Transshipment Optimization - Plant to Distribution Center to Customer

Purpose

This calculator finds the cheapest way to move goods from plants to customers when shipments must pass through an intermediate layer of distribution centers (DCs), rather than going direct. It is useful for distribution and logistics planners who route product through DCs and need to decide how much to ship on each plant-to-DC and DC-to-customer leg, at the lowest total shipping cost, while fully meeting every customer's demand without exceeding any plant's capacity.

Background

A two-stage network

Goods flow in two stages: Plant → Distribution Center, then Distribution Center → Customer. Each plant can only ship up to its Capacity in total. Each customer's Demand must be fully met. Distribution centers themselves do not generate or consume goods — whatever arrives at a DC from the plants must equal what leaves it to customers, so DCs act purely as routing points, not storage. Shipping a unit on any given leg (plant-to-DC or DC-to-customer) has its own cost, and the calculator searches all the ways to route goods through the network to find the combination that meets every constraint at the lowest 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 distribution centers.

Distribution

A table listing each distribution center by its DC name/identifier. Distribution centers in this calculator have no capacity limit of their own — they simply pass through whatever flow the optimal solution routes through them.

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 distribution centers.

Cost

A table with one row per usable leg, giving a From location, a To location, and the Cost of shipping one unit between them. This table covers both stages of the network: plant-to-DC legs and DC-to-customer legs. Only legs listed here are considered as possible routes.

Results

Network

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

Solution

A text summary of the optimization outcome:

• Status — whether an optimal solution was found. Optimal means a feasible routing 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 leg used, of quantity shipped multiplied by its Cost, across both the plant-to-DC and DC-to-customer stages.
• One line per plant-to-DC leg actually used, stating how many units are shipped from that plant to that distribution center.
• One line per DC-to-customer leg actually used, stating how many units are shipped from that distribution center to that customer.

Understanding the Calculation

The calculator solves an optimization model that:

• Minimizes total cost — the sum of quantity shipped × Cost over every plant-to-DC and DC-to-customer leg.
• Respects each plant's Capacity — total shipments out of a plant, across all distribution centers, cannot exceed its capacity.
• Balances flow at each distribution center — the total quantity arriving at a DC from all plants must equal the total quantity leaving it to all customers; a DC cannot accumulate or create stock.
• Meets each customer's Demand exactly — the total received by a customer, from all distribution centers combined, must equal its demand.

Because distribution centers have no capacity limit here, the model is free to route any amount of flow through a given DC as long as the flow-balance condition holds; only plant capacity and customer demand constrain the solution.

Example

Using the default inputs — two plants (P1 with capacity 100, P2 with capacity 125), two distribution centers (D1, D2), three customers (C1 demanding 25, C2 demanding 95, C3 demanding 80), and the given cost table — the calculator finds:

• Status: Optimal
• Total Cost: 69200.0
• Ship 75 units from P1 to D2
• Ship 105 units from P2 to D1
• Ship 20 units from P2 to D2
• Ship 25 units from D1 to C1
• Ship 80 units from D1 to C3
• Ship 95 units from D2 to C2

Every unit that arrives at D1 (105) is passed on to customers from D1 (25 + 80 = 105); every unit that arrives at D2 (75 + 20 = 95) is passed on to C2 (95) — confirming the flow-balance requirement at each distribution center. Total demand of 200 units is met using 75 units of P1's capacity and 125 of P2's capacity, at the lowest total cost across both shipping stages.

Important Assumptions and Interpretation

• Distribution centers have no throughput capacity in this calculator — any volume can pass through a DC as long as inflow equals outflow.
• A customer's demand can be split across more than one distribution center, and a distribution center can be fed by more than one plant; the model does not require single-sourcing at either stage.
• The Cost values should use one consistent currency or cost unit throughout the table.
• If total customer 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 routing plan for the inputs given; it does not account for factors not modeled here, such as delivery time, minimum shipment sizes, or DC capacity/cost changes over time.