane, propane, and naphtha, enter a steam cracking task. Its single output splits into five linked co-products: ethylene, propylene, crude C4, pygas, and fuel gas with hydrogen. Fuel gas returns to the cracker furnaces. Purchased ethylene can supplement produced ethylene. Ethylene feeds a polyethylene line, propylene a polypropylene line, and crude C4 a butadiene extraction unit. Products go to silos, a sphere, and a tank, then to a shipping task that uses a limited fleet of rail cars, and on to contract, spot, and export customers. Decision markers: D1 cracker rates and severity, D2 the polyethylene grade cycle, D3 the feed slate, D4 allocation at shipping, D5 inventory in storage, D6 turnaround timing on the cracker's availability, and D7 make versus buy and the polyethylene line debottleneck. Dollar values appear on feed costs, customer prices, the value of more rail cars, and the value of more polyethylene line capacity. Feed prices, yields, availability, and customer demand are marked as ranges.FEEDSCRACKINGCO-PRODUCTSCONVERSIONSTORAGELOGISTICSCUSTOMERSFUEL GAS TO FURNACESPURCHASED ETHYLENEETHANE$±PROPANE$±NAPHTHA$±CRACKsteam cracker± yieldsAVAILABILITY ±ETHYLENEPROPYLENECRUDE C4PYGASFUEL GAS, H2PE LINEPP LINEBD EXTRACTλ cap $PE SILOSPP SILOSBD SPHEREPYGAS TANKSHIPrail, truck,pipelineRAIL CARSλ $ / carCONTRACT$±SPOT$±EXPORT$±D1D2D3D4D5D6D7
An ethylene chain in resource-task form. Feeds enter the cracker, its linked co-product outputs feed polymer and extraction units, products move through storage and logistics to customers. Numbered markers show where Mizahn makes decisions. Values in green are dollars: prices, and what relaxing a constraint is worth.

Notation

  • Resource: a material, such as a feed, an intermediate, or a product
  • Task: an operation that consumes and produces resources, such as crack or polymerize
  • Storage: tanks, silos, and spheres, with capacity limits
  • Decision: a choice Mizahn makes, numbered to match the use cases
  • Dollar value: a price, or what relaxing a constraint is worth
  • Range: an uncertain input, planned across its spread instead of its average

Decisions on this network

  1. D1Production and campaign planning
  2. D2Product wheel and grade transitions
  3. D3Feedstock selection
  4. D4Allocation when supply is short
  5. D5Inventory positioning
  6. D6Turnaround and outage planning
  7. D7Make versus buy and capacity

02Economics

One objective, in dollars.

Every plan is valued by margin: product revenue, minus feed, energy, freight, inventory carrying, and contract penalties. Volume, utilization, and service level are not the goal. They are inputs to the margin, and Mizahn shows what each one is worth.

Where the business has set a target, such as a service level at a terminal or a minimum run rate, Mizahn can hold it as a constraint and tell you what it costs. For the constraints that bind, it reports the value of relaxing each one: one more rail car, a debottleneck, a turnaround moved by a week.

Margin by decision
What each decision contributes, so the plan can be read line by line.
Value of relaxing a constraint
Dollars per unit of extra capacity, feed, storage, or time, for the constraints that bind.
The cost of a target
What a service level, run-length rule, or inventory target costs in margin.
Value of each co-product
What each output is worth through its best route: sold, stored, converted, or burned as fuel.

Fig. 02Value of relaxing each constraint

Illustrative

Value of relaxing each binding constraint (illustrative)Ranked horizontal bars without values. From largest to smallest: one more rail car at site A, a debottleneck on the polyethylene line, moving the cracker turnaround one week later, more butadiene storage, and more ethane under contract. The last row, more polypropylene line capacity, has slack and is worth nothing to relax.CONSTRAINT RELAXEDMARGIN GAINED, $One more rail car, site ALOGISTICSPE line debottleneckCAPACITYTurnaround one week laterTIMINGMore butadiene storageINVENTORYMore ethane under contractFEEDMore PP line capacityCAPACITYslack, worth zeroλ, $ PER STEP OF RELAXATION
What Mizahn reports for binding constraints, ranked. Each bar is the margin gained per unit of relaxation. Constraints with slack are worth nothing to relax. No values are shown: bar lengths carry no data.

03Uncertainty

Ranges, not averages.

