On bilevel machine scheduling problems

Bilevel scheduling problems constitute a hardly studied area of scheduling theory. In this paper, we summarise the basic concepts of bilevel optimisation, and discuss two problem classes for which we establish various complexity and algorithmic results. The first one is the bilevel total weighted completion time problem in which the leader assigns the jobs to parallel machines and the follower sequences the jobs assigned to each machine. Both the leader and the follower aims to minimise the total weighted completion time objective, but with different job weights. When the leader’s weights are arbitrary, the problem is NP-hard. However, when all the jobs are of unit weight for the leader, we provide a heuristic algorithm based on iterative LP-rounding along with computational results, and provide a sufficient condition when the LP-solution is integral. In addition, if the follower weights induce a monotone (increasing or decreasing) processing time order in any optimal solution, the problem becomes polynomially solvable. As a by-product, we characterise a new polynomially solvable special case of the MAX m-CUT problem, and provide a new linear programming formulation for the P||?_j C_j{P||\sum_j C_j} problem. Finally, we present some results on the bilevel order acceptance problem, where the leader decides on the acceptance of orders and the follower sequences the jobs. Each job has a deadline and if a job is accepted, it cannot be late. The leader’s objective is to maximise the total weight of accepted jobs, whereas the follower aims at minimising the total weighted job completion times. For this problem, we generalise some known single-level machine scheduling algorithms.     

Robust scheduling of a two-stage hybrid flow shop with uncertain interval processing times

This paper studies the makespan minimisation scheduling problem in a two-stage hybrid flow shop. The first stage has one machine and the second stage has m identical parallel machines. Neither the processing time nor probability distribution of the processing time of each job is uncertain. We propose a robust (min–max regret) scheduling model. To solve the robust scheduling problem, which is NP-hard, we first derive some properties of the worst-case scenario for a given schedule. We then propose both exact and heuristic algorithms to solve this problem. In addition, computational experiments are conducted to evaluate the performance of the proposed algorithms.     

A computational study of heuristics for two-stage flexible flowshops

We consider the scheduling of two-stage flexible flowshops. This manufacturing environment involves two machine centres representing two consecutive stages of production. Each machine centre is composed of multiple parallel machines. Each job has to be processed serially through the two machine centres. In each machine centre, a job may be processed on any of the machines. There are n independent jobs to be scheduled without preemption. The jobs can wait in between the two machine centres and the intermediate storage is unlimited. Our objective will be to minimize the maximum completion time of the jobs. We formulate the problem as a mixed integer program. Given this problem class is NP-hard in the strong sense, we present three lower bounds to estimate the optimal solution. We then propose a sequence-first, allocate-second heuristic approach for its solution. We heuristically decompose the problem by first creating a priority list to order the jobs and then assign the jobs to the available machines in each machine centre based on this order. We describe seven rules for the sequencing phase. The assignment phase consists of a heuristic which attempts to minimize each partial schedule length while looking ahead at the future assignment of the currently unscheduled jobs. The computational performance of the heuristic approach was evaluated by comparing the value of each heuristic variant to the best among the three lower bounds. Its effectiveness was tested on scenarios pertinent to flexible flowshop environments, such as cellular manufacturing, by conducting a computational study of over 3400 problems. Our computational results indicate that the most effective approach used Johnson's rule to provide the priority list for job assignment. This provided integrality gaps which on the average were less than 0·73%.     

A polynomial algorithm for the two machine job-shop scheduling problem with a fixed number of jobs

It is shown that the job-shop problem with two machines and a fixed number ofk jobs with makespan criterionJ2¦n=k¦C ^max is polynomially solvable. Sotskov and Shakhlevich (1993) have shown that problemJ3¦n=3¦C _maxisNP-hard. Furthermore it is well known that J¦n=2¦C _maxin polynomially solvable. Thus, our result settles the remaining open question concerning the complexity status of job-shop problems with fixed numbers of jobs and machines.Supported by Deutsche Forschungsgemeinschaft, Project Jop-TAG     

Collaborative reinforcement learning for a two-robot job transfer flow-shop scheduling problem

