Supply chain models attempt to replicate mathematically the processes followed by business managers in decisions pertaining to replenishment and distribution, such as order frequency, shipment size, and the like. Multiple considerations come into play when managers decide on the combination of order frequency and shipment sizes to be used for a given time period. In relatively “steady” conditions, where the demand for a given product is reasonably “constant,” managers could select the combination of order frequency and shipment size that minimizes the total logistic costs, i.e., the summation of the transportation and inventory cost. In this context, transportation costs that are “high” relative to inventory costs lead to infrequent orders of large shipments; while the converse lead to frequent orders of small shipments. Thus, in the former case the use of “large” freight vehicles or modes is favored; while the latter favors the use of “small” freight vehicles or modes. A different situation arises if the demand for the product is highly variable. In these cases, the need to maintain a safety stock may influence order patterns and ultimately freight vehicle and mode choice. Inventory management models are used to make these decisions.
Inventory management models calculate the shipment size needed to minimize the total logistic cost, which includes inventory as well as transportation costs, to prevent out-of-stock situations. The inventory required depends on the choice of mode, frequency, reliability, transit time, freight rate, and capacity of the in-flow. The inventory quantity also depends on the cost of storage, the quantity required in a time of crisis to run the business or maintain the customer loyalty, and the difference between inflow and outflow rates. The outflow rate is affected by the demand, which in turn depends on factors such as season, price of substitutes and complements, economy, and others, as shown in Figure 33. The economic order quantity (EOQ) is widely used in supply chain modeling approaches (Sampson 2014).
The Economic Order Quantity (EOQ) model assumes that demand is constant, and does not change over time. The optimal shipment size is that which minimizes the total logistic cost to the firm, including the inventory and transportation costs, which can be calculated by the EOQ. The basic formulation of the EOQ model is shown in Equation (9) and (10).
Intermodal Transportation and Inventory Cost (ITIC) Model
The Federal Railroad Administration (2005) developed the ITIC model to estimate the impacts of alternative policies on freight mode choice. The ITIC model was preceded by the Translog Shipper Cost Model developed by the Massachusetts Institute of Technology (MIT) (Roberts 1981) and the Intermodal Competitive Model (ICM) by Association of American Railroads (AAR). Two different versions of the ITIC were developed, State Tool (ST) and Intermodal Tool (IM). ITIC-IM helps users estimate the shift from truck to rail intermodal service. ITIC-ST estimates potential shifts from highway freight traffic to different truck configurations or rail intermodal service. The ITIC models are disaggregate models that minimize the total logistics costs. The ITIC models consider various attributes of shipment, shipper/receiver, commodity, and modes under consideration to select the mode that minimizes the total logistic costs. The costs include: ordering, capital carrying in transit, capital carrying in inventory, warehousing, loading and unloading, safety stock carrying, loss and damage claims. The ITIC also considers reliability, described as the variability in the ordering lead-time, using a Gamma distribution. The following table summarizes the inputs, parameters and models used by ITIC tools.
As shown in Table 14, the ITIC’s data input requirements are onerous. The data it requires, such as storage and handling and line-haul charges, vary widely depending on the type of commodity, where using average values will lead to erroneous results. It also requires commercially sensitive data, which are practically impossible to obtain, such as the annual volume of cargo sent by the shipper to each individual customer (after all, the ITIC is a shipment-level model).
Essentially, the ITIC requires data that are either extremely expensive, or in some cases virtually impossible to collect, particularly for planning and policy studies, which also involve forecasts of future conditions. As a result, notwithstanding its practicality and ease of use, the ITIC would probably not provide a reliable approach to study the impacts of public- ector policies on freight mode choice.