Chapter 8 of 8

Integrated Capstone: Designing a Network End to End

3 sections · ~10 min read · 3 practice questions · part of Supply Chain Analytics

Learning objectives

  • Combine forecast quality, inventory, transportation, disruption exposure, and emissions into one comparable annual cost
  • Identify which assumption the recommendation is most sensitive to and quantify the flip point
  • Communicate a close decision honestly, separating what the model shows from what it cannot

Putting the pieces on one page

Each preceding chapter produced a number in isolation, and each of those numbers is annual and denominated in dollars, which is what makes them addable. An end-to-end design comparison assembles five components for each candidate configuration. Freight cost is annual volume times the blended rate per unit. Fixed facility cost is the annual cost of keeping the required buildings open. Inventory cost is safety stock in units times the annual holding cost per unit, where the safety stock depends on the replenishment lead time the configuration implies and on the demand variability that forecast validation measured. Disruption exposure is expected annual loss, computed as probability times residual duration times daily contribution margin at risk. Emissions cost is annual tonnes of carbon dioxide equivalent times whatever internal price the firm applies to carbon in investment decisions. Assembling them requires consistency checks that are easy to skip: the same annual volume everywhere, the same holding rate, the same time period, and no double counting of an item such as inbound freight that might already sit inside a landed unit cost. Note that the emissions term is included only because the firm has chosen to apply an internal price; that price is a management decision about how it wants to weigh future exposure, and the analysis should present the result both with and without it so the effect of that choice is visible rather than buried.

Reading the sensitivity rather than the total

The total cost of each configuration is the least interesting output of an integrated model. What matters is the gap between the leading options and how that gap responds to the inputs the analyst is least sure of. A structured way to do this is to take each assumption in turn, move it to a plausible alternative value, and record whether the ranking changes. Assumptions that never flip the ranking can be set aside no matter how uncertain they are. Assumptions that flip it under a modest change are where the remaining analytical effort belongs. Two patterns recur. First, inputs that affect both configurations in the same direction, such as a fuel surcharge that raises every freight rate, usually move both totals without changing the ranking, and so matter less than their size suggests. Second, inputs that appear in only one configuration, or that appear with different exponents in each, are the ones that decide. Safety stock is a classic example, because it scales with the square root of lead time, so a change in demand variability affects a long-lead-time configuration more than a short-lead-time one and can widen or narrow the gap on its own. The disciplined output is a short list of flip points expressed in the units the decision maker recognizes: a fixed cost premium, a freight rate, a probability.

Reporting a close call without pretending it is not close

When two configurations differ by a fraction of a percent of total cost, the model has not chosen; it has narrowed. The temptation is to present the winner with a precise number and let the precision imply confidence, which misrepresents what the analysis established. The better report states the gap in both absolute and per-unit terms, names the two or three assumptions that would reverse it and the values at which they do, and then explicitly lists what the model does not contain. Typical omissions are worth stating because they are often larger than the modelled gap: transition and implementation cost, lease flexibility and exit terms, labour availability at each site, customer delivery lead time, management attention, and the option value of being able to change course later. A recommendation that says the two options are within roughly one percent on modelled cost, that the difference reverses if a specific premium exceeds a specific value, and that the decision therefore rests on service and flexibility grounds is more useful and more defensible than one that reports a winner to the nearest dollar. The analyst's job at this point is to make the trade-off legible, not to manufacture a verdict the numbers do not support.

Worked example

Problem

Marlow Instruments must choose a distribution configuration for 600,000 units per year of a product costing 24 dollars per unit, with an annual holding rate of 24 percent. Configuration A uses one facility and a single overseas supplier: replenishment lead time 5 weeks, freight 1.28 dollars per unit, fixed facility cost 900,000 dollars per year, disruption probability 10 percent per year with 20 days of residual exposure, and 0.041 kilograms of carbon dioxide equivalent per unit. Configuration B uses two facilities and dual sourcing with a regional second supplier: lead time 3 weeks, freight 0.94 dollars per unit, fixed facility cost 1,150,000 dollars per year, disruption probability 10 percent with 7 days of residual exposure, and 0.030 kilograms per unit. Weekly demand standard deviation is 4,200 units and the service factor is 1.65 in both cases. Contribution margin at risk is 38,000 dollars per day and the firm applies an internal carbon price of 85 dollars per tonne. Compute total annual cost for each and identify the flip point.