A two-robot flow-shop scheduling problem with n identical jobs and m machines is defined and evaluated for four robot collaboration levels corresponding to different levels of information sharing, learning and assessment: Full – robots work together, performing self and joint learning sharing full information; Pull – one robot decides when and if to learn from the other robot; Push – one robot may force the second to learn from it and None – each robot learns independently with no information sharing. Robots operate on parallel tracks, transporting jobs between successive machines, returning empty to a machine to move another job. The objective is to obtain a robot schedule that minimises makespan (C_max) for machines with varying processing times. A new reinforcement learning algorithm is developed, using dual Q-learning functions. A novel feature in the collaborative algorithm is the assignment of different reward functions to robots; minimising robot idle time and minimising job waiting time. Such delays increase makespan. Simulation analyses with fast, medium and slow speed robots indicated that Full collaboration with a fast–fast robot pair was best according to minimum average upper bound error. The new collaborative algorithm provides a tool for finding optimal and near-optimal solutions to difficult collaborative multi-robot scheduling problems.     

Comparative Bioavailability Study of a Generic Naltrexone Tablet Preparation

The bioavailability of a generic preparation of naltrexone (Narpan) was compared with the innovator product, Trexan. Twelve healthy volunteers participated in the study, conducted according to a completely randomized, two-way crossover design. The preparations were compared using the parameters area under the plasma concentration–time curve AUC_0–∞, peak plasma concentration C_max, and time to reach peak plasma concentration T_max. No statistically significant difference was observed between the logarithmic transformed AUC_0–∞ and the logarithmically transformed C_max values of the two preparations. Also, no statistically significant difference was observed between the untransformed T_max values. In addition, the 90% confidence interval for the ratio of the logarithmic transformed AUC_0–∞ values of Narpan over those of Trexan was found to lie between 0.87 and 1.01, while that of the logarithmic transformed C_max values was between 0.94 and 1.23, both being within the bioequivalence limit of 0.80–1.25. The numerical values of the elimination half-life (t_1/2) obtained with the two preparations were also not significantly different and were comparable to those reported in the literature.     

A genetic algorithm for the multi-stage and parallel-machine scheduling problem with job splitting – A case study for the solar cell industry

This paper studies a multi-stage and parallel-machine scheduling problem with job splitting which is similar to the traditional hybrid flow shop scheduling (HFS) in the solar cell industry. The HFS has one common hypothesis, one job on one machine, among the research. Under the hypothesis, one order cannot be executed by numerous machines simultaneously. Therefore, multiprocessor task scheduling has been advocated by scholars. The machine allocation of each order should be scheduled in advance and then the optimal multiprocessor task scheduling in each stage is determined. However, machine allocation and production sequence decisions are highly interactive. As a result, this study, motivated from the solar cell industry, is going to explore these issues. The multi-stage and parallel-machine scheduling problem with job splitting simultaneously determines the optimal production sequence, multiprocessor task scheduling and machine configurations through dynamically splitting a job into several sublots to be processed on multiple machines. We formulate this problem as a mixed integer linear programming model considering practical characteristics and constraints. A hybrid-coded genetic algorithm is developed to find a near-optimal solution. A preliminary computational study indicates that the developed algorithm not only provides good quality solutions but outperforms the classic branch and bound method and the current heuristic in practice.     

Evaluation of Bioequivalence of Two Formulations Containing 100 Milligrams of Aceclofenac

ABSTRACT

The bioequivalence of two oral formulations containing aceclofenac 100 mg was determined in 24 healthy Indian male volunteers. The study was designed as a single dose, fasting, two-period two-sequence crossover study with a washout period of 1 week. The content of aceclofenac in plasma was determined by a validated HPLC method with UV detection. The preparations were compared using the parameters area under the plasma concentration–time curve (AUC_0–t), area under the plasma concentration–time curve from zero to infinity (AUC_0–∞), peak plasma concentration (C_max), and time to reach peak plasma concentration (t_max). No statistically significant difference was observed between the logarithmic transformed AUC_0–∞ and C_max values of the two preparations. The 90% confidence interval for the ratio of the logarithmic transformed AUC_0–t, AUC_0–∞, and C_max were within the bioequivalence limit of 0.80–1.25.     

