Risk Pooling & Postponement: Dye to Forecast or Dye to Order

How to read this sheet

Buffers combine through variances rather than through standard deviations, which is why pooling eight colours does not divide the buffer by eight. With a uniform average pairwise correlation the combination here is exact rather than approximate, since the cross terms are the correlation times every off-diagonal product and those sum to the square of the sum less the sum of the squares. The correlation input is where the honesty lives. Zero is the textbook case and it is almost never true of a colour range: the colours belong to one garment, one season and one marketing calendar, and they rise and fall together. On the seeded range independence would have shown a pooled buffer at 37% of the separate ones, against 59% at a correlation of 0.25 - so an analysis that quietly assumes independence recommends postponement on a saving that is not there. The service level is converted with Acklam's rational approximation to the inverse normal, the same one the free spare-parts reorder calculator uses, and it presumes demand near enough normal over the lead time. That holds better for a steady replenishment programme than for a short fashion drop, where demand is skewed and a normal buffer is the wrong shape entirely. Several real effects are outside this. Postponement shortens the exposure but does not remove it - somebody still forecasts total greige. Dyeing to order needs the dyehouse to have the capacity when the order lands, which is a queueing question rather than a costing one. Minimum dye lots can make small colours impossible to postpone at any price. And the cost of an extra dye lot is genuinely incremental only while the dyehouse has spare machine time; once it does not, the right figure is what the machine hour earns elsewhere, and it is much larger than the chemicals.