George R. Wilson

An Integrated Model and Solution Approach for Fleet Sizing with Heterogeneous Assets

This paper addresses a fleet-sizing problem in the context of the truck-rental industry. Specifically, trucks that vary in capacity and age are utilized over space and time to meet customer demand. Operational decisions (including demand allocation and empty truck repositioning) and tactical decisions (including asset procurements and sales) are explicitly examined in a linear programming model to determine the optimal fleet size and mix. The method uses a time-space network, common to fleet-management problems, but also includes capital cost decisions, wherein assets of different ages carry different costs, as is common to replacement analysis problems. A two-phase solution approach is developed to solve large-scale instances of the problem. Phase I allocates customer demand among assets through Benders decomposition with a demand-shifting algorithm assuring feasibility in each subproblem. Phase II uses the initial bounds and dual variables from Phase I and further improves the solution convergence without increasing computer memory requirements through the use of Lagrangian relaxation. Computational studies are presented to show the effectiveness of the approach for solving large problems within reasonable solution gaps.

Using a facility location algorithm to solve large set covering problems

Erlenkotter has developed an efficient exact (guarantees optimality) algorithm to solve the uncapacitated facility location problem (UFLP). In this paper, we use his algorithm to solve large instances of an important subset of the UFLP; the set covering problem (SCP). In addition, we present further empirical evidence that a heuristic algorithm developed by Vasko and Wilson for the SCP is capable of quickly generating good solutions to large SCPs.

An approach to postoptimality and sensitivity analysis of zero-one goal programs

In this article we present a methodology for postoptimality and sensitivity analysis of zero‐one goal programs based on the set of k‐best solutions. A method for generating the set of k‐best solutions using a branch and bound algorithm and an implicit enumeration scheme for multiple objective problem are discussed. Rules for determining the range of parameter changes that still allows a member of the k‐best set to be optimal are developed. An investigation of a sufficient condition for postoptimality analysis is also presented.

A demand-shifting feasibility algorithm for Benders decomposition

Abstract Benders decomposition is a popular method for solving problems by resource-directive decomposition. Often, the resource allocations from the master problem lead to infeasible subproblems, as resources are insufficient to meet demand. This generally requires the use of feasibility cuts to reach a feasible solution, which can be computationally expensive. For problems in which subproblems have limited capacity, we propose an efficient algorithm which shifts excess demand to other sources of capacity. The advantages of the algorithm are that it is quick, requires only one solution of each subproblem in each Benders iteration, and does not add any feasibility cuts into the master problem. A computational study is performed on a fleet sizing problem to illustrate the algorithm’s efficiency when compared to the traditional feasibility cut method.

An on-line controller for production systems with seasonal demands

Abstract This paper investigated a hirarchical production planning and control model for flexible manufacturing systems that simultaneously make multiple parts subject to periodic demands. The off-line planning and on-line control strategy is utilized in the aggregate planning model. First, the optimal inventory levels are determined by the off-line planning model. The problem is formulated as a boundary-free discrete optimal control problem. When the actual inventory levels deviate from the optimal levels due to random interruptions, an on-line control problem is solved. The problem is formulated as a boundary-fixed discrete optimal control problem. The resulting large-scale problem is broken into a network flow problem and several single part aggregate production planning problems. The network flow problem determines the alternative routings among cells for given production rates. Single part production planning problems determine the production rates for each part in each period. Numerical examples illustrate the algorithms efficiency.

Aggregating performance measures of a multi-echelon supply chain using the analytical network and analytical hierarchy process

Performance measures of a multi-echelon Supply Chain (SC) assist SC Managers in making strategic decisions. The measures associated with an inter-organisational SC are an aggregation of the performance measures of the SC members. However, two types of dependencies exist in a multi-echelon SC: intra- and inter-organisational. The former type accounts for the relationship between various parts or departments of a firm, while the latter accounts for the influence of one organisation upon another. Traditional hierarchical techniques are inaccurate to use as an aggregation method for the performance measures as they do not account for dependency. The level of dependency within and among firms needs to be determined. In this paper, a two-dimensional approach is taken using the analytical hierarchy process with the analytical network process to overcome the deficiency with a hierarchical approach.

Approximations for the mean and variance of the throughput of flexible manufacturing cells

Abstract A large complex flexible manufacturing system consisting of a number of manufacturing cells can be modeled as a composite of open and closed queueing networks. The entire manufacturing system is modeled as an open queueing network, and individual manufacturing cells are modeled as closed queueing networks. The means and variances of the cell throughput are needed so that the overall system performance can be estimated. The analysis provided in this paper focuses on the distribution of the interdeparture time of the loading/unloading station in the cell. The distribution is formulated as a phase-type function. Three cell structures are investigated: stations in series, stations in parallel, and stations with feedback. Numerical results are given to illustrate the effect of the cell structures on the means and variances of the cell throughput.

The Inmate Assignment and Scheduling Problem and Its Application in the Pennsylvania Department of Corrections

The authors developed a hierarchical, multiobjective mixed-integer linear optimization model, which assigns inmates to correctional institutions and schedules their programs, while considering best...

Lateral Transshipment and Rationing Policies for Multi-Retailer Systems

Many retailers discriminate among their customers based on their value to the firm. Instead of losing a customer due to this discrimination or lack of inventory, a retailer might prefer to request that other retailers satisfy the customers demand. The system as a whole can benefit from this types of transshipments. In this paper, we study a multi-retailer system with each retailer serving two types of customers: high and low priority. Each retailer employs a rationing, critical-level policy in the context of a continuous-review (r,Q) inventory model with lost sales. Retailers can transship items from either other retailers or a central depot. Therefore, no demand is lost; all demand is satisfied by the system. We propose an approximate iterative procedure to find the cost-minimizing policy parameters for individual retailers and propose an iterative heuristic, which relies on adjusting the demand arrival rates and the transshipment costs for both types of customers at all retailers, to solve the overall rationing and transshipment problem. Via numerical analysis, we identify the conditions under which a retailer can benefit from transshipments by changing its rationing policy. In addition, we study the sensitivity of the cost benefit resulting from transshipments with regard to different system parameters.