Gregory Dobson

Flexible Service Capacity: Optimal Investment and the Impact of Demand Correlation

We consider a firm that provides multiple services using both specialized and flexible capacity. The problem is formulated as a two-stage, single-period stochastic program. The firm invests in capacity before the actual demand is known and optimally assigns capacity to customers when demand is realized. Sample applications include a car rental companys use of mid-sized cars to satisfy unexpectedly high demand for compact cars and an airlines use of business-class seats to satisfy economy-class demand. We obtain an analytical solution for a particular case, when services may be upgraded by one class. The simple form of the solution allows us to compare the optimal capacities explicitly with a solution that does not anticipate flexibility. Given that demand follows a multivariate normal distribution, we analytically characterize the effects of increasing demand correlation on the optimal solution. For the case with two customer classes, the effects of demand correlation are intuitive: Increasing correlation induces a shift from flexible to dedicated capacity. When there are three or more classes, there are also adjustments to the resources not directly affected by the correlation change. As correlation rises, these changes follow an alternating pattern (for example, if the optimal capacity of one resource rises, then the optimal capacity of the adjacent resource falls). These results make precise conjectures based on numerical experiments that have existed in the literature for some time.

Competitive location on a network

In this paper we study the problem of locating facilities on a network in the presence of competition. Customers at each node in the network choose from the available facilities so as to minimize the distance traveled. The problem is to find a set of facilities that is stable in the sense that each facility is economically viable and no competitor can successfully open any facilities. We define several versions of stability and establish certain relationships between them. We then present integer programming formulations that identify stable sets, and describe an enumeration algorithm for constructing a profit-maximizing stable set.

The Cyclic Lot Scheduling Problem with Sequence-Dependent Setups

In this paper, we formulate the cyclic lot scheduling problem on a single facility with sequence-dependent setup costs and times and provide a heuristic solution procedure. A Lagrangian relaxation of the formulation leads to a partial separation of the embedded lot sizing and traveling salesman problems. The relaxation results in a new combinatorial problem related to the minimum spanning tree problem. The information about frequency of production, gained from the solution to this relaxation, is used to find heuristic solutions for the entire problem. Computational work on randomly generated problems shows that the problem becomes more difficult as the diversity in the sequence-dependent parameters increases.

Scheduling independent tasks on uniform processors

A worst-case analysis is given for the LPT (longest processing time) heuristic applied to the problem of scheduling independent tasks on uniform processors. A bound of

Profit-Optimizing Product Line Design, Selection and Pricing with Manufacturing Cost Consideration

\frac{19}{12}

Simultaneous Resource Scheduling to Minimize Weighted Flow Times

is derived on the ratio of the heuristic to the optimal makespan and an example is given where the error is greater than

A Model of ICU Bumping

\frac{{3}}{{2}}

Cyclic scheduling to minimize inventory in a batch flow line

. A generalization of the classic result of Graham for the case of identical processors is given. Here tight bounds are derived for the ratio of the heuristic to the optimal makespan which depends on the ratio of the longest task to the makespan.

Sensitivity of the EOQ model to parameter estimates

Much of the literature on product line design or product line selection focuses on revenue or market share maximization, but in many cases, the true objective is to maximize profit. In this paper, we survey the literature on models that address decisions regarding the conceptual design of products to be offered, or the selection of products among a large set of potential products, and, in some cases, the prices of the offered products. We focus on the combined effects of multiple product offerings on both revenue and manufacturing costs, and emphasize models that would accommodate variable manufacturing costs, the cost of manufacturing facilities, and/or engineering design costs of some form. The paper concludes with promising directions for future research.

Optimal Workflow Decisions for Investigators in Systems with Interruptions

Many scheduling problems in manufacturing and service firms involve tasks that require more than one resource to be used simultaneously to execute the task. Two formulations of this scheduling problem are given. We develop a Lagrangian relaxation for the problem that has an intuitive interpretation. The relaxation suggests heuristics and provides a lower bound on the optimal solution. Next a surrogate relaxation is developed that provides a second bound and a heuristic solution. An enumeration procedure to determine the optimal solution is described, and computational results on the effectiveness of the bounds and the heuristics are presented. The Lagrangian relaxation performs better on problems with a low degree of simultaneity, and the surrogate relaxation does better with a high degree of simultaneity.