Johnson's approximate method for the 3 × n job shop problem

The effectiveness of Johnson's Approximate Method (JAM) for the 3 × n job shop scheduling problems was examined on 1,500 test cases with n ranging from 6 to 50 and with the processing times A_i, B_i, C_i (for item i on machines A, B, C) being uniformly and normally distributed. JAM proved to be quite effective for the case B_i ? max (A_i, C_i) and optimal for B_i, ? min (A_i, C_i).     

Elimination methods in the m × n sequencing problem

This paper considers elimination methods in solving the sequencing problem where no passing is permitted. An elimination method consists of reducing (according to some criterion) the initial set of n solutions to a smaller set. A crucial question arises as to whether this reduced set contains an optimal solution. The answer is affirmative if this elimination criterion implies condition (3).     

Permutation flow-shop theory revisited

The paper provides a new theoretical framework for generating dominance conditions and lower bounds and for solving special cases. All existing and new results have been derived in a routine and simple manner.     

Transshipment along a single road

This article explores the problem of the transshipment of goods between centers that are situated along a single road. Costs are incurred both for goods that are shipped and for goods that remain in their original centers. A procedure is developed that determines a partial optimal assignment by use of a northwest corner rule solution. This partial assignment then is completed by solving a number of smaller tridiagonal transportation problems.     

Adjacent orderings in single-machine scheduling with earliness and tardiness penalties

This article deals with a single-machine n job earliness-tardiness model with job-independent penalties. It demonstrates that the arrangement of adjacent jobs in an optimal schedule depends on a critical value of the start times. Based on these precedence relations, the article develops criteria under which the problem can be decomposed into smaller subproblems. The branching scheme that used the developed results was tested on 70 examples of size n = 10. This scheme should be incorporated in any branch-and-bound method once a lower bound is found. The branching scheme can easily handle small problems without a lower bound. © 1993 John Wiley & Sons, Inc.     

The transportation paradox

A paradox arises when a transportation problem admits to a total cost solution which is lower than the optimum and is attainable by shipping larger quantities of goods over the same routes that were previously designated as optimal. That is, falling total costs are present in moving to the greater shipment quantities. Necessary conditions for this to occur are established and an algorithm for solving this expanded transportation problem is supplied.     

Optimal timing schedules in earliness-tardiness single machine sequencing

The article deals with a single machine earliness-tardiness scheduling model where idle times are permitted in job processing. Based on a cluster concept we develop properties of the model that lead to a very fast algorithm to find an optimal timing schedule for a given sequence of jobs. The performance of this algorithm is tested on 480 randomly generated problems involving 100, 200, 400 and 500 jobs. It takes less than two seconds to solve a 500 job problem on a PC. © 1995 John Wiley & Sons, Inc.     

Instant transportation solutions

This paper presents direct noniterative methods for solving such known problems as shoploading and aggregate scheduling. There is given a simple optimal rule for the shop-loading problem which is quite surprising. The crucial point in solving this problem is what not to assign rather than what to assign. The development of those methods was possible since the discussed problems can be converted into a special transportation model where the given cost coefficients c_ij assume a form cij = ui + uj.