Re-entrant flow shop scheduling problem with time windows using hybrid genetic algorithm based on auto-tuning strategy

The re-entrant flow shop scheduling problem considering time windows constraint is one of the most important problems in hard-disc drive (HDD) manufacturing systems. In order to maximise the system throughput, the problem of minimising the makespan with zero loss is considered. In this paper, evolutionary techniques are proposed to solve the complex re-entrant scheduling problem with time windows constraint in manufacturing HDD devices with lot size. This problem can be formulated as a deterministic Fm?|?fmls, rcrc, temp?|?C_max problem. A hybrid genetic algorithm was used for constructing chromosomes by checking and repairing time window constraints, and improving chromosomes by a left-shift heuristic as a local search algorithm. An adaptive hybrid genetic algorithm was eventually developed to solve this problem by using fuzzy logic control in order to enhance the search ability of the genetic algorithm. Finally, numerical experiments were carried out to demonstrate the efficiency of the developed approaches.     

Relating In Vitro/In Vivo Data of Two Controlled-Release Metformin Formulations

This study was conducted to compare the bioavailability of two controlled-release metformin preparations (Diabetmin Retard and Glucophage Retard) and also to correlate the in vitro and in vivo data obtained with the two preparations. Twelve healthy volunteers participated in the study, conducted according to a completely randomized, two-way crossover design. The preparations were compared using area under the plasma concentration–time curve AUC_0?∞, time to reach peak plasma concentration T_max, and peak plasma concentration C_max, while correlation was determined between in vitro release and in vivo absorption. Diabetmin Retard demonstrated a slower rate of in vitro release, but a faster rate of in vivo absorption than Glucophage Retard. However, the in vivo absorption of both products was found to be slower than that of drug released in vitro. A satisfactory relationship could be established between the in vitro and in vivo results, but there was no rank order correlation. No statistically significant difference was observed between the two preparations in the parameters AUC_0?∞ and C_max. However, a slight but statistically significant difference was observed between the T_max values, but it may not be therapeutically significant. Moreover, the 90% confidence interval for the ratio of the logarithmic transformed AUC_0?∞ values, as well as the logarithmic transformed C_max values, of Diabetmin Retard over those of Glucophage Retard was within the acceptance criteria of 0.80–1.25.     

Prediction of area under the curve for a p-glycoprotein,a CYP3A4 and a CYP2C9 substrate using a single time point strategy: assessment using fexofenadine,itraconazole and losartan and metabolites

Abstract

Background: In the present age of polypharmacy, limited sampling strategy becomes important to verify if drug levels are within the prescribed threshold limits from efficacy and safety considerations. The need to establish reliable single time concentration dependent models to predict exposure becomes important from cost and time perspectives.

Methods: A simple unweighted linear regression model was developed to describe the relationship between C_max versus AUC for fexofenadine, losartan, EXP3174, itraconazole and hydroxyitraconazole. The fold difference, defined as the quotient of the observed and predicted AUC values, were evaluated along with statistical comparison of the predicted versus observed values.

Results: The correlation between C_max versus AUC was well established for all the five drugs with a correlation coefficient (r) ranging from 0.9130 to 0.9997. Majority of the predicted values for all the five drugs (77%) were contained within a narrow boundary of 0.75- to 1.5-fold difference. The r values for observed versus predicted AUC were 0.9653 (n?=?145), 0.8342 (n?=?76), 0.9524 (n?=?88), 0.9339 (n?=?89) and 0.9452 (n?=?66) for fexofenadine, losartan, EXP3174, itraconazole and hydroxyitraconazole, respectively.

Conclusions: C_max versus AUC relationships were established for all drugs and were amenable for limited sampling strategy for AUC prediction. However, fexofenadine, EXP3174 and hydroxyitraconazole may be most relevant for AUC prediction by a single time concentration as judged by the various criteria applied in this study.     

