Inventory, supply chains and logistics networks

Define the account behind the decision

On-hand inventory is physically available stock under the stated usability definition. On-order inventory is expected incoming supply. Backorders are unfilled obligations carried forward. A simple inventory position is on hand plus on order minus backorders. Reserved, quarantined or unusable stock needs clear treatment so the record matches the decision.

For the original account, 14+20−5=29 units of inventory position. That is neither 29 usable units on the shelf nor a guaranteed incoming delivery. Supplier timing and quality may be uncertain. A logistics network connects sources, storage, processing and destinations; transfer time, capacity and information affect whether the right item reaches the right place when needed.

Connect the trigger to the replenishment interval

For an elementary continuous-review policy, suppose demand is a constant 8 units/day, replenishment lead time is exactly 3 days, and a chosen buffer is 6 units. Lead-time demand is 24, so choose reorder threshold R=24+6=30 units of inventory position and order quantity Q=40. In this lesson’s convention, a review finding position at or below R triggers the order.

The separate plot starts with 30 on hand and no other supply or obligations, places one order and uses the deterministic demand rate. Six units remain just before the day 3 delivery; the 40-unit receipt raises on hand to 46. The buffer is an explicit assumption, not a calculated service-level guarantee. Delivery delay, variable demand, spoilage or unusable receipts would change the path.

A local reduction can move a burden

More stock can protect against some interruptions while increasing storage, capital, obsolescence or handling burdens. Less local stock can shift buffering to a supplier or increase transport frequency. Compare the end-to-end function, including where the waiting and risk move, rather than treating one small warehouse count as a complete improvement.

Periodic review checks at selected intervals and may order up to a target. Continuous review responds to inventory position under its policy. Their protection periods and information needs differ. Shared disruptions can affect several suppliers together, so two supplier names do not automatically provide independent resilience. Preserve lead-time evidence, definitions and exception records when evaluating the rule.

A unit must be at the right node before its deadline

Make the network account time-specific. At each location, closing usable stock equals opening usable stock plus usable receipts minus dispatches and fulfilled demand. A dispatch leaves its source immediately but enters the destination only on arrival. Keep unmet due demand as an obligation, rather than pretending a negative shelf quantity can serve it. Network-flow models express conservation and link capacities; adding dates makes a feasible quantity depend on the route as well.

Consider a separate original one-deadline network. At day 0, depot D holds 12 units and local stores A and B hold 4 and 2. Demand is due immediately after the start of day 1: A needs 8 and B needs 6. Stock is interchangeable and usable; there are no other orders, losses, reservations or receipts. The total is 18, but local demand cannot be filled from depot stock until it travels.

At day 0 a standard service can dispatch at most 8 units in total, with at most 6 to either store. Its usual lead time is 1 day: delivery occurs just before the day 1 demand. A separate express service can carry at most 4 units in total, to either store, with lead time 0.5 day. These are shared service capacities, not 8 and 4 for each branch. Both modes draw from the same depot stock; all dispatch decisions occur at day 0. There is no store-to-store route.

The baseline sends 4 standard units to each store. At the deadline, A has 4+4=8 and B has 2+4=6; depot stock is 12−8=4. Both obligations are met, and the final network stock is 4 after serving 14. That conservation check catches an impossible plan which sends the same depot unit down two routes.

Compare a local saving with its transport consequence

Now move 2 units from each local store back to D before the decision window. The lean arrangement starts with A=2, B=0, D=16: total stock is still 18. Day 1 replenishment must now supply 6 to each store, or 12 in total. Standard capacity covers only 8. A feasible dispatch sends 4 standard and 2 express units to each store. The express capacity is fully used, so lowering local stock has consumed a scarce alternative route rather than removing the need for a buffer.

To make a bounded cost comparison, assign 1 credit per initially stored local unit for this protection window, 1 per standard unit shipped and 3 per express unit shipped. Procurement and depot-space charges are treated as equal fixed charges across these cases. Any cost of establishing the initial stock positions is outside this one-window score; shortages are unacceptable, not converted into a guessed monetary penalty. Baseline cost on this normal case is 6+8=14 credits. Lean cost is 2+8+3×4=22. Its 4-credit local saving creates 12 extra transport credits. These declared scores are teaching assumptions, not quoted logistics prices or a complete company cost model.

