Scheduling with earliness and tardiness penalties

We show that the deterministic nonpreemptive scheduling problem with earliness and tardiness penalties can be solved in polynomial time for certain forms of an objective function provided that a certain optimization problem can be solved. We give instances where this problem has a solution and show that this generalizes several results from the literature. These results do not require symmetric penalization and the penalty functions need only be lower semicontinuous.     

Minimizing mean tardiness and earliness in single-machine scheduling problems with unequal due dates

We consider a single-machine scheduling problem with the objective of minimizing the mean (or equivalently, total) tardiness and earliness when due dates may differ among jobs. Some properties of the optimal solution are discussed, and these properties are used to develop both optimal and heuristic algorithms. Results of computational tests indicate that optimal solutions can be found for problems with up to 20 jobs, and that two of the heuristic procedures provide optimal or very near optimal solutions in many instances. © 1994 John Wiley & Sons, Inc.     

Minimizing weighted earliness and tardiness penalties in single‐machine scheduling with idle time permitted

In this paper, a single‐machine scheduling problem with weighted earliness and tardiness penalties is considered. Idle time between two adjacent jobs is permitted and due dates of jobs could be unequal. The dominance rules are utilized to develop a relationship matrix, which allows a branch‐and‐bound algorithm to eliminate a high percentage of infeasible solutions. After combining this matrix with a branching strategy, a procedure to solve the problem is proposed. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 760–780, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10039     

A dual criteria sequencing problem with earliness and tardiness penalties

We consider the problem of sequencing n jobs on a single machine, with each job having a processing time and a common due date. The common due date is assumed to be so large that all jobs can complete by the due date. It is known that there is an O(n log n)‐time algorithm for finding a schedule with minimum total earliness and tardiness. In this article, we consider finding a schedule with dual criteria. The primary goal is to minimize the total earliness and tardiness. The secondary goals are to minimize: (1) the maximum earliness and tardiness; (2) the sum of the maximum of the squares of earliness and tardiness; (3) the sum of the squares of earliness and tardiness. For the first two criteria, we show that the problems are NP‐hard and we give a fully polynomial time approximation scheme for both of them. For the last two criteria, we show that the ratio of the worst schedule versus the best schedule is no more than . © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 422–431, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10020     

Heuristics for multimachine minmax scheduling problems with general earliness and tardiness costs

We consider the problem of scheduling N jobs on M parallel machines so as to minimize the maximum earliness or tardiness cost incurred for each of the jobs. Earliness and tardiness costs are given by general (but job-independent) functions of the amount of time a job is completed prior to or after a common due date. We show that in problems with a nonrestrictive due date, the problem decomposes into two parts. Each of the M longest jobs is assigned to a different machine, and all other jobs are assigned to the machines so as to minimize their makespan. With these assignments, the individual scheduling problems for each of the machines are simple to solve. We demonstrate that several simple heuristics of low complexity, based on this characterization, are asymptotically optimal under mild probabilistic conditions. We develop attractive worst-case bounds for them. We also develop a simple closed-form lower bound for the minimum cost value. The bound is asymptotically accurate under the same probabilistic conditions. In the case where the due date is restrictive, the problem is more complex only in the sense that the set of initial jobs on the machines is not easily characterized. However, we extend our heuristics and lower bounds to this general case as well. Numerical studies exhibit that these heuristics perform excellently even for small- or moderate-size problems both in the restrictive and nonrestrictive due-date case. © 1997 John Wiley & Sons, Inc.     

Minimizing absolute and squared deviations of completion times with different earliness and tardiness penalties and a common due date

We consider a single-machine scheduling problem in which all jobs have the same due date and penalties are assessed for both early and late completion of jobs. However, earliness and tardiness are penalized at different rates. The scheduling objective is to minimize either the weighted sum of absolute deviations (WSAD) or the weighted sum of squared deviations (WSSD). For each objective we consider two versions of the problem. In the unconstrained version an increase in the due date does not yield any further decrease in the objective function. We present a constructive algorithm for the unconstrained WSAD problem and show that this problem is equivalent to the two-parallel, nonidentical machine, mean flow-time problem. For the unconstrained WSSD and the constrained WSAD and WSSD problems we propose implicit enumeration procedures based on several dominance conditions. We also report on our computational experience with the enumeration procedures.     

