Rejection Cost Research Articles

Minimizing the maximum lateness for scheduling with release times and job rejection

We study scheduling problems with release times and rejection costs with the objective function of minimizing the maximum lateness. Our main result is a PTAS for the single machine problem with an upper bound on the rejection costs. This result is extended to parallel, identical machines. The corresponding problem of minimizing the rejection costs with an upper bound on the lateness is also examined. We show how to compute a PTAS for determining an approximation of the Pareto frontier on both objective functions on parallel, identical machines. Moreover, we present an FPTAS with strongly polynomial time for the maximum lateness problem without release times on identical machines when the number of machines is constant. Finally, we extend this FPTAS to the case of unrelated machines.

Single machine scheduling with the total weighted late work and rejection cost

AbstractWe study a single machine scheduling problem with the total weighted late work and the total rejection cost. The late work of a job is the part of this job executed after its due date, and the rejection cost of a job is the fee of rejecting to process it. We consider a Pareto scheduling and two restricted scheduling problems. The Pareto scheduling problem aims to find all non‐dominated values of the total weighted late work and the total rejection cost. The restricted scheduling problems are dedicated to minimizing the total weighted late work with the total rejection cost not greater than a given threshold, and minimizing the total rejection cost with the total weighted late work not greater than a given threshold, respectively. For the Pareto scheduling problem, we prove that it is binary NP‐hard by providing a pseudo‐polynomial time algorithm, and give a fully polynomial time approximation scheme (FPTAS). For the restricted scheduling problems, we prove that there are no FPTASes unless , which answers an open problem. Moreover, we develop relaxed FPTASes for these two restricted scheduling problems.

Adaptive virtual team planning and coordination: a mathematical programming approach

Purpose The rise of remote work increasingly requires organizations to coordinate a single large, consolidated talent pool into ad-hoc, short-term project teams on demand. This problem involves many simultaneous considerations including project revenues and rejection costs, conflicting projects and roles, worker assignment costs, worker utilization preferences and limits, worker reassignment costs, and arbitrary role start and end times. Moreover, plans must be continuously updated in response to changing circumstances. This paper addresses the problem of dynamic virtual team planning and coordination. Design/methodology/approach We show this problem is NP-hard and provide a dynamic mixed integer linear programming (MILP) formulation for both optimal initial plan generation as well as continuous plan adjustment and re-optimization. We utilized a factorial experiment design to generate benchmark problems spanning a wide range of characteristics and conducted extensive computational experimentation using a common MILP solver. Findings Exactly optimal solutions to large, realistically sized problems were consistently obtained in short amounts of time. All observed solution times were sufficient to support the operational decision-making requirements of real-world virtual team coordination, demonstrating the viability of this approach. Practical implications The approach developed in this research can enable organizations to optimally coordinate virtual teams on a large scale and continually adjust plans in response to changing circumstances, all in an automated manner. Originality/value This paper addresses a new and complex problem of increasing importance to organizations due to the rise in remote work. We provide a problem formulation and exact approach for optimally solving both the planning and re-planning aspects of this problem.

Costly conspicuousness reveals benefits of sexual dimorphism in brood parasitic diederik cuckoos.

The existence of adult sexual dimorphism is typically explained as a consequence of sexual selection, yet coevolutionary drivers of sexual dimorphism frequently remain untested. Here, I investigate the role of sexual dimorphism in host-parasite interactions of the brood parasitic diederik cuckoo, Chrysococcyx caprius. Female diederik cuckoos are more cryptic in appearance and pose a threat to the clutch, while male diederik cuckoos are conspicuous and not a direct threat. Specifically, I examine whether sexual dimorphism in diederik cuckoos provokes threat-level sensitive responses in Southern red bishop, Euplectes orix, hosts. I use experimentally simulated nest intrusions to test whether hosts have the capacity to differentially (i) detect, and/or (ii) discriminate between, male and female diederik cuckoos, relative to harmless controls. Overall, I found no evidence that diederik cuckoos differ in detectability, since both sexes are comparable to controls in the probability and speed of host detection. Furthermore, neither male nor female hosts discriminate between sexually dimorphic diederik cuckoos when engaging in frontline nest defences. However, hosts that witnessed a male diederik cuckoo during the trial were more likely to reject odd eggs. Moreover, experimental eggs were significantly more likely to be rejected when female bishops observed a male compared to a female diederik cuckoo. While the cryptic appearance of female diederik cuckoos does not reduce detection by hosts, it does provide the benefit of anonymity given the egg rejection costs of conspicuous male-like appearance in the nest vicinity. These findings have implications for the evolution and maintenance of sexual dimorphism across the Cuculidae, and highlight the value of testing assumptions about the ecological drivers of sexual dimorphism.