Exact and approximate methods for parallel multiple-area spatial scheduling with release times

Spatial scheduling problems involve scheduling jobs that each require certain amounts of two-dimensional space within a processing area of limited width and length. Thus, this requires not only assigning time slots to each job but also locations and orientations within the limited physical processing space as well. Such problems, often encountered in shipbuilding and aircraft manufacturing, are generally difficult to solve, and there is a relatively small amount of literature addressing these problems compared to other types of scheduling. In this paper, we consider a particularly complex class of spatial scheduling problems that involve scheduling each job into one of several possible processing areas in parallel to minimize the total amount of tardy time. In addition, each job has a release time before which it may not be processed. We introduce two methods for solving this type of problem: an integer programming (IP) model and a heuristic algorithm. We perform computational tests and comparisons of each method over a large number of generated benchmark problems with varying characteristics, and also compare these to a more naïve heuristic. Solving the IP model was effective for small problems but required excessive amounts of time for larger ones. The heuristic was effective and produced solutions of comparable quality to the IP model for many problems while requiring very little computational time.     

ABC β–a heuristic for dynamic capacitated lot sizing with random demand under a fill rate constraint

This paper deals with the dynamic multi-item capacitated lot-sizing problem (CLSP) with random demand over a finite discrete time horizon. Unfilled demands are backordered. It is assumed that a fill rate constraint is in effect. We propose a heuristic solution procedure called ABC _β that extends the A/B/C heuristic introduced by Maes and Van Wassenhove for the deterministic CLSP to the case of random demands.     

Steady-State Pharmacokinetics of a Multiparticulate Matrix Sustained-Release Theophylline Preparation

Abstract

A novel multiparticulate matrix sustained-release theophylline preparation was evaluated in comparison with a reference product, Neulin-SR®, in a multiple-dose administration study, conducted according to a randomized, two-way crossover design involving 12 healthy volunteers. Comparison was made using the parameters, area under the serum concentration-time curve from time 0 to 12 hr (AUC_0-12), time to reach peak serum concentration (T_max), peak serum concentration (C_max), trough serum concentration (C_min), average drug concentration (C_av), degree of fluctuation (DF), percentage of time serum drug concentrations lie within the therapeutic range (occupancy time) and time for 50% of dose absorbed (T_50%). The parameters, C_max, C_min, AUC_0-12 C_av, and DF were logarithmic transformed prior to statistical analysis. A statistically significant difference was obtained between the values of the two preparations in the T_max, C_min, DF, and T_50%; but not in the C_max, AUC_0-12, C_av, and occupancy time. These findings suggest that the novel preparation has a more sustained rate but equivalent extent of absorption compared to Neulin-SR, leading to a more uniform steady-state serum profile.     

Bioequivalence Evaluation of Two Formulations of Doxazosin Tablet in Healthy Thai Male Volunteers

ABSTRACT

The bioequivalence of two doxazosin 2 mg tablets was determined in 24 healthy Thai male volunteers after one single dose in a randomized cross-over study with a one week washout period. The study was conducted at Faculty of Pharmaceutical Sciences and Health Sciences Research Institute, Naresuan University, Phitsanulok, Thailand. Reference (Cardura®, Heinrich Mack Nachf. GmbH & Co. GK, Illertissen, Germany) and test (Dozozin-2®, Umeda Co., Ltd., Bangkok Thailand) were administered to volunteers after overnight fasting. Blood samples were collected at specified time intervals and plasma was separated. The validated HPLC method with fluorescence detection was used for quantification of doxazosin in plasma samples. The pharmacokinetic parameters, T_max, C_max, AUC_t, AUC_∞, T_1/2, λ_z, Cl and V_d, were determined from plasma concentration time profile of both formulations by using non-compartment analysis. The calculated pharmacokinetic parameters were compared statistically to evaluate bioequivalence between the two brands. The analysis of variance (ANOVA) using log-transformed C_max, AUC_t, and AUC_∞ did not show any significant difference between two formulations. The point estimates and 90% confidence intervals for C_max, AUC_t and AUC_∞ were within the acceptance range (0.80–1.25), satisfying the bioequivalence criteria of the Thailand Food and Drug Administration Guidelines. These results indicate that Dozozin-2® is bioequivalent to Cardura® and, thus, may be prescribed interchangeably.     

Minimising interference for scheduling two parallel machines with a single server

In this paper, we consider the problem of scheduling a set of jobs on two parallel machines with set-up times. The set-up has to be performed by a single server. The objective is to minimise the forced idle time. The problem of minimising the forced idle time (interference problem) is known to be unary NP-hard for the case of two machines and equal set-up and arbitrary processing times. We propose a mixed integer linear programming model, which describes a special class of schedules where the jobs from a list are scheduled alternatively on the machines, and a heuristic algorithm is tested on instances with up to 100,000 jobs. The computational results indicate that the algorithm has an excellent performance even for very large instances, where mostly an optimal solution is obtained within a very small computational time.     