Step by step

  1. Annual holding cost per unit = 24 x 0.24 = 5.76 dollars per unit per year.
  2. Configuration A safety stock = 1.65 x 4,200 x square root of 5 = 1.65 x 4,200 x 2.2361 = 15,496.0 units. Cost = 15,496.0 x 5.76 = 89,256.68 dollars.
  3. Configuration B safety stock = 1.65 x 4,200 x square root of 3 = 1.65 x 4,200 x 1.7321 = 12,003.1 units. Cost = 12,003.1 x 5.76 = 69,137.93 dollars. Inventory advantage to B = 20,118.75 dollars.
  4. Freight: A = 600,000 x 1.28 = 768,000 dollars. B = 600,000 x 0.94 = 564,000 dollars. Freight advantage to B = 204,000 dollars.
  5. Fixed facility: A = 900,000 dollars, B = 1,150,000 dollars. Fixed cost disadvantage to B = 250,000 dollars.
  6. Expected annual disruption loss: A = 0.10 x 20 days x 38,000 = 76,000 dollars. B = 0.10 x 7 days x 38,000 = 26,600 dollars. Risk advantage to B = 49,400 dollars.
  7. Emissions: A = 0.041 kilograms per unit x 600,000 = 24,600 kilograms = 24.6 tonnes, priced at 24.6 x 85 = 2,091 dollars. B = 0.030 x 600,000 = 18,000 kilograms = 18.0 tonnes, priced at 18.0 x 85 = 1,530 dollars. Carbon advantage to B = 561 dollars.
  8. Configuration A total = 768,000 + 900,000 + 89,256.68 + 76,000 + 2,091 = 1,835,347.68 dollars per year.
  9. Configuration B total = 564,000 + 1,150,000 + 69,137.93 + 26,600 + 1,530 = 1,811,267.93 dollars per year.
  10. Difference = 1,811,267.93 - 1,835,347.68 = negative 24,079.75 dollars, so B is cheaper by 24,079.75 dollars, which is 1.31 percent of A's total. Per unit: A = 3.0589 dollars, B = 3.0188 dollars, a gap of 4.01 cents per unit.
  11. Excluding the carbon price entirely: A = 1,833,256.68 and B = 1,809,737.93, a gap of 23,518.75 dollars still favouring B. The carbon price contributes only 561 dollars of the 24,079.75-dollar advantage, so it is not decisive at any plausible price and no positive carbon price would reverse the ranking.
  12. Flip point on fixed cost: B's fixed premium would have to rise from 250,000 dollars to 250,000 + 24,079.75 = 274,079.75 dollars, an increase of 9.6 percent, to erase B's advantage.
  13. Flip point on freight: A's rate would have to fall from 1.28 to (768,000 - 24,079.75) / 600,000 = 1.2399 dollars per unit, a reduction of 4.01 cents or 3.14 percent.

Answer. Configuration B totals 1,811,267.93 dollars against Configuration A's 1,835,347.68 dollars, an advantage of 24,079.75 dollars per year or 4.01 cents per unit, which is 1.31 percent of total cost. The advantage is built from 204,000 dollars of freight savings, 49,400 dollars of reduced disruption exposure, 20,119 dollars of inventory savings from the shorter lead time, and 561 dollars of carbon, against a 250,000-dollar fixed cost premium. The carbon term is immaterial here and the recommendation does not depend on the internal price. The decision is genuinely close and turns on two assumptions: it reverses if B's fixed cost premium proves 9.6 percent higher than estimated, or if the incumbent supplier can cut A's freight rate by just 3.14 percent. Neither is far-fetched. The model also excludes transition cost, lease terms, and the customer-facing lead time improvement that two facilities provide, and any of those could exceed 24,080 dollars in value. The honest recommendation is that B is modestly preferred on modelled annual cost, that the case rests mainly on freight and disruption exposure rather than on carbon or inventory, and that the firm should verify the fixed cost premium and re-tender the A freight rate before committing.

Practice

Work each question before opening the solution.

  1. Forecast validation on a longer holdout shows weekly demand variability is 25 percent higher than assumed, so the standard deviation is 5,250 units rather than 4,200. Recompute both safety stock costs and state the effect on the recommendation.

    Show solution for question 1

    Configuration A safety stock = 1.65 x 5,250 x 2.2361 = 19,369.9 units, costing 111,570.85 dollars, an increase of 22,314.17 dollars. Configuration B safety stock = 1.65 x 5,250 x 1.7321 = 15,003.9 units, costing 86,422.41 dollars, an increase of 17,284.48 dollars. Because safety stock scales with the square root of lead time, the longer-lead-time configuration absorbs more of the increase, so B's advantage widens by 22,314.17 - 17,284.48 = 5,029.69 dollars to 29,109.44 dollars. Higher demand uncertainty strengthens the case for the shorter-lead-time configuration, which is a general result worth remembering: lead time reduction is worth more precisely when demand is harder to forecast.

  2. A risk review concludes the annual disruption probability is 5 percent, not 10 percent, for both configurations. Recompute the expected losses and the total gap, and comment on what this reveals about the structure of the decision.

    Show solution for question 2

    Expected loss becomes A = 0.05 x 20 x 38,000 = 38,000 dollars and B = 0.05 x 7 x 38,000 = 13,300 dollars, so A falls by 38,000 dollars and B by 13,300 dollars. B's advantage narrows by 38,000 - 13,300 = 24,700 dollars, from 24,079.75 dollars to a disadvantage of 620.25 dollars, meaning A becomes marginally cheaper. The probability assumption alone therefore flips the recommendation, so that assumption needs further scrutiny before choosing a design. Since a point estimate of disruption probability is rarely defensible, the better framing is that the two configurations are within about 600 dollars of each other across the plausible probability range, and the choice should be made on non-cost grounds.

  3. An executive asks for the recommendation as a single number with a payback period. Draft a two-sentence response that answers the question without overstating the analysis.

    Show solution for question 3

    Configuration B is cheaper by about 24,000 dollars per year on modelled cost, roughly 1.3 percent, but that gap disappears entirely if the disruption probability is 5 percent rather than 10 percent, or if the fixed cost premium comes in 10 percent above estimate, so a payback figure would imply a precision the analysis does not have. The defensible statement is that the two designs are within roughly one to two percent on cost and the choice should rest on delivery lead time, contingency capability, and lease flexibility, none of which the cost model captures.