Scheduling on parallel dedicated machines with job rejection

We study scheduling problems on parallel dedicated machines. Thus, each job can be processed on one specific machine only. The option of job-rejection is considered, and the total permitted rejection cost of all the jobs is bounded. Six scheduling problems are solved: ( i ) minimising makespan, ( ii ) minimising makespan with release-dates, ( iii ) minimising total completion time, ( iv ) minimising total weighted completion time, ( v ) minimising total load, and ( vi ) minimising maximum tardiness. Pseudo-polynomial dynamic programming algorithms are introduced for all these NP-hard problems.

Coordinating scheduling and rejection decisions in a two-machine flow shop scheduling problem

We study a two-machine flow shop scheduling problem where any operation can be rejected at a certain cost. A solution for such a problem requires two sets of decisions. The first involves the partition of the set of operations into two subsets: the set of operations that are accepted for scheduling in the shop, and the set of rejected operations. The second decision involves scheduling the set of accepted operations in the shop. The objective is to find a solution that minimizes the sum of the makespan and the total rejection cost. We prove that the problem is NP-hard even if all processing operations have identical processing times and identical rejection costs on either one of the two machines. We show, however, that the problem is fixed parameterized tractable with respect to a parameter that combine the number of different processing times on both machines with the number of different rejection costs on one out of the two machines. We also provide a pseudo-polynomial time algorithm for the problem, which we then convert into a fully polynomial time approximation scheme. This is achieved by dividing the problem into a set of subproblems and deriving a fully polynomial time approximation scheme for each one of them, separately. Finally, we present an integer linear programming formulation of the problem and two simple 2-approximation algorithms.

New Results on Single-Machine Scheduling with Rejection to Minimize the Total Weighted Completion Time

Abstract In this paper, we study eight single-machine scheduling problems with rejection and position-dependent parameters. We consider two position-dependent parameters as follows: (1) position-dependent weights and (2) position-dependent processing times. In addition, we also introduce a weight-modifying activity or a rate-modifying activity into our problems. In the first six problems, the task is to minimize the sum of the total weighted completion time of accepted jobs and the total rejection cost of rejected jobs. We show that all six problems can be solved in polynomial time. In the last two problems, the task is to minimize the total weighted completion time of accepted jobs under the constraint that the total rejection cost of rejected jobs can not exceed a given upper bound. We show that these two problems are binary NP-hard and each problem admits an FPTAS.

Common due-date assignment problems with fixed-plus-linear earliness and tardiness costs

We study single machine scheduling and common due-date assignment problems. The cost considered is fixed plus linear, i.e., jobs are penalized by two cost components: (i) a variable cost which is proportional to their earliness/tardiness values, (ii) a fixed cost which is independent of their actual earliness/tardiness values. For the general version of this problem, three heuristics are introduced and tested. We also study a number of modifications and special cases. We focus first on the special case of identical job processing times. Both versions of minsum and minmax are shown to have a polynomial time solution, even with the additional option of job rejection. Another special case of variable earliness cost and fixed tardiness cost is also studied. For this NP-hard problem, a pseudo-polynomial dynamic programming algorithm is introduced and tested. An extension to the case of bounded rejection cost, and a modified version with an additional bound on the total tardiness cost, are also studied. The solution algorithms for these problems are tested numerically as well. The last studied problem is that of job-independent cost components. This version, which generalizes the first and most cited due-date assignment model, is shown to have a polynomial time solution.

Planning container inspection and repair: A case study

The aim of this paper is to introduce a real-life problem of optimal planning of container inspection and repair on several facilities over several time periods assuring effective supply of empty containers indispensable for seamless global maritime transportation. The containers are of several types and quality levels. The objective is to minimize the total holding, inspection, repair, transportation and rejection costs. We formulate a deterministic min-cost multi-commodity network flow problem and prove NP-hardness for two special cases. Values of the rejection costs are determined such that no container is rejected in an optimal solution if there exists a feasible solution with no container rejected. An algorithmic mechanism is proposed to support a negotiation of periodic container demands between the container provider and the container users with the aim to reduce the overall costs. Computer experiments with instances obtained by random deviation from industrial data demonstrate that the majority of instances with up to 4 facilities, 4 container types, 7 quality levels, and 7, 14 or 30 time periods can be solved with an acceptable quality using an academic version of CPLEX in two hours on a standard PC.