Transient inter-production scheduling based on Petri nets and constraint programming

In this article, we focus on the transient inter-production scheduling problem between two cyclic productions in the framework of flexible manufacturing systems. This problem is first formulated as a reachability problem in timed Petri nets (TPN), then solved using a methodology based on constraint programming. Our work is based on the controlled executions proposed by Chretienne to model the sequence of transition firing dates. Our methodology is based on a preliminary resolution of the state equation between initial and final states in the underlying non-TPN. Then, we choose a duration T _max corresponding to the maximal duration time of the scheduling. For each solution S of the state equation, we build a controlled execution from the sequence of firings in S. After the propagation of firing date constraints and reachability constraints in the TPN, we use constraint programming to enumerate the set of feasible controlled executions.     

Comparison of pharmacokinetics in beagle dogs of nimesulide bilayer tablets with dispersible tablets

The purpose of this study was to compare the in vitro release and the in vivo pharmacokinetics of bilayer tablets with the conventional dispersible tablets of nimesulide. The tablets were administered to beagle dogs and the plasma levels of nimesulide were determined by high-performance liquid chromatography-MS/MS. The pharmacokinetic parameters were calculated using a noncompartmental model. The bilayer tablets showed a biphasic in vitro release pattern with initial burst release and sustained release following the quasi-Fickian diffusion-based release mechanism. The C_max, t_max, mean residence time (MRT), and area under the curve from 0 to 36 h were 10.8 ± 4.2 μg/mL, 2.3 ± 1.0 h, 6.7 ± 2.1 h, 81.5 ± 26.7 μg·h/mL for the bilayer tablets and 14.8 ± 5.8 μg/mL, 2.7 ± 0.8 h, 5.6 ± 0.9 h, 95.4 ± 44.2 μg·h/mL for the dispersible tablets. Compared with the dispersible tablets, the bilayer tablets have lower C_max, similar t_max, and longer MRT. The aforementioned pharmacokinetic parameters, especially the MRT demonstrated to be valuable for evaluating the biphasic characteristics. This study provides a promising in vivo evaluation method for the bilayer tablets with biphasic release pattern.     

Cyclic scheduling heuristics for a re-entrant job shop manufacturing environment

Two efficient cyclic scheduling heuristics for re-entrant job shop environments were developed. Each heuristic generated an efficient and feasible cyclic production schedule for a job shop in which a single product was produced repetitively on a set of machines was to determine an efficient and feasible cyclic schedule which simultaneously minimized flow time and cycle time. The first heuristic considered a repetitive production re-entrant job shop with a predetermined sequence of operations on a single product with known processing times, set-up and material handling times. The second heuristic was a specialization of the first heuristic where the set-up for an operation could commence even while the preceding operation was in progress. These heuristics have been extensively tested and computational results are provided. Also, extensive analysis of worst-case and trade-offs between cycle time and flow time are provided. The results indicate that the proposed heuristics are robust and yield efficient and superior cyclic schedules with modest computational effort.     

A linear programming approach to capacity estimation of automated production lines with finite buffers

This paper considers a highly automated manufacturing line which consists of a sequence of workstations. Relatively small buffers are assigned between workstations in order to guarantee a small manufacturing interval and quick feedback in the event of process failure to make acceptable product. These small buffers could lead to a noticeable loss of line capacity due to the phenomenon of blocking and starvation. We show by means of simple examples how the buffer sizes and the mix and loading sequence of different types of jobs could significantly affect the production rate of the line. A linear programming based method is then developed to estimate the line capacity for a given configuration of machines and buffers sizes and for a given job mix and sequence. This method also gives the expected machine utilizations, the time machines are blocked/starved and, more importantly, the reason for this lost production capacity. By judiciously interpreting this information, one or more of the following steps can be taken to improve the production rate: (a) change the loading sequence, (b) increase the buffer space selectively, (c) make the products in smaller or larger batches, and (d) add new machines.