A theoretical analysis of the phenomenon of diminishing marginal productivity of gangs employed for (un)loading a vehicle

Abstract

The experience of (un)loading ships and other vehicles in sea ports shows that the rate of (un)loading (i. e. the amount of cargo being (un)loaded (from)onto a vehicle per time unit) does not increase in direct proportion to the number of gangs employed; in accordance with the law of diminishing marginal productivity each additional gang adds less and less to the rate of (un)loading. Despite its importance in operations planning, this phenomenon has not been given careful consideration and clear explanation in the literature related to port operations. This paper attempts to fill this gap by offering a theoretical explanation for why the marginal rate of (un)loading decreases with the addition of each extra gang. This paper suggests two reasons behind the phenomenon: the interference effect, and the conjunction effect. Both of these effects are due to the fact that (un)loading a vehicle is not a deterministic but a stochastic process. Each of the effects is examined in the paper both quantitatively and qualitatively.