ITLS6002 Chap.5 Facility Location and Network Optimisation
Facility Location and Network Optimisation
Facility-location models decide which sites to open and how demand should flow through the resulting network. Their logic combines binary opening choices with continuous allocations, fixed costs with transport costs, and customer assignment with site capacity.
A centre-of-gravity estimate can generate a candidate location, but a discrete optimisation model is needed when candidate sites, fixed charges and capacity restrictions matter.
This chapter turns a verbal network brief into sets, variables, objective terms and constraints, then shows how to interpret shadow trade-offs, test scenarios and distinguish a mathematically optimal network from one that is resilient and implementable. Demand constraints ensure every zone is served, capacity constraints restrict flow through each facility, and a binary link prevents a closed site from carrying allocation.
Fixed opening costs reward consolidation while distance, production, handling or transport costs may reward proximity. Scenario analysis changes demand, costs or capacity rather than assuming the base forecast is certain. A defensible recommendation reports opened sites, flows, utilisation and total cost, then explains which change would make another configuration preferable.
What this chapter covers
- 01
Strategic network-design drivers
- 02
Centre-of-gravity approximation
- 03
Fixed-charge facility location
- 04
Demand allocation constraints
- 05
Capacity and opening-link constraints
- 06
Scenario and resilience interpretation
Worked example · free
Comparing two candidate warehouse sites
- 2Total annual cost for A is 120,000 + 7 x 25,000 = $295,000.
- 2Total annual cost for B is 180,000 + 4 x 25,000 = $280,000.
- 2The break-even volume solves 120,000 + 7D = 180,000 + 4D, giving D = 20,000 units.
- 2At 25,000 units, B saves $15,000, provided its capacity and service assumptions remain valid.
Key terms
- Fixed-Charge Model
- An optimisation model that incurs a fixed cost when a facility or activity is activated.
- Assignment Variable
- A decision variable describing how customer demand is allocated to facilities.
- Capacity Constraint
- A restriction preventing assigned flow from exceeding an available facility limit.
- Centre Of Gravity
- A weighted-coordinate method that estimates a continuous location from demand points.
Facility Location and Network Optimisation FAQ
Why is centre of gravity only a starting point?
It treats location as continuous and usually simplifies distance and cost. Real choices are discrete and affected by capacity, fixed cost, infrastructure, risk and service requirements, so the estimate should generate candidates rather than settle the decision.
What role does the binary opening variable play?
It records whether a facility is selected and activates its fixed cost. Linking constraints multiply capacity by that binary variable so customer flow cannot pass through a closed facility.
How should an optimal network recommendation be stress-tested?
Re-solve or recalculate under demand growth, cost changes, capacity loss and service constraints. A small base-case saving may not justify a fragile configuration if plausible scenarios cause large shortages or expensive reallocations.
Why is a demand constraint usually written for every customer zone?
Each zone must receive its required volume, so the model needs a separate conservation rule for every destination. A correct total flow can still leave one zone short and another oversupplied if only a network-wide demand total is imposed.
How can an analyst verify that fixed cost is charged correctly?
Inspect the opening variable and its linking constraint. Fixed cost should enter once for each selected site, and positive flow must be impossible when its opening variable is zero. Test a deliberately closed site to confirm the spreadsheet or solver obeys the link.
What does facility utilisation add to the final recommendation?
Utilisation reveals whether the chosen network has spare capacity or operates near a fragile limit. Two solutions with similar cost can have different resilience, so report flow divided by capacity and test how growth or disruption changes feasibility.
Exam move
Sketch nodes and arcs before writing algebra. Define customer and facility index sets, then label opening and flow decisions with units. Check that the objective contains every fixed and variable cost exactly once. Read each constraint aloud as a business rule. After solving, report opened sites, allocations, utilisation and total cost, then test at least one demand or capacity scenario before defending the network.
Practise translating a short case into sets, parameters and variables before looking at a finished formulation. Recalculate one site's capacity link by hand and confirm that a closed site carries zero flow. Use a small two-site example to find a volume break-even point, then explain why the threshold may change when capacity or service constraints bind.
For scenario revision, keep the base solution beside the changed solution and identify whether sites, flows, utilisation or only total cost moved. End with an implementation concern such as site availability, lead time or resilience.
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