Inverse scheduling: two machine flow shop problem

We study an inverse counterpart of the two-machine flow-shop scheduling problem that arises in the context of inverse optimization. While in the forward scheduling problem all parameters are given and the objective is to find job sequence(s) for which the value of the makespan is minimum, in the inverse scheduling the exact values of processing times are unknown and they should be selected within given boundaries so that pre-specified job sequence(s) become optimal. We derive necessary and sufficient conditions of optimality of a given solution for the general case of the flow-shop problem when the job sequences on the machines can be different. Based on these conditions we prove that the inverse flow-shop problem is NP-hard even in the case of the same job sequence on both machines and produce a linear programming formulation for a special case which can be solved efficientl

A polynomial-time algorithm for a flow-shop batching problem with equal-length operations

A flow-shop batching problem with consistent batches is considered in which the processing times of all jobs on each machine are equal to p and all batch set-up times are equal to s. In such a problem, one has to partition the set of jobs into batches and to schedule the batches on each machine. The processing time of a batch B i is the sum of processing times of operations in B i and the earliest start of B i on a machine is the finishing time of B i on the previous machine plus the set-up time s. Cheng et al. (Naval Research Logistics 47:128–144, 2000) provided an O(n) pseudopolynomial-time algorithm for solving the special case of the problem with two machines. Mosheiov and Oron (European Journal of Operational Research 161:285–291, 2005) developed an algorithm of the same time complexity for the general case with more than two machines. Ng and Kovalyov (Journal of Scheduling 10:353–364, 2007) improved the pseudopolynomial complexity to O(n √ ) . In this paper, we provide a polynomial-time algorithm of time complexity O(log 3 n)

Decomposition algorithms for submodular optimization with applications to parallel machine scheduling with controllable processing times

In this paper we present a decomposition algorithm for maximizing a linear function over a submodular polyhedron intersected with a box. Apart from this contribution to submodular optimization, our results extend the toolkit available in deterministic machine scheduling with controllable processing times. We demonstrate how this method can be applied to developing fast algorithms for minimizing total compression cost for preemptive schedules on parallel machines with respect to given release dates and a common deadline. Obtained scheduling algorithms are faster and easier to justify than those previously known in the scheduling literature

Scheduling divisible loads with time and cost constraints

In distributed computing, divisible load theory provides an important system model for allocation of data-intensive computations to processing units working in parallel. The main task is to define how a computation job should be split into parts, to which processors those parts should be allocated and in which sequence. The model is characterized by multiple parameters describing processor availability in time, transfer times of job parts to processors, their computation times and processor usage costs. The main criteria are usually the schedule length and cost minimization. In this paper, we provide the generalized formulation of the problem, combining key features of divisible load models studied in the literature, and prove its NP-hardness even for unrestricted processor availability windows. We formulate a linear program for the version of the problem with a fixed number of processors. For the case with an arbitrary number of processors, we close the gaps in the study of special cases, developing efficient algorithms for single criterion and bicriteria versions of the problem, when transfer times are negligible

Scheduling patient appointments via multilevel template: a case study in chemotherapy

This paper studies a multi-criteria optimization problem which appears in the context of booking chemotherapy appointments. The main feature of the model under study is the requirement to book for each patient multiple appointments which should follow a pre-specified multi-day pattern. Each appointment involves several nurse activities which should also follow a pre-specified intra-day pattern. The main objectives are to minimize patients’ waiting times and peaks of nurses’ workload for an outpatient clinic. Our solution approach is based on the concept of a multi-level template schedule which is generated for a set of artificial patients with typical treatment patterns. There are two stages in template generation: the multi-day stage, which fixes appointment dates for all artificial patients, and the intra-day stage, which fixes for each day appointment starting times and patient allocation to nurses. The running schedule is created by considering actual patients one by one as they arrive to the clinic. Booking appointments for each new patient is performed by assigning appropriate dates and times of the template schedule following the prescribed multi-day and intra-day patterns. Additional rescheduling procedure is used to re-optimize intra-day schedules on a treatment day or shortly beforehand. The key stages of the scheduling process are modeled as integer linear programs and solved using CPLEX solver. We demonstrate the effectiveness of our approach through case-based scenarios derived from a real clinic and discuss the advantages that the multi-level template can bring

Two-machine open shop problem with controllable processing times

2007-2008 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Scheduling bag-of-tasks applications to optimize computation time and cost

Bag-of-tasks applications consist of independent tasks that can be performed in parallel. Although such problems are well known in classical scheduling theory, the distinctive feature of Grid and cloud applications is the importance of the cost factor: in addition to the traditional scheduling criterion of minimizing computation time, in Grids and clouds it also important to minimize the cost of using resources. We study the structural properties of the time/cost model and explore how the existing scheduling techniques can be extended to handle the additional cost criterion. Due to the dynamic nature of distributed systems, one of the major requirements to scheduling algorithms is related to their speed. The heuristics we propose are fast and, as we show in our experiments, they compare favourably with the existing scheduling algorithms for distributed systems

Minimizing non-decreasing separable objective functions for the unit-time open shop scheduling problem

Note: Pre-published version entitled: Minimizing Nondecreasing separable objective functions for the unit-time open shop scheduling problem. Project Management and Scheduling.2004-2005 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe