A note on the “value” of bounds on EVPI in stochastic programming

The existing literature concentrates on determining sharp upper bounds for EVPI in stochastic programming problems. This seems to be a problem without an application. Lower bounds, which we view as having an important application, are only the incidental subject of study and in the few instances that are available are obtained at an extremely high cost. In order to suggest a rethinking of the course of this research, we analyze the need for bounds on EVPI in the context of its significance in decision problems.     

Scheduling workers in a constricted area

A generalization of the equi-partitioning problem, termed the 2D-Partition Problem, is formulated. The motivation is an aircraft maintenance scheduling problem with the following characteristics. The complete maintenance overhaul of a single aircraft requires the completion of some 350 tasks. These tasks require a varying number of technicians working at the same time. For large subsets of these 350 tasks, the constraining resource is physical space—tasks must be completed in a physical space of limited size such as the cockpit. Furthermore, there is no precedence relationship among the tasks. For each subset, the problem is to schedule the tasks to minimize makespan. Let m denote the maximum number of technicians that can work at the same time in the physical area under consideration. We present optimization algorithms for m = 2 and 3. © 1996 John Wiley & Sons, Inc.     

Scheduling on a single machine with a single breakdown to minimize stochastically the number of tardy jobs

Jobs with known processing times and due dates have to be processed on a machine which is subject to a single breakdown. The moment of breakdown and the repair time are independent random variables. Two cases are distinguished with reference to the processing time preempted by the breakdown (no other preemptions are allowed): (i) resumption without time losses and (ii) restart from the beginning. Under certain compatible conditions, we find the policies which minimize stochastically the number of tardy jobs.     

A proof for the longest-job-first policy in one-machine scheduling

We consider a one-machine scheduling problem with earliness and tardiness penalties. All jobs are assigned a common due date and the objective is to minimize the total penalty due to job earliness and tardiness. We are interested in finding the optimal combination of the common due-date value and the job sequence. Despite the fact that this problem in general is very hard to solve, we prove that there exists at least a common property for all optimal solutions: The first job in an optimal sequence is one of the longest jobs. We also prove that this property holds for a general class of unimodal penalty functions.     

Discount pricing policies for inventories subject to declining demand

Until only recently, the mechanism behind determining item price has been ignored and the discount price taken as a given in quantity-discount inventory decision problems. Inventory subject to declining demand further complicates both pricing and replenishment decisions. This article provides the vendor with the means for optimally determining both the discount price and replenishment order frequency for all buyers in the system in an environment of declining demand. In the multiple-buyer case, we provide an efficient algorithm for classifying buyers into homogeneous subgroups to further enhance joint cost savings among all system participants.     

Fire truck relocation during major incidents

The effectiveness of a fire department is largely determined by its ability to respond to incidents in a timely manner. To do so, fire departments typically have fire stations spread evenly across the region, and dispatch the closest truck(s) whenever a new incident occurs. However, large gaps in coverage may arise in the case of a major incident that requires many nearby fire trucks over a long period of time, substantially increasing response times for emergencies that occur subsequently. We propose a heuristic for relocating idle trucks during a major incident in order to retain good coverage. This is done by solving a mathematical program that takes into account the location of the available fire trucks and the historic spatial distribution of incidents. This heuristic allows the user to balance the coverage and the number of truck movements. Using extensive simulation experiments we test the heuristic for the operations of the Fire Department of Amsterdam‐Amstelland, and compare it against three other benchmark strategies in a simulation fitted using 10 years of historical data. We demonstrate substantial improvement over the current relocation policy, and show that not relocating during major incidents may lead to a significant decrease in performance.     

Single‐machine scheduling with deadlines to minimize the total weighted late work

We consider scheduling a set of jobs with deadlines to minimize the total weighted late work on a single machine, where the late work of a job is the amount of processing of the job that is scheduled after its due date and before its deadline. This is the first study on scheduling with the late work criterion under the deadline restriction. In this paper, we show that (i) the problem is unary NP‐hard even if all the jobs have a unit weight, (ii) the problem is binary NP‐hard and admits a pseudo‐polynomial‐time algorithm and a fully polynomial‐time approximation scheme if all the jobs have a common due date, and (iii) some special cases of the problem are polynomially solvable.