A plan that is optimal for average demand, average yields, and average prices can be fragile on any real day. Mizahn represents demand, feedstock and product prices, yields, and unit availability as ranges or scenarios built from your data and your planners' judgment. Mizahn uses your existing demand forecasts as the starting point.

It looks for the plan that does best across the range. Commitments that must be made now, such as feed purchases, campaign starts, and turnaround dates, are fixed across scenarios. Decisions that can wait, such as rates, allocations, and shipments, adapt to each one.

Scenario sets
Built from your history, your price views, and the outages your planners worry about.
Now versus later
Separates the commitments you make today from the decisions that can adapt.
Downside in view
See how a plan performs in the bad cases, not only on average.
Protection priced
The margin difference between a plan built on averages and one built on ranges, made explicit.

Fig. 03Margin outcomes, averages versus ranges

Illustrative

Margin outcomes for a plan built on averages and a plan built on ranges (illustrative)Two curves over a horizontal margin axis, without values. The dashed curve, the plan built on averages, peaks toward the high end of the margin axis and has a long tail of low-margin outcomes, which is shaded and labeled as missed orders, distressed sales, and buy-ins. The solid curve, the plan built on ranges, peaks a little lower on the margin axis but has almost no low tail.SHARE OF OUTCOMESBAD CASESmissed orders,distressed sales, buy-insPLAN ON AVERAGESPLAN ON RANGESLOWERHIGHERMARGIN, $
Two plans for the same network, evaluated across the same range of outcomes. The plan built on averages peaks at a higher margin but carries a long tail of bad outcomes. The plan built on ranges gives up a little at the peak to cut the tail. No values are shown.

04Optimization

Decisions from mathematical programming.

Mizahn formulates the plan as a mixed-integer program. Integer variables carry the yes-or-no and discrete choices planners make every week: whether a unit runs, which grade a line makes, how many rail cars go where, when a turnaround starts. Continuous variables carry rates, flows, and inventories.

Mixed-integer linear programming (MILP) covers most planning problems. Mixed-integer nonlinear programming (MINLP) is used where the relationships are nonlinear, such as some blending properties. [TODO: confirm MINLP licensing language before launch]

Feasible is not the same as optimal. Rules-based planners find a plan that works. Mizahn looks for the plan that earns the most, and reports how close the solution is to the best possible plan within the model.

Discrete decisions in the model
Runs, campaigns, shipments, and start dates are decided by the solver, not fixed by hand.
Optimality you can check
Every solve reports its status and how far it is from the best possible plan.
Binding constraints named
The constraints that limit margin are listed by name, with their dollar value.
Re-plan when things change
Update a price, an outage, or an order and solve again from the same model.

05Your assets

A model of your plant, not a black box.

Every unit, tank, route, and constraint in the model is named after its counterpart in your network. Planners and engineers can trace a recommendation back to the yields, prices, and limits behind it, and the model is extended when the plant changes.

Mizahn is built with modern software engineering, so adding a unit, a product, or a site extends the model. It does not mean waiting for a vendor release or starting a re-platforming project.

Named units and streams
The model reads like your flowsheet and your logistics map.
Inspectable constraints
Capacities, yields, contracts, and specs are visible, so planners can check what the model assumes.
Built from your data
The first model starts from the capacities, yields, costs, prices, and forecasts you already maintain.
Extends with the plant
New units, grades, and sites are added to the same model.

06Outputs

What to run, where, when, and for whom.

Each solve returns decisions a planner can act on, with the economics behind them. Planners, operations, and commercial teams see the same numbers, and the numbers trace back to the model.

Production plan
Unit, mode, rate, campaign, and timing, period by period.
Allocation
Which customer, contract, or market gets which product, by route.
Inventory plan
Where each product is held, how much, and why.
Economics
Margin by decision, binding constraints, and the value of relaxing each one.

Decision

Illustrative

run
PE line, grade B campaign, weeks n to n+2, then grade C
hold
butadiene in the sphere ahead of the turnaround window
ship
propylene by rail to contract customers, spot capped at q
binding
rail cars at site A, week n+1
value of relaxing
λ, $ per added rail car per week
changes if
propylene spot falls below p*, or the turnaround slips past week m

Next step

See Mizahn on a network like yours.

Book a working session with the team. Bring a decision you are working on now: a feed slate, a campaign plan, a turnaround date. Or start with the technical brief.

Book a demoGet the technical brief