Chapter 4 of 4

Multi-Echelon, Allocation, and Working Capital

3 sections · ~5 min read · 3 practice questions · part of Demand & Inventory Planning

Learning objectives

  • Explain why a single-echelon view of inventory can mislead decisions in a multi-echelon network
  • Use a simple base-stock allocation rule across downstream locations
  • Translate inventory decisions into working capital and cash conversion cycle

Beyond single echelon

Most firms hold inventory at more than one echelon: raw materials and WIP at the plant, finished goods at a central DC, finished goods at regional DCs or cross-docks, and sometimes safety stock at the supplier. A decision that looks optimal at one echelon (e.g., reduce DC safety stock by 20 percent) can raise total system inventory if the upstream plant must compensate with longer runs or higher WIP. Multi-echelon inventory theory recognizes that the right place to hold buffer is the echelon with the lowest unit cost of carry and the highest cost of a stockout, which is often the finished good at the regional DC for high-margin items and the supplier side for low-margin, long-lead-time raw materials. The arithmetic gets harder, but the principle is the same: spend each unit of safety stock where it buys the most service per dollar.

Allocation across locations

When a constrained supply must be split among several downstream locations, allocation by past sales beats allocation by current orders because it dampens bullwhip and protects the locations whose customers actually consume the product. A simple rule: allocate pro rata to each location's share of the last 13 or 26 weeks of shipments, with a small manual adjustment when local demand is genuinely shifting. Publish the rule and stick to it during shortages so that downstream planners can plan. The temptation to over-allocate in response to a single loud customer request should be resisted because it teaches every other customer to inflate orders next time, which is exactly the bullwhip mechanism in a new costume.

Inventory and the cash conversion cycle

Days inventory outstanding (DIO) plus days sales outstanding (DSO) minus days payable outstanding (DPO) is the cash conversion cycle, the number of days the firm's cash is tied up in operations before it comes back from customers. The conversion is easy and worth memorizing: one day of DIO equals one day of COGS. At $4.8 million of annual revenue and 50 percent gross margin, COGS is $2.4 million, so one day of DIO is $2,400,000 / 365 = $6,575 of working capital. Cutting DIO from 91.25 days to 73 days therefore releases 18.25 x $6,575 = $120,000. The point is that supply chain decisions are financial decisions, and the financial framing is what gets them prioritized at the leadership level. A good inventory plan is not the one with the lowest unit cost or the highest fill rate in isolation; it is the one that delivers the chosen service level at the chosen working capital footprint, with the resilience posture the firm has decided to buy.

Worked example

Problem

A firm has annual revenue $4,800,000 at 50 percent gross margin. Current DIO = 91.25 days and DSO = 30 days. DPO = 25 days. (a) Compute the cash conversion cycle (CCC) and the working capital tied up in operations assuming a 365-day year. (b) A project reduces DIO by 18.25 days (the same magnitude as the earlier Foundations example). Compute the new CCC and the working capital released.

Step by step

  1. CCC = DIO + DSO - DPO = 91.25 + 30 - 25 = 96.25 days.
  2. Cost of goods sold = 0.50 x $4,800,000 = $2,400,000.
  3. Average inventory = (91.25 / 365) x $2,400,000 = 0.25 x $2,400,000 = $600,000. This is the same firm used in the Foundations course, so the figures tie out.
  4. Average receivables = (30 / 365) x $4,800,000 = $394,520.55. Note that receivables are driven by revenue, not COGS, because that is what the customer is billed.
  5. Average payables = (25 / 365) x $2,400,000 = $164,383.56. Payables are driven by COGS, because that is what the firm is billed.
  6. Working capital tied up = inventory + receivables - payables = $600,000 + $394,520.55 - $164,383.56 = $830,136.99.
  7. After the project, DIO_new = 91.25 - 18.25 = 73.00 days. New inventory = (73 / 365) x $2,400,000 = $480,000. Reduction = $120,000.
  8. New CCC = 73 + 30 - 25 = 78 days. New working capital = $480,000 + $394,520.55 - $164,383.56 = $710,136.99. Released = $120,000.
  9. Sanity check against the per-day rule: 18.25 days x ($2,400,000 / 365) = 18.25 x $6,575.34 = $120,000. Consistent.

Answer. Original CCC = 96.25 days with $830,137 of working capital. After the project, CCC = 78 days and working capital = $710,137, a release of $120,000. Every dollar of that release is inventory: receivables and payables are untouched, which is why an inventory project is usually the fastest lever a supply chain team has on the cash conversion cycle.

Practice

Work each question before opening the solution.

  1. Why can lowering DSO by 10 days while raising DIO by 10 days leave CCC unchanged but still change the firm's risk profile?

    Show solution for question 1

    CCC is unchanged so working capital is the same, but the mix has shifted toward inventory risk (obsolescence, shrinkage) and away from credit risk (bad debts). For perishable or fast-moving items, the inventory risk is the bigger concern, so the firm may prefer to finance customers longer rather than hold more stock.

  2. A firm holds 60 days of finished goods and 20 days of raw materials. Where is the cheaper place to add a one-week buffer for a critical component that has long and variable lead time?

    Show solution for question 2

    Upstream at the raw material stage, because component unit cost is usually lower than finished good cost and the buffer compounds through the chain. The trade-off is that a raw material buffer consumes working capital without being sellable; the right call depends on whether the component is on a long fixed lead time and whether the firm can substitute or expedite downstream.

  3. During a shortage, two customers each ask for 1,000 units but historical shipments have been 700 to customer A and 300 to customer B. Under pro-rata allocation to historical share, how should 1,000 available units be split?

    Show solution for question 3

    Allocate 700 to customer A and 300 to customer B. This protects the customer whose downstream demand is most credible and avoids rewarding the customer with the louder order.