Mark A. Turnquist

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.

Service frequency, schedule reliability and passenger wait times at transit stops

Abstract A model is developed to evaluate the sensitivity of expected passenger wait time at transit stops to service frequency and schedule reliability. This model represents an advance over previous models because it explicitly incorporates a passenger decision-making process, rather than assuming that passengers arrive at random instants in time. The model is tested against more traditional models using data from the Chicago area. These tests indicate that the passenger-choice model represents a significant improvement in predictive ability. The implications of this model are that passenger wait time is much more sensitive to schedule reliability and much less sensitive to service frequency than previously believed.

APPROXIMATE ALGORITHMS FOR THE DISCRETE NETWORK DESIGN PROBLEM

The discrete network design problem is one of finding a set of feasible actions (projects) from among a collection of possible actions, that when implemented, optimizes some objective function(s). This is a combinatorial optimization problem that is very expensive to solve exactly. This paper proposes two algorithms for obtaining approximate solutions to the discrete network design problem with much less computational effeort. The computational savings are achieved by approximating the original problem with a new formulation which is easier to solve. The first algorithm proposed solves this approximate problem exactly, while the second is even more efficient, but provides only a near-optimal solution to the approximate problem. Experience with test problems indicates that these approximations can reduce the computational effort by a factor of 3-5, with little loss in solution accuracy.

A Model for Fleet Sizing and Vehicle Allocation

There are important interactions between decisions on sizing a vehicle fleet and decisions on utilizing that fleet. A model is formulated to optimize both sets of decisions simultaneously under dynamic and uncertain conditions. A network approximation to this model is presented and a solution procedure proposed. The convergence behavior of the solution procedure and the potential consequences of using simpler models to solve the fleet sizing and vehicle allocation problem are illustrated using several hypothetical problems. We conclude that this model is useful in identifying good strategies for the sizing of vehicle fleets and for the allocation of empty vehicles.

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.

Pre-positioning planning for emergency response with service quality constraints

Pre-positioning of emergency supplies is a means for increasing preparedness for natural disasters. Key decisions in pre-positioning are the locations and capacities of emergency distribution centers, as well as allocations of inventories of multiple relief commodities to those distribution locations. The location and allocation decisions are complicated by uncertainty about if, or where, a natural disaster will occur. An earlier paper (Rawls and Turnquist 44:521–534, 2010) describes a stochastic mixed integer programming formulation to minimize expected costs (including penalties for unmet demand) in such a situation. This paper extends that model with additional service quality constraints. The added constraints ensure that the probability of meeting all demand is at least α, and that the demand is met with supplies whose average shipment distance is no greater than a specific limit. A case study using hurricane threats is used to illustrate the model and how the additional constraints modify the pre-positioning strategy.

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.