A note on the single-machine scheduling problem with minimum weighted completion time and maximum allowable tardiness

This paper analyzes the Smith-heuristic for the single-machine scheduling problem where the objective is to minimize the total weighted completion time subject to the constraint that the tradiness for any job does not exceed a prespecified maximum allowable tardiness. We identify several cases of this problem for which the Smith-heuristic is guaranteed to lead to optimal solutions. We also provide a worst-case analysis of the Smith-heuristic; the analysis shows that the fractional increase in the objective function value for the Smith-heuristic from the optimal solution is unbounded in the worst case.     

Scheduling to minimize release-time resource consumption and tardiness penalties

We consider the problem of scheduling a set of jobs with a common due-date on a single-machine where the release time of a job is related to the amount of resource consumed. The objective is to minimize the total resource consumption and the total tardiness. While the problem is strongly NP-hard in general, we discuss two different special cases for which special properties are identified and used to develop efficient pseudo-polynomial time algorithms. © 1995 John Wiley & Sons, Inc.     

A single-machine scheduling problem with random processing times

We consider the problem of scheduling n jobs with random processing times on a single machine in order to minimize the expected variance of the completion times. We prove a number of results, including one to the effect that the optimal schedule must be V shaped when the jobs have identical means or variances or have exponential processing times.     

Minimizing the sum of absolute lateness in single-machine and multimachine scheduling

Kanet addressed the problem of scheduling n jobs on one machine so as to minimize the sum of absolute lateness under a restrictive assumption on their common due date. This article extends the results to the problem of scheduling n jobs on m parallel identical processors in order to minimize the sum of absolute lateness. Also, a heuristic algorithm for a more general version with no restriction on the common due date, for the problem of n-job single-machine scheduling is presented and its performance is reported.     

Simultaneous optimization of efficiency and performance balance measures in single-machine scheduling problems

Manufacturing and service organizations routinely face the challenge of scheduling jobs, orders, or individual customers in a schedule that optimizes either (i) an aggregate efficiency measure, (ii) a measure of performance balance, or (iii) some combination of these two objectives. We address these questions for single-machine job scheduling systems with fixed or controllable due dates. We show that a large class of such problems can be optimized by solving either a single instance or a finite sequence of instances of the so-called (SQC) problem, in which the sum of general quasiconvex functions of the jobs' completion times is to be minimized. To solve a single instance of (SQC), we develop an efficient, though pseudopolynomial algorithm, based on dynamic programming. The algorithm generates a solution that is optimal among all schedules whose starting time is restricted to the points of a prespecified (arbitrary) grid. The algorithm is embedded in an iterative procedure, where in each iteration a specific instance of (SQC) is solved. Special attention is given to the simultaneous minimization of the mean and variance of completion times. © 1993 John Wiley & Sons, Inc.     

Note: Bicriteria scheduling for minimizing flow time and maximum tardiness

We consider the bicriteria problem of minimizing total flow time and maximum tardiness penalties for a given set of jobs on a single machine. We develop an algorithm that finds the optimal schedule for any given monotonic function of the two criteria by generating only a small subset of the efficient schedules.     

Sequencing with setup time and order tardiness trade-offs

We consider the problem of scheduling customer orders on a single facility where each order consists of several jobs that can be clustered into several groups. When a facility is changed over to another group, a setup time associated with the new group is required. Two particular problems are considered in this context. One is to consider the total setup time and the number of tardy orders jointly. The other is to consider the total setup time and the maximum tardiness jointly. The total setup time in both problems represents a measure of internal efficiency, whereas the number of tardy orders and the maximum tardiness represent a measure of external efficiency. In any shop, the decision maker must consider the tradeoffs between large setup costs associated with a more frequent changeover schedule versus the cost of tardy orders that might be induced by a less-frequent changeover schedule. In this article branch-and-bound algorithms are proposed to identify the set of nondominated schedules for the two bicriteria problems. © 1996 John Wiley & Sons, Inc.     

