Transportation Optimization - Plant to Customer

Purpose

This calculator finds the cheapest way to ship goods from a set of plants, each with a fixed capacity, to a set of customers, each with a fixed demand, given the cost of shipping between every plant-customer pair. It is useful for distribution and logistics planners who need to decide how much each plant should send to each customer to fully meet demand at the lowest total shipping cost.

Background

The classic transportation problem

Each plant can only supply up to its Capacity, and each customer's Demand must be fully met. Shipping a unit from a given plant to a given customer has its own cost, which can vary widely by plant-customer pair (for example, due to distance). When several plants could serve the same customer, and a plant could serve several customers, there are many possible ways to divide the shipments — this calculator searches all of them and picks the combination that meets every customer's demand, without exceeding any plant's capacity, at the lowest possible total cost.

Inputs

Supply

A table listing each plant with its Plant name/identifier and its Capacity — the maximum quantity it can ship in total, across all customers.

Demand

A table listing each customer with its Customer name/identifier and its Demand — the quantity it must receive, in total, from one or more plants.

Cost

A table with one row per plant-customer pair that can be used, giving the Plant, the Customer, and the Cost of shipping one unit between them. Only pairs listed here are considered as possible shipping routes; a pair not listed cannot be used to supply that customer.

Results

Network

A diagram of the plants and customers, with a line drawn between every plant-customer pair listed in the Cost table. Each line is labeled with the quantity the optimal solution ships along it (0 if that route is not used in the optimal solution).

Solution

A text summary of the optimization outcome:

• Status — whether an optimal solution was found. Optimal means a feasible shipping plan meeting every constraint was found at the lowest possible cost.
• Total Cost — the total shipping cost of the optimal plan: the sum, over every plant-customer pair used, of quantity shipped multiplied by its Cost.
• One line per plant-customer pair actually used in the optimal plan, stating how many units are shipped from that plant to that customer. Pairs not used are omitted from this list.

Understanding the Calculation

The calculator solves an optimization model that:

• Minimizes total cost — the sum of quantity shipped × Cost over every plant-customer pair.
• Respects each plant's Capacity — the total shipped out of a plant, across all customers, cannot exceed its capacity.
• Meets each customer's Demand exactly — the total received by a customer, from all plants combined, must equal its demand.

Total plant capacity does not need to equal total customer demand; capacity can exceed demand, in which case some plants will ship less than their full capacity, but total demand must not exceed total capacity or no feasible plan exists.

Example

Using the default inputs — two plants (P1 with capacity 100, P2 with capacity 125) and three customers (C1 demanding 25, C2 demanding 95, C3 demanding 80, for a total demand of 200) with the given cost table — the calculator finds:

• Status: Optimal
• Total Cost: 66625.0
• Ship 25 units from P1 to C1
• Ship 75 units from P1 to C3
• Ship 95 units from P2 to C2
• Ship 5 units from P2 to C3

This uses all 100 units of P1's capacity and 100 of P2's 125-unit capacity, meeting all 200 units of total demand at the lowest possible combined shipping cost. Splitting C3's demand across both plants (75 from P1, 5 from P2) is cheaper overall than any single-plant assignment, given the cost table.

Important Assumptions and Interpretation

• Demand for a single customer can be split across more than one plant; the model does not require each customer to be served by only one plant.
• The Cost values should use one consistent currency or cost unit throughout the table.
• If total demand exceeds total plant capacity, no feasible plan exists and Status will not show Optimal — reduce demand or increase capacity and try again.
• The result is a cost-minimizing shipping plan for the inputs given; it does not account for factors not modeled here, such as delivery time, minimum shipment sizes, or capacity/cost changes over time.