Donald P. Warsing

(Q,r) Inventory policies in a fuzzy uncertain supply chain environment

Managers have begun to recognize that effectively managing risks in their business operations plays an important role in successfully managing their inventories. Accordingly, we develop a (Q,r) model based on fuzzy-set representations of various sources of uncertainty in the supply chain. Sources of risk and uncertainty in our model include demand, lead time, supplier yield, and penalty cost. The naturally imprecise nature of these risk factors in managing inventories is represented using triangular fuzzy numbers. In addition, we introduce a human risk attitude factor to quantify the decision makers attitude toward the risk of stocking out during the replenishment period. The total cost of the inventory system is computed using defuzzification methods built from techniques identified in the literature on fuzzy sets. Finally, we provide numerical examples to compare our fuzzy-set computations with those generated by more traditional models that assume full knowledge of the distributions of the stochastic parameters in the system.

Determining the value of dedicated multimodal cargo facilities in a multi-region distribution network

Abstract This paper presents an analytic model of a multi-region distribution problem that addresses the operational benefits of serving a global market using a network of dedicated multimodal cargo facilities (DMCFs). The model allows an explicit evaluation of the comparative value of using a dedicated air cargo-based multimodal distribution facility in an established network of supply and demand points as opposed to more traditional methods for inter-regional shipments. We develop a large-scale, non-linear programming model to evaluate the corresponding logistics costs, incorporating the congestion effects of aircraft loading/unloading on dock-to-dock lead times in the network. We then demonstrate how this difficult problem can be decomposed into its linear (LP) and non-linear (multi-class queueing) sub-problems. An iterative solution scheme is devised to compute the comparative costs of traditional and DMCF-based cargo operations.

Estimating LTL rates using publicly available empirical data

We develop a shipper-oriented model to estimate less-than-truckload (LTL) truck rates for transporting goods between origin–destination (O–D) pairs located anywhere in the continental United States. The rate estimate is developed from internet-accessible tariff tables and allows straightforward computation of optimal shipment sizes (minimising total logistics costs) and comparison with the total cost of other modes. The model uses publicly available nominal rates along with a characterisation of the distribution of LTL shipments, based on other publicly available data, to determine a rate that also accounts for the estimated industry average discount from the nominal rate. We use nonlinear regression to build the estimate, with tariff-based rates serving as the dependent variable and load density, shipment weight, and O–D pair distance as the explanatory variables. The model is normalised to reflect average industry rates and current economic conditions using the Producer Price Index for LTL service. Although our results are specific to US markets for truck freight, the method of analysis serves as a model for similar international studies.

Comparing traditional and fuzzy-set solutions to Q, r inventory systems with discrete lead-time distributions

Using a previously published approach to computing Q, r policies for an inventory system with uncertain parameters described by fuzzy sets, we compare thee methods for specifying lead-time demand for four different empirically-specified, non-normal distributions of replenishment lead time. This general distribution of lead time results in a situation in which the distribution of demand over the lead time, or lead-time demand LTD, is not easily specified. We compare Q, r policies generated by using a traditional normal approximation to LTD, a fuzzy-set approximation, and the optimal policy computed via a simulation-optimization approach that utilizes the explicit LTD distribution. We show that, on average, the results from the fuzzy-set model are significantly more accurate than the traditional normal approximation, especially when the LTD distribution is highly skewed.