This paper develops an analytic method for minimizing the cost of distributing freight by truck from a supplier to many customers. It derives formulas for transportation and inventory costs, and determines the optimal trade-off between these costs. The paper analyzes and compares two distribution strategies: direct shipping (i.e., shipping separate loads to each customer) and peddling (i.e., dispatching trucks that deliver items to more than one customer per load). The cost trade-off in each strategy depends on shipment size. Our results indicate that, for direct shipping, the optimal shipment size is given by the economic order quantity (EOQ) model, while for peddling, the optimal shipment size is a full truck. The peddling cost trade-off also depends on the number of customers included on a peddling route. This trade-off is evaluated analytically and graphically. The focus of this paper is on an analytic approach to solving distribution problems. Explicit formulas are obtained in terms of a few easily measurable parameters. These formulas require the spatial density of customers, rather than the precise locations of every customer. This approach simplifies distribution problems substantially while providing sufficient accuracy for practical applications. It allows cost trade-offs to be evaluated quickly using a hand calculator, avoiding the need for computer algorithms and mathematical programming techniques. It also facilitates sensitivity analyses that indicate how parameter value changes affect costs and operating strategies.

This paper introduces the problem of finding the least expected travel time path between two nodes in a network with travel times that are both random and time-dependent (e.g., a truck, rail, air or bus network). It first shows that standard shortest path algorithms (such as the Dijkstra algorithm) do not find the minimum expected travel time path on such a network, then proposes a method which does find the minimum path. Next, this paper shows that the optimal “route choice” is not a simple path but an adaptive decision rule. The best route from any given node to the final destination depends on the arrival time at that node. Because the arrival time is not known before departing the origin, a better route can be selected by deferring the final choice until later nodes are reached. A method for finding the optimal adaptive decision rule is proposed.

This paper evaluates and compares strategies for routing a manual picker through a simple warehouse. It expands on previous work, in which optimization algorithms were developed, by deriving equations which relate route length to warehouse attributes. Several rules of thumb are derived for selection of order picking strategies and optimization of warehouse shape.

Fleet sizing and empty equipment redistribution are important issues in managing transportation systems. Most of the mathematical models that have been developed for these problems are complex and computationally demanding, including dynamic linear programming and stochastic/dynamic mathematical programs. Our research takes an alternate approach by building from inventory theory and developing decentralized stock control policies for empty equipment. This approach is applied to hub-and-spoke networks (i.e., center-terminal networks), by first analytically modeling the stochastic processes representing various stock-control variables, and then comparing the analytical results to monte-carlo simulations. A decomposition approach is also developed to determine stock-out probabilities as a function of the fleet size as a whole, and as a function of localized control parameters.