Reforestation pipeline: case for quality management of NIR-region grading of Scots pine seeds and FLR-algorithm for information processing

When controlling the process of improving the quality of seeds by separating on a spectrometric basis, the primary information about the state of Scots pine seeds is carried by the wavelengths of optical fluxes and their amplitudes. The algorithm for analyzing the required characteristics of small forest seeds in the infrared range is a corresponding sequence of logical terms that provide the ability to determine the specified seed parameters by a combination of spectral frequencies and light flux amplitudes taken from the corresponding photodetectors. At ΔС = 0.5, the efficiency of the algorithm was 77.6 %, and at ΔС = 0.9, respectively, 99.5 %. In this regard, the choice of ΔС is the result of a compromise between the cost of rejection of high-quality seeds and losses when using unrecognized low-quality seeds and it is made according to the results of relevant experiments.

Impact of potassium test sample rejections on routine laboratory service, South Africa.

Accurate potassium measurements are necessary for effective clinical management of hyperkalaemia. Pre-analytical factors may affect laboratory measurements, leading to erroneous results and inappropriate patient management and negatively impact the efficiency and finances of laboratories and hospitals. This study evaluated the impact of rejected potassium test requests on laboratory service. We conducted a retrospective descriptive study to assess potassium test data at a public laboratory in Pretoria, Gauteng, South Africa, using samples collected from an academic hospital, peripheral hospitals, and outpatient clinics between January 2018 to December 2018. We assessed the relationship between reasons for rejection and health facility type, as well as financial implications for the laboratory. The potassium result rejection rate was 15.1% (29 806 samples), out of the 197 405 requests received. The most common reasons for rejection were old sample (> 1 day old) (41.4%; 12 348 rejections) and haemolysis (38.2%; 11 398 rejections). The most frequent reason for rejections at the central, academic hospital was haemolysis (42.0%), while old sample was the most common reason for rejection at peripheral hospitals (43.4%; 4119/9493 requests) and outpatient health facilities (57.2%; 7208/12 605 requests) (p = 0.022). The total cost of potassium sample rejection over the study period was substantial, given the resource constraints in this setting. Peripheral hospitals and outpatient departments accounted for the majority of rejected potassium testing results, possibly resulting from delays in transportation; causing substantial financial impact on the laboratory. Improved sample collection, handling, and expedited transportation are recommended. This study highlights the importance of appropriate sample collection and handling and the undesirable consequences of non-adherence to these pre-analytical considerations.

Logic-based Benders decomposition for order acceptance and scheduling in distributed manufacturing

This paper studies an order acceptance and scheduling problem in distributed manufacturing to minimize the total costs consisting of rejection cost, production cost, transportation cost and tardiness cost. Two mixed-integer programming models are formulated, which are further improved by the proposed enhancement techniques. A logic-based Benders decomposition (LBBD) method and a branch and check search framework are developed in an attempt to realize the optimal and intelligent decisions of order acceptance, order assignment and scheduling. The proposed LBBD method following the principle of “divide and conquer” divides the original problem into determining the master problem of order acceptance and assignment, and determining the subproblem of order sequencing in each factory. A dynamic programming algorithm is also proposed to efficiently solve the subproblems. Extensive computational experiments are conducted, and the results demonstrate the effectiveness and efficiency of the enhancement techniques for the formulations, as well as the LBBD method. Besides, the value of distributed manufacturing is verified and the sensitivity of key cost factors is presented.

Scheduling problems with rejection to minimize the k-th power of the makespan plus the total rejection cost

Scheduling problems with rejection to minimize the k-th power of the makespan plus the total rejection cost

Dual objective bounded abstaining model to control performance for safety-critical applications

Abstaining models have been widely used in safety-critical fields to avoid uncertain classification and reduce misclassification costs. Previous abstaining models have two main disadvantages. First, the costs of classification and rejection need to be set. Unfortunately, it is difficult to obtain or estimate costs in practical applications. When costs change, the trained model will be no longer applicable. Second, a single indicator, such as the error rate or AUC, is optimized, which has poor robustness for different application requirements. To solve such problems, a dual objective bounded abstaining (DOBA) model is proposed. DOBA optimizes the binary confusion matrix with rejection by minimizing the false positive and negative rates under class-specific reject constraints. The DOBA model is solved using an evolutionary multi-objective optimization algorithm. The requirement-oriented abstaining classifier can be selected from a set of Pareto-optimal solutions. Extensive experiments prove the effectiveness and superiority of DOBA compared to other abstaining models.