Note: “Simultaneous optimization of efficiency and performance balance measures in single-machine scheduling problems”

n independent jobs are to be scheduled nonpreemptively on a single machine so as to minimize some performance measure. Federgruen and Mosheiov [2] show that a large class of such scheduling problems can be optimized by solving either a single instance or a finite sequence of instances of the so-called SQC problem, in which all the jobs have a fixed or controllable common due date and the sum of general quasiconvex functions of the job completion times is to be minimized. In this note we point out that this is not always true. In particular, we show that the algorithm proposed in [2] does not always find a global optimal schedule to the problem of minimizing the weighted sum of the mean and variance of job completion times. © 1996 John Wiley & Sons, Inc.     

On scheduling with ready-times,due-dates and vacations

A single machine sequencing problem is considered in which there are ready-time and due-date constraints on jobs and vacation constraints on the machine. Each vacation has fixed starting and finish time and no preemption is allowed for the jobs. The objective is to minimize maximum lateness. An intriguing feature of this formulation is that it allows sequencing in disconnected time windows. A relaxation of the problem is obtained by modeling the vacations as a set of jobs with flexible ready-times and artificial due-dates and a branch and bound algorithm is developed for the problem. In the algorithm, the search is not only guided by the bounds but also by a careful manipulation of the artificial due-dates. Consequently; while searching in the relaxed solution space, solutions of the original problem are implicitly enumerated. Computational results indicate that the algorithm can satisfactorily solve problems with multiple vacations.     

Single-machine scheduling with early and tardy completion costs

We address a single-machine scheduling problem in which penalties are assigned for early and tardy completion of jobs. These penalties are common in industrial settings where early job completion can cause the cash commitment to resources in a time frame earlier than needed, giving rise to early completion penalties. Tardiness penalties arise from a variety of sources, such as loss of customer goodwill, opportunity costs of lost sales, and direct cash penalties. Accounting for earliness cost makes the performance measure nonregular, and this nonregularity has apparently discouraged researchers from seeking solutions to this problem. We found that it is not much more difficult to design an enumerative search for this problem than it would be if the performance measure were regular. We present and demonstrate an efficient timetabling procedure which can be embedded in an enumerative algorithm allowing the search to be conducted over the domain of job permutations.© 1993 John Wiley & Sons, Inc.     

Dynamic scheduling in single-server multiclass service systems with unit buffers

The problem of optimal dynamic sequencing for a single-server multiclass service system with only unit storage (buffer) space at each queue is considered. The model is applicable to many computer operating and telecommunicating systems (e.g., polling systems). Index policies to minimize costs for the special case of symmetric arrival rates are derived. Simulations suggest that using these indices provides a substantial improvement over cyclic schedules.     

Single-machine scheduling with dynamic arrivals: Decomposition results and an improved algorithm

This article considers the single-machine dynamic scheduling problem where the jobs have different arrival times and the objective is to minimize the sum of completion times. This problem is known to be strongly NP-hard. We develop decomposition results for this problem such that a large problem can be solved by combining optimal solutions for several smaller problems. The decomposition results can be used with any implicit enumeration method to develop an optimal algorithm. Our computational experiment indicates that the computational efficiency of the currently best available branch-and-bound algorithm can be improved with the use of our decomposition results. © 1996 John Wiley & Sons, Inc.     

One- and two-stage scheduling of two products with distributed inserted idle time: The benefits of a controllable production rate

Consider the problem of scheduling two products on a single machine or through two machines in series when demand is constant and there is a changeover cost between runs of different products on the same machine. As well as setting batch sizes, it is assumed that the production scheduler can choose the production rate for each product, provided an upper bound is not exceeded. This is equivalent to permitting distributed inserted idle time over the production run. It is shown that characteristic of the optimum schedule is that there is no idle time concentrated between runs; it is all distributed over the run. If the inventory charge is based on average inventory then one product is always produced at maximum rate on the bottleneck stage; however, if there is an inventory constraint based on maximum inventory then in the single-stage case it can occur that neither product is produced at maximum rate.