Let a disruption change the policy decision

Choose initial stock before knowing which listed scenario will occur; its demand and route condition are revealed at day 0 before dispatch. Normal demand is A=8, B=6. High demand is A=9, B=7. Compare the baseline, lean arrangement and a protected arrangement A=8, B=6, D=4, all with total stock 18. The table gives the smallest number of due units left unfilled after using the available on-time routes; express capacity is shared across both stores.

In the delayed case, standard shipments arrive on day 2 and cannot satisfy day 1 demand. Baseline local stock covers 6 of 14 due units; express can supply only 4 of the remaining 8, leaving 4 unfilled. Lean leaves 8 unfilled. Protected stock meets normal demand locally. In the high-demand, normal-route case, baseline needs 10 incoming units, served by 8 standard plus 2 express. Lean needs 14, but its two services together can move only 12, leaving 2 unfilled. Protected needs only 1 standard unit at each store.

Use this decision criterion: first meet every listed deadline in every listed scenario; among candidates that pass, minimise the largest scenario cost under the stated score. Only protected stock passes the first test. Its scenario costs are 14, 16 and 14 credits, so its largest is 16. This is a comparison of declared candidates, not a proof of a globally optimal stock allocation. A delayed route combined with high demand is not listed: protected local stock would then need 2 express units, but other unlisted disruptions could still defeat it. No scenario probabilities or universal service guarantee have been supplied.

The useful operational question is therefore not simply how much inventory to remove. It is where to locate it, which timed paths can replace it, and what service obligation each policy can actually meet. Add evidence for demand, route delays and shared failures before adopting a policy in an actual network.

Place an order without pretending it has arrived

With on hand 14, on order 20 and backorders 5, position is 29. Under the declared threshold rule, 29≤30 triggers an additional 40-unit order. Position becomes 69 once that order is recorded; physical on hand remains 14 until a receipt occurs or demand changes it.

In a second record with 30 on hand, 20 on order and 5 backorders, position is 45, so this simple rule does not trigger. Neither result proves that all immediate obligations can be met: check reservations, due dates and actual receipts as well as the aggregate position.

Try the reasoning

1. Why is inventory position useful for a reorder decision?

   Show the answer and reasoning

   It includes expected incoming supply and outstanding obligations, reducing the risk of treating shelf quantity as the whole account.

2. Does ordering 40 units immediately increase on hand by 40?

   Show the answer and reasoning

   No. It changes on-order supply and position; on hand changes when usable goods are received.

3. What does the chosen 6-unit buffer guarantee about service probability?

   Show the answer and reasoning

   Nothing by itself. A probability claim requires an appropriate demand/lead-time model and evidence, not just an arbitrary buffer.

4. For normal demand, suppose standard capacity becomes 10 total units and express capacity is only 2. Can the lean arrangement meet the deadline, and at what declared cost?

   Show the answer and reasoning

   Yes. Its deficit is still 12 units. Send 5 standard plus 1 express to each store: A receives 6 and reaches 8; B receives 6 and reaches 6. Each standard branch remains below its 6-unit limit, standard total is 10, express total 2, and depot dispatch 12 is below its stock 16. Cost is 2 local-stock credits+10+3×2=18. This feasible normal case says nothing about a delayed standard route.

5. Evaluate a new arrangement A=7, B=5, D=6 in the three listed scenarios. Does it beat protected stock under the declared criterion?

   Show the answer and reasoning

   It meets all three: normal needs 2 standard units, high demand 4 standard, and the delayed normal case needs 2 express. Its local-stock score is 12, so costs are 14, 16 and 18; the largest is 18. Protected stock has largest cost 16 and therefore wins among these two under this criterion. A different valuation of local space, express access or unlisted conditions could change that choice.

6. Why can a network with 18 total usable units fail to meet 14 requests due at one deadline?

   Show the answer and reasoning

   Quantity conservation alone does not establish timed delivery. In the delayed-route scenario, units remaining at D cannot arrive by day 1 except through the 4-unit express service. Lean local stock of 2 plus 4 on-time express units can fill only 6 of the 14 due units; 8 remain unfilled despite sufficient network-wide stock.

What to carry forward

Use dated stock balances, shared route capacities and explicit service criteria to judge where a buffer is needed; inventory position alone cannot establish delivery feasibility.