Order acceptance and scheduling with delivery under generalized parameters

AbstractInspired by the concept of generalized due dates introduced by Hall (IIE Transactions, 18(2), 220–222), in this article we first define four new generalized parameters in machine scheduling: the generalized release dates (GRD), generalized processing times (GPT), generalized rejection costs (GRC), and generalized delivery times (GDT). We then study order acceptance and scheduling problems with delivery consideration under the generalized parameters of GRD, GPT, GRC, and GDT, respectively. The objective of each scheduling problem in consideration is to minimize the maximum delivery completion time of the accepted jobs plus the total rejection penalty cost of the rejected jobs. We show that two of the six problems studied in this article are weakly NP‐hard while the other four ones can be solved in polynomial time. For each NP‐hard problem, we provide a pseudo‐polynomial time algorithm, a 2‐approximation algorithm and a fully polynomial‐time approximation scheme.

An iterated greedy algorithm for distributed flowshops with tardiness and rejection costs to maximize total profit

Distributed permutation flowshop scheduling problems (DPFSP) have become research hotspots. However, a DPFSP with tardiness and rejection costs (DPTR), which has important practical significance, has not yet been addressed. As manufacturers are most concerned about the maximization of the total profit, this study addresses the DPFSP to maximize the total profit. A mixed-integer linear programming model is used to describe the DPTR. An iterated greedy algorithm named IG_TR is proposed. IG_TR generates initial solutions using an improved NEH heuristic using four rules based on the deadline, due date, tardiness and rejection costs. For IG_TR, a dynamic number of jobs are removed from factories in the destruction phase. In the reconstruction phase, the removed jobs and those waiting to be processed are selected to be inserted into appropriate positions in the factories. Two local search methods are designed to improve the quality of solutions generated in the reconstruction phase. During the acceptance phase, a restart mechanism is proposed to avoid falling into local optimal. The experimental results of the component analysis demonstrate the effectiveness of IG_TR. Several comprehensive experiments show that IG_TR outperforms five related algorithms.

Single Machine Scheduling with Rejection and a Non-Availability Interval to Minimize the Maximum Delivery Completion Time Plus the Total Rejection Cost

In this paper, we consider the single machine scheduling with rejection and a nonavailability interval. Two types of non-availability intervals are studied, namely the machine non-availability (MNA) intervals and the operator non-availability (ONA) intervals. The objective is to minimize the sum of the maximum delivery completion time of accepted jobs and the total rejection cost of rejected jobs. For these two problems, a pseudo-polynomial-time dynamic programming algorithm and a fully polynomial-time approximation scheme (FPTAS) are proposed, respectively.

A common due-date assignment problem with job rejection on parallel uniform machines

We study a common due-date assignment problem on two parallel uniform machines. The jobs are assumed to have identical processing times, and job-dependent and asymmetric earliness and tardiness unit costs. The scheduler may process only a subset of the jobs, i.e. the option of job-rejection is allowed. The objective function consists of three cost components: the total earliness-tardiness cost of all scheduled jobs, the cost of the common due-date, and total rejection cost. For a given number of rejected jobs and a given due-date, the problem is reduced to a non-standard linear assignment problem. Consequently, the optimal solution is shown to be obtained in polynomial time in the number of jobs. The case of a given (possibly restrictive) due-date, the extension to a setting of more than two machines, and a number of special cases, are also discussed.

Scheduling on proportionate flow shop with job rejection and common due date assignment

We study proportionate flow shop scheduling problem allowing job rejection. The objective function is to minimize the earliness, tardiness, due date cost, and rejection cost. We consider the collaboration between the manufacturer and supplier. The common due date is measured in two-ways, which is only related to accepted jobs (total rejection case) or all jobs share a common due date (semi-rejection case). We show the relation between proportionate flow shop and single-machine problems, use the properties of single-machine to solve proportionate flow shop problems with job rejection, and propose the corresponding dynamic programming algorithm and algorithm complexity for the problems.

Effective league championship algorithm and lower bound procedure for scheduling a single batch-processing machine with non-identical job sizes and job rejection

We address the scheduling problem of a set of non-identical size jobs on a single batch-processing machine (SBPM) wherein the scheduler can make decision whether to schedule a job in batches or not to schedule it with a job-dependent penalty. The processing time of a batch is the greatest job processing time in that batch (parallel batching or p-batching). The scheduler wants to minimize a given objective function f, where f is the total rejection penalties of the rejected jobs (rejection cost) plus the makespan of the scheduled ones. We formulate the aforementioned problem as a 0–1 mixed integer programming model. We also apply an effective dynamic programming algorithm (DPA) to calculate a lower bound (LB) on the optimal cost of the problem. To tackle the problem, we propose a grouping algorithm, based on league championship algorithm (LCA), with new updating equations maintaining the major characteristics of the original updating equations of the LCA and well-suited to the structure of the problem. For small problems, performance of the proposed LCA is compared with GAMS/CPLEX solver. For large-scale instances, a genetic algorithm is adopted as a basis for comparison. Simulated experiments confirm the performance of the proposed methods.