Faruk Güder

Fixed cycle ordering policies for capacitated multiple item inventory systems with quantity discounts

We consider the problem of stocking inventories of multiple items that share a common resource, like a warehouse space, where the vendor of the items offers quantity discounts. For the classic version of this problem without quantity discounts, it is well known that a fixed cycle approach, where the time between order replenishments for all items is the same, is a cost effective heuristic solution methodology, one that in some instances is preferred to both independent cycle and non-stationary approaches. In this paper, we demonstrate that a fixed cycle approach can also be used to heuristically solve the quantity discount case. Computational results suggest that this approach is often more cost effective than competing solution methodologies, particularly when the resource constraint is tight.

Ordering policies for multi-item inventory systems subject to multiple resource constraints

Abstract We study the multi-item inventory problem with multiple resource constraints. For the simplified variant of this problem with a single resource constraint, known heuristic solution approaches assume independent cycles, fixed cycles, and non-stationary order quantities. For the multiple constraint problem, however, only independent cycle solution algorithms exist in the literature. In this paper, we devise both fixed cycle and non-stationary approaches to the multiple constraint problem, and give computational results showing their potential cost-effectiveness over independent cycle methods. Scope and purpose We consider the problem of stocking inventories of multiple items that share common resources, like a warehouse space and a budget. For the classic version of this problem with a single resource constraint, independent cycle, fixed cycle, and non-stationary methods are available to provide heuristic solutions. The first two methodologies assume that order quantities do not vary over time, while the third relaxes this assumption. For the multiple constraint problem, however, only independent cycle solution approaches have been devised. In this paper, we demonstrate that both fixed cycle and non-stationary approaches are feasible and cost-effective ways of solving the multiple constraint problem.

Non-stationary ordering policies for multi-item inventory systems subject to a single resource constraint and quantity discounts

The multi-item inventory problem with a single resource constraint and quantity discounts is studied in this paper. Known solution approaches to this problem, both heuristic and enumerative, assume that ordering policies are stationary. A new heuristic approach is presented here for generating non-stationary ordering policies, with order quantities that can vary over time. Computational results for comparing these methods are given. The non-stationary approach is shown in these experiments to outperform heuristic stationary approaches, and an enumerative stationary approach when the non-stationary approach is suitably initialized.

Optimal objective function approximation for separable convex quadratic programming

We present an optimal piecewise-linear approximation method for the objective function of separable convex quadratic programs. The method provides guidelines on how many grid points to use and how to position them for a piecewise-linear approximation if the error induced by the approximation is to be bounded a priori.

Parallel and serial successive overrelaxation for multicommodity spatial price equilibrium problems

Computational experience is reported for various serial implementations of successive overrelaxation (SOR) applied to a linear multicommodity spatial price equilibrium problem posed as linear complementarity problem. Computational schemes that neglect the vast majority of the variables during most iterations are shown to be relatively efficient. A parallel implementation based on the same neglect is shown to exhibit encouraging average speedup over the single processor case. The SOR approach is shown empirically to converge for nonsymmetric problems. Dense network problems with up to 60 regions (each a potential supply or demand region) and 10 commodities, representing on the order of 36,000 variables, as well as sparse network problems with up to 140 regions, are typically solved in a few seconds of CPU time.

A restricted-entry method for a transportation problem with piecewise-linear concave costs

Abstract This paper presents a heuristic solution method for a transportation problem with piecewiselinear concave costs. The solution algorithm extends the restricted-entry-basis rule for the simplex method to the transportation method. The method not only finds a local optimum (as in the simplex version), but also efficiently searches for better local optima. Computational experience indicates that the algorithm finds optimal or near optimal solutions within a reasonable time on a personal computer.

Objective Function Approximation: An Application to Spatial Price Equilibrium Models

This paper describes a method for selecting a grid size for the piece wise-linear approximation of a separable quadratic program. It describes and demonstrates application of the procedure to a spatial price equilibrium model. The method is based on an a priori bound relating the amount of objective function approximation error to the suboptimality induced in the solution of the actual optimization problem.

Spatial price equilibrium, distribution center location and successive over-relaxation

A spatial price equilibrium problem is modeled which allows piecewise linear convex flow costs, and a capacity limit on the trade flow between each supply/demand pair of regions. Alternatively, the model determines the locations of intermediate distribution centers in a market economy composed of separate regions, each with approximately linear supply and demand functions. Equilibrium prices, regional supply and demand quantities, and commodity flows are determined endogenously. The model has a quadratic programming formulation which is then reduced by exploiting the structure. The reduced model is particularly well suited to solution using successive over-relaxation.

Parallel computation of intertemporal multicommodity spatial price equilibria in the presence of quotas

An intertemporal, spatial price equilibrium is determined for multiple commodities where the net import of each commodity in a given time period is a linear function of the prices of all commodities in that region and time period. Temporal and spatial flows are subject to fixed unit costs, and quotas in the form of upper bounds. A parallel decomposition scheme exploits characteristics of equilibria.

An iterative SOR algorithm for multi-period spatial equilibria

Abstract This paper presents an iterative algorithm for the solution of multi-period spatial equilibrium problems formulated in a net import format. We first present a net import formulation for the problem and then apply the SOR-based iterative algorithm for its solution. We later show that the algorithm can be extended to problems with sparse network and with congestion on the flows. Finally, we report computational experience with the proposed algorithm for the solution of some large problems.