Optimization of Single Machine Job Scheduling Using Permutations and Combinatorial Approaches in R

In this paper the multiple projects resource-constrained project scheduling problem is considered. Several projects are to be scheduled simultaneously with sharing several kinds of limited resources in this problem. Each project contains non-preemptive and deterministic duration activities which compete limited resources under resources and precedence constraints. Moreover, there are the due date for each project and the tardy cost per day that cause the penalty when the project cannot be accomplished before its due date. The objective is to find the schedules of the considered projects to minimize the total tardy cost subject to the resource and precedence constraints. Since the resource-constrained project scheduling problem has been proven to be NP-Hard, we cannot find a deterministic algorithm to solve this problem efficiently and metaheuristics or evolutionary algorithms are developed for this problem instead. The problem considered in this paper is harder than the original problem because the due date and tardy cost of a project are considered in addition. The metaheuristic method called ANGEL was applied to this problem. ANGEL combines ant colony optimization (ACO), genetic algorithm (GA) and local search strategy. In ANGEL, ACO and GA run alternately and cooperatively. ANGEL performs very well in the multiple projects resource-constrained project scheduling problem as revealed by the experimental results.

An optimal procedure for minimizing total weighted resource tardiness penalty costs in the resource-constrained project scheduling problem

We study single-machine bicriteria scheduling problems with position-dependent weights. Due date costs and penalty costs can affect the decision-maker’s profit. Therefore, how to optimize the benefits and balance of these costs for decision-makers is the focus of this research. This paper discusses three models: weighted-sum scheduling problem, constrained scheduling problem, Pareto scheduling problem. It analyzes the properties of bicriteria schedule, determines the optimal due dates (usually referred to as different due dates: DIF), and gives the corresponding polynomial solvable algorithms.

In the universal facility location problem, we are given a set of clients and facilities. Our goal is to find an assignment such that the total connection and facility cost is minimized. The connection cost is proportional to the distance between each client and its assigned facility, whereas the facility cost is a nondecreasing function with respect to the total number of clients assigned to the facility. The universal facility location problem generalizes several classical facility location problems, including the uncapacitated facility location problem and the capacitated facility location problem (both hard and soft capacities). This work considers the universal facility location problem with linear penalties, where each client can be rejected for service with a penalty. The objective is to minimize the total connection, facility and penalty cost. We present a $$(5.83+\epsilon )$$ -approximation local search algorithm for this problem.

This paper investigates a multi-objective parallel machine scheduling problem under fully fuzzy environment with fuzzy job deterioration effect, fuzzy learning effect and fuzzy processing times. Due dates are decision variables for the problem and objective functions are to minimise total tardiness penalty cost, to minimise earliness penalty cost and to minimise cost of setting due dates. Due date assignment problems are significant for Just-in-Time (JIT) thought. A JIT company may want to have optimum schedule by minimising cost combination of earliness, tardiness and setting due dates. In this paper, we compare different approaches for modelling fuzzy mathematical programming models with a local search algorithm based on expected values of fuzzy parameters such as job deterioration effect, learning effect and processing times.

Supply chain management is becoming an increasingly important issue, especially when in most industries the cost of materials purchased comprises 40–60% of the total sales revenue. Despite the benefits cited for single sourcing in the popular literature, there is enough evidence of industries having two/three sources for most parts. In this paper we address the operational issue of quantity allocation between two uncertain suppliers and its effects on the inventory policies of the buyer. Based on the type of delivery contract a buyer has with the suppliers, we suggest three models for the supply process. Model I is a one-delivery contract with all of the order quantity delivered either in the current period with probability β, or in the next period with probability 1 – β. Model II is also a one-delivery contract with a random fraction of the order quantity delivered in the current period; the portion of the order quantity not delivered is cancelled. Model III is similar to Model II with the remaining quantity delivered in the next period. We derive the optimal ordering policies that minimize the total ordering, holding and penalty costs with backlogging. We show that the optimal ordering policy in period n for each of these models is as follows: for x ≥ ūn, order nothing; for v̄n ≤ x < ūn, use only one supplier; and for x < v̄n, order from both suppliers. For the limiting case in the single period version of Model I, we derive conditions under which one would continue ordering from one or the other or both suppliers. For Model II, we give sufficient conditions for not using the second (more expensive) supplier when the demand and yield distributions have some special form. For the single period version of Models II and III with equal marginal ordering costs we show that the optimal order quantities follow a ratio rule when demand is exponential and yields are either normal or gamma distributed.

