Indivisibilities in Distribution

Indivisibilities arise in the distribution sector when, for example, dividing a shipment in half does not necessarily divide cost in half. Such indivisibilities are common: an ocean container shipping half empty, or a truck delivering a half-empty trailer, generally ship for the same price as a full load. Indivisibilities tend to be particularly relevant when the variety of products shipped is large and volume shipped of any particularly product is small, perhaps only a tiny fraction of the size of a container. In such a case, consolidation of many different varieties into the same shipment can ensure a full load, though potentially there are coordination costs and other frictions associated with such consolidation. Indivisibilities can be expected to have greater bite for low value goods; if expensive goods ship in a half-full container it matters less as a share of value. Indivisibilities tend to be relevant when firms set a high level of delivery frequency or ship to a large number of downstream distribution locations. Everything else the same, dividing shipments more finely over time or space only makes shipments smaller. Into this environment, a distribution system like that of Walmart and Target provides a means of overcoming indivisibilities. These firms use advanced information processing capability that help minimize consolidation frictions. With their massive sales volumes, the firms are able to consolidate a wide variety of low-value goods, with shipments finely divided over time and over space, taking care that ocean containers and delivery trucks are fully utilized. In this paper, we develop and estimate a model of indivisibilities in shipping, We use unique, highly-detailed data on container shipments to lay out a set of facts, including a fact that big retailers like Walmart and Target consolidate shipments more intensively, and pack shipments fuller, compared to smaller firms. In particular, we show that while intermediaries do exist to provide consolidation services to small firms, the extent of this consolidation in ocean shipping is relatively small. We also examine the geographic footprint of import distribution. As discussed in Leachman and Davidson (2012), in recent years many large retailers have adopted what the logistics industry calls a "four corners" import strategy, which entails using multiple ports on both the east and west costs to minimize inland transportation costs. We present facts connecting the geographic footprint to the indivisibility issue. In our model, we allow firms to adapt to indivisibility constraints both by consolidation and adjustments to shipment size, as well as the choice of the geographic footprint of distribution. We estimate the cost effects of indivisibilities, including the magnitudes of consolidation frictions. We find these frictions tend to be very small for firms like Walmart and Target at their main source locations where they enjoy huge economies of scale (Shenzhen, China in particular). At other locations with less volume, the frictions are higher. We have enough data on Walmart to estimate the friction over different time periods, and we find the friction faced by Walmart declined over our sample period, consistent with advances in communications technology. We estimate the model for small firms and find they tend to have high consolidation frictions from all source locations. As one application of the analysis, we simulate the effects on distribution costs of a "Brexit" like event where a customs union is fragmented into pieces. The effects are small on large firms like Walmart, because they are already using their scale to achieve self-contained targeting of relatively narrow geographic areas. Relatedly, we note that the Walmart's import distribution system in Canada and the U.S. are not connected, and our results suggest there would be little gain from doing so.