Ömer Kirca

Tardiness minimization on parallel machines

We consider the NP-hard problem of scheduling jobs on identical parallel machines to minimize total tardiness. We present properties that characterize the structure of an optimal schedule. We propose a branch and bound algorithm that incorporates the properties along with an efficient lower bounding scheme. We find that optimal solutions can be obtained in reasonable times for problems with up to 15 jobs. In the last part of the study we extend the results to uniform parallel machines.

Selecting transfer station locations for large solid waste systems

Abstract In a city with a population over 6 000 000, solid waste collection activities require a lot of attention. The resources used for collection and transport, trucks and labor, can be utilized more effectively if waste is transported to the disposal area via transfer stations. The location of transfer stations becomes especially important when the daily average of solid waste to be transferred is around 6 000 tons and disposal areas are at least 30 kilometres away from the metropolitan. A general mathematical programming approach with four stages is proposed to determine the locations of transfer stations. Certain modifications are required for the case considered, all resulting in a model which identifies the trade-off between costs of carrying the waste by different transportation modes. The identification of the trade-off requires the estimation of relative cost values rather than individual costs. On the basis of the results obtained, economic feasibility of different alternatives can be evaluated upon the availability of cost information. The application of the model to Istanbul is summarized together with the details of analysis.

A branch and bound algorithm to minimize the total weighted flowtime for the two-stage assembly scheduling problem

In this paper, a two-stage assembly scheduling problem is considered with the objective of minimizing the total weighted flowtime. A lower bounding procedure and a dominance criterion are developed and incorporated into a branch and bound procedure. A heuristic procedure is also used to derive an initial upper bound. Computational results of the algorithm are presented.

On the minimization of total weighted flow time with identical and uniform parallel machines

We consider the NP-hard problem of scheduling jobs on identical parallel machines to minimize total weighted flow time. We discuss the properties that characterize the structure of an optimal solution, present a lower bound and propose a branch and bound algorithm. The algorithm is superior to prior methods presented in the literature. We also extend the algorithm to uniform parallel machines and solve medium-sized problem instances.

A branch and bound algorithm to minimize the total flow time for m-machine permutation flowshop problems

Abstract The m -machine permutation flowshop problem with the total flow-time objective is a common scheduling problem, which is known to be NP-hard for m ⩾2. In this article, we develop a branch and bound algorithm to solve both the weighted and unweighted version of this problem. Our algorithm incorporates a new machine-based lower bound and a dominance test for pruning nodes. Computational experiments suggest that the algorithm can handle test problems with n ⩽15. It also seems capable of dealing with larger problems for the unweighted objective, especially when the processing times are correlated.

A new heuristic approach for the multi-item dynamic lot sizing problem

Abstract In this paper a framework for a new heuristic approach for solving the single level multi-item capacitated dynamic lot sizing problem is presented. The approach uses an iterative item-by-item strategy for generating solutions to the problem. In each iteration a set of items are scheduled over the planning horizon and the procedure terminates when all items are scheduled. An algorithm that implements this approach is developed in which in each iteration a single item is selected and scheduled over the planning horizon. Each item is scheduled by the solution of a bounded single item lot sizing problem where bounds on inventory and production levels are used to ensure feasibility of the overall problem. The performance of this algorithm is compared to some well-known heuristics over a set of test problems. The computational results demonstrated that on the average our algorithm outperforms other algorithms. The suggested algorithm especially appears to outperform other algorithm for problems with many periods and few items. In the literature these problems are considered as hard.

Scheduling jobs on unrelated parallel machines to minimize regular total cost functions

In this paper we consider unrelated parallel machine scheduling problems that involve the minimization of regular total cost functions. We first present some properties of optimal solutions and then provide a lower bound. These mechanisms are tested on the well-known practical problem of minimizing total weighted flow time on unrelated parallel machines. In doing so, we design a branch and bound algorithm incorporating the mechanisms derived for the general total cost function along with the ones derived specifically for the total weighted flow time criterion. Computational experience indicates that incorporating reduction and bounding mechanisms significantly improves the performance of the branch and bound algorithm.

Bicriteria scheduling problem involving total tardiness and total earliness penalties

Abstract This paper considers the problem of minimizing the weighted sum of earliness and tardiness penalties on a single machine. A simple and efficient lower bound is developed and several upper bounds are proposed. A branch and bound procedure incorporating the bounds, precedence relations and dominance properties is proposed. An experiment is designed to test the efficiency of the bounds, precedence relations, etc. Computational experience with problems up to 20 jobs is reported.

A multi-item newsvendor problem with preseason production and capacitated reactive production

Abstract Given items with short life cycles or seasonal demands, one can potentially improve profits by producing during the selling season, especially when its production capacity is substantial. We develop a two-stage, multi-item model incorporating reactive production that employs a firm’s internal capacity . Production occurs in an uncapacitated preseason stage and a capacitated reactive stage . Demands occur in the reactive stage. Reactive capacities are pre-allocated to each item in the preseason stage and cannot be changed during the reactive stage. Reactive production occurs during the selling season with full knowledge of demands. The objective is expected profit maximization. Unsatisfied demand is lost. The revenue, salvage value, and production and lost sales costs are proportional. Assuming no fixed costs, we present a simple algorithm for computing optimal policies. For a model with fixed costs for allocating preseason stage production and reactive stage capacity to product families, we characterize optimal policies and develop optimal and heuristic algorithms.

An efficient algorithm for the capacitated single item dynamic lot size problem

Abstract A dynamic programming based algorithm is developed for the single item lot size problem with concave costs and arbitrary capacities. By making use of the extreme point properties of the problem, first the set of all feasible cumulative production levels that may occur in an optimal solution is generated. In the second stage, a dynamic programming procedure is carried out over this set. The worst case computational effort is equal to that of the standard dynamic programming approach but extensive computational tests with the algorithm indicate that for T period problems the computational effort does not exceed O(T4). The performance of the algorithm is compared with the performance of the existing procedures in the literature for the general, the constant capacity, and the constant unit cost problems. The computational results demonstrate that our algorithm is at least three times faster than the other procedures for all problem types considered.