Heuristics for multimode scheduling problems with dedicated resources

BackgroundConventional echocardiography is a safe, available, and accurate tool for cardiac structural and functional evaluation, but it should not cancel clinical assessment and history tacking, and indeed both are complementary. A pre-employment assessment is important for employees and community safety and suitability for a specific work requirement.ResultsAiming to assess the value of routine pre-employment echocardiography for the detection of cardiac abnormalities, we examined seven hundred ninety-five persons who were routinely referred to us for pre-employment conventional echocardiography. Only 9 persons had structural cardiac abnormalities (1.3%) and distributed as follows: two had bicuspid aortic valve with isolated aortic regurgitation, one of them had mild AR, and the other had moderate AR. Two cases had mitral valve prolapse, one of them had trivial MR, while the other had a flail anterior leaflet with severe MR. One patient had atrial septal defect 1.5 cm with mild pulmonary hypertension and right-sided chambers dilatation. One patient had dextrocardia (situs inversus totalis) without other cardiac problems. One had moderate pulmonary hypertension and modest right-sided chambers dilation. Two patients had left ventricular hypertrophy. Surprisingly, we did not detect rheumatic valvular heart disease. The money cost of echocardiography tests for those 795 persons was 198,750 Egyptian pounds (LE); their transportation cost was about 19.800LE. The total group time cost of the tests was 265 h, total time lost at the waiting room was 1590 h, total transportation time lose was 2385 h, so the total time cost was about 4000 h. Using psychological stress questionnaire, 33 participants (4.2%) had results suggestive of a low sense of psychological pressure due to echocardiography examination, 221 participants (27.8%) had results suggestive of a moderate feeling of stress, while 541 participants (68%) had results suggestive of a high sense of stress.ConclusionWe recommend against routine echocardiography for cardiac assessment in pre-employment assessment and to do it only for persons with abnormal clinical or ECG findings.

This paper describes a tabu search approach for a multiprocessor scheduling problem, where a list of jobs has to be scheduled on identical parallel processors. Each job in the list has a release date, a due date, a processing time and a set of predecessors. The objective is to minimize the number of processors used while respecting the constraints imposed by release dates, due dates and precedences. Two versions of this problem are considered here, in the first one precedence constraints are relaxed, they are taken into account in the second one. The proposed method is used to solve High Level Synthesis problem instances. The results show the effectiveness of our approach for both versions of the problem. A comparison with an exact method is also conducted.

Setting due dates to minimize the total weighted possibilistic mean value of the weighted earliness–tardiness costs on a single machine

We study the scheduling of multiple tasks under varying processing costs and derive a priority rule for optimal scheduling policies. Each task has a due date, and a non‐completion penalty cost is incurred if the task is not completely processed before its due date. We assume that the task arrival process is stochastic and the processing rate is capacitated. Our work is motivated by both traditional and emerging application domains, such as construction industry and freelance consulting industry. We establish the optimality of Shorter Slack time and Longer remaining Processing time (SSLP) principle that determines the priority among active tasks. Based on the derived structural properties, we also propose an effective cost‐balancing heuristic policy and demonstrate the efficacy of the proposed policy through extensive numerical experiments. We believe our results provide operators/managers valuable insights on how to devise effective service scheduling policies under varying costs.

V-shape property for optimal schedules with monotone penalty functions

ABSTRACT: A versatile computer model for audit-staff scheduling based on a zero-one integer program was presented by Balachandran and Zoltners [1981] (BZ). This paper extends the work of BZ by demonstrating how precedence constraints, due dates, penalty costs, resource leveling, and other audit considerations can be added to the zero-one integer program for audit scheduling. These additional features help improve the realism of the scheduling model, thus making the model more practical for applications.

The precedence relationships between the operations are important constraints in planning and scheduling of manufacturing systems and project management. This paper presents a method to obtain a global solution for operation sequencing with precedence constraints which are one of the most influential factors in the performance of planning and scheduling problems. An integer programming model is proposed for the operation sequencing with precedence constraints. And an adaptive evolutionary approach for the problem is developed by employing the adaptive genetic operation functions to obtain a good solution for relatively large problems in a reasonable computational time. Computational experiments for the model are performed and the results are analyzed.

An iterative algorithm for scheduling UET tasks with due dates and release times