Linda K. Nozick

Inventory, transportation, service quality and the location of distribution centers

Abstract A crucial question in the design of efficient logistics systems is the identification of locations for distribution centers (DCs). However, the optimization of these location decisions requires careful attention to the inherent trade-offs among facility costs, inventory costs, transportation costs, and customer responsiveness. This paper presents a modeling approach that provides such an integrated view, and illustrates how it works in the context of a specific example involving the distribution of finished vehicles by an automotive manufacturer.

INTEGRATING INVENTORY IMPACTS INTO A FIXED-CHARGE MODEL FOR LOCATING DISTRIBUTION CENTERS

An important question in the design of efficient logistics systems is the identficaton of locations for distribution centers. Optimal designs should be based on consideration of inventory, transportation, construction and operating costs. This paper describes a method for including inventory costs within a fixed-charge facility location model, allowing such a model to be used more effectively for the development of optimal system designs. A realistic application of the model is discussed.

Robust optimization for fleet planning under uncertainty

We create a formulation and a solution procedure for fleet sizing under uncertainty in future demands and operating conditions. The formulation focuses on robust optimization, using a partial moment measure of risk. This risk measure is incorporated into the expected recourse function of a two-stage stochastic programming formulation, and stochastic decomposition is used as a solution procedure. A numerical example illustrates the importance of including uncertainty in the fleet sizing problem formulation, and the nature of the fundamental tradeoff between acquiring more vehicles and accepting the risk of potentially high costs if insufficient resources are available.

A two-echelon inventory allocation and distribution center location analysis

Abstract The optimization of locations for distribution centers is influenced by the demand for individual products. Lower demand products are often more effectively held in more centralized locations than higher demand products. This paper presents a model for optimizing the location of inventory for individual products in a multi-product two-echelon inventory system and the integration of those decisions into the location analysis for distribution centers. A realistic application of the analysis process is discussed.

Multiobjective Path Finding in Stochastic Dynamic Networks, with Application to Routing Hazardous Materials Shipments

We describe a method for finding nondominated paths for multiple routing objectives in networks where the routing attributes are uncertain, and the probability distributions that describe those attributes vary by time of day. This problem is particularly important in routing and scheduling of shipments of very hazardous materials. Our method extends and integrates the work of several previous authors, resulting in a new algorithm that propagates means and variances of the uncertain attributes along paths and compares partial paths that arrive at a given node within a user-specified time window. The comparison uses an approximate stochastic dominance criterion. We illustrate the effects of changing primary parameters of the algorithm using a small test network, and we show how the nondominated solution set achieved is larger than the set that would be identified if the uncertainty in routing attributes were ignored. We then demonstrate how the algorithm creates an effective solution set in a case study using a large network.

Modeling supplier selection and the use of option contracts for global supply chain design

As supply chains become more and more dependent on the efficient movement of materials among facilities that are geographically dispersed there is more opportunity for disruption. One of the common disruptions is the loss of production capability at supplier sites. We formulate a two-stage stochastic program and a solution procedure to optimize supplier selection to hedge against these disruptions. This model allows for the effective quantitative exploration of the trade-off between cost and risks to support improved decision-making in global supply chain design. A realistic case study is explored.

Integrated Routing and Scheduling in Hazardous Materials Transportation

Recognition of time-varying patterns of accident rates and exposure parameters can be used to improve routing and scheduling decisions for hazardous materials shipments. An integrated routing/scheduling approach can be used to reduce overall risk, and find preferred solutions in a multiobjective context. We describe a method for performing an integrated routing/scheduling analysis, and illustrate its use in a case study. We also construct estimates of the “value of information” for incorporation of this time-dependent data.

THE FIXED CHARGE FACILITY LOCATION PROBLEM WITH COVERAGE RESTRICTIONS

Abstract This paper develops a fixed charge facility location model with coverage restrictions, minimizing cost while maintaining an appropriate level of service, in identifying facility locations. Further, it discusses the insights that can be gained using the model. Two Lagrangian relaxation based heuristics are presented and tested. Both heuristics use a greedy adding algorithm to calculate upper bounds and subgradient optimization to calculate lower bounds. While both procedures are capable of generating good solutions, one is computationally superior.

A model for medium-term operations planning in an intermodal rail-truck service

This paper describes a model developed for medium-term operations planning in an intermodal rail-truck system. It was motivated by the need to redesign such systems to produce 1. (1) more reliable service, 2. (2) multiple service classes, and 3. (3) better equipment and facility utilization. The model is an integer linear program, which is computationally difficult to solve. A heuristic procedure was developed which provides excellent solutions, generally within 1% of the known optimal solution to the relaxed (non-integer) problem. Thus the model and heuristic could be used on large networks. Uses of the model and possible extensions are briefly discussed.

Sizing the US destroyer fleet

Abstract For the US Navy to be successful, it must make good investments in combatant ships. Historically a vital component in these decisions is expert opinion. This paper illustrates that the use of quantitative methods in conjunction with expert opinion can add considerable insight. We use the analytic hierarchy process (AHP) to gather expert opinions. Then, distributions are derived based on these expert opinions, and integrated into a mixed integer programming model to derive a distribution for the “effectiveness” of a fleet with a particular mix of ships. These ideas are applied to the planning scenario for the 2015 conflict on the Korean Peninsula, one of the two key scenarios that the Department of Defense uses for planning.