Article

Scheduling training for a tank battalion: How to measure readiness

Authors:
To read the full-text of this research, you can request a copy directly from the authors.

Abstract

This paper shows how to measure the readiness for a military unit, with the example of a tank battalion. We first show that training readiness can be measured by the minimum makespan of the training schedule. We call this the train-up problem. Second, the effect of a peacetime budget on the training readiness can be calculated by solving the readiness budget problem. Third, the resources required for training can be determined with the readiness capacity problem. To solve these problems, we give a dynamic program (DP) for one unit such as a company, and a column generation algorithm for an aggregate unit such as a battalion.

No full-text available

Request Full-text Paper PDF

To read the full-text of this research,
you can request a copy directly from the authors.

... I have given the volume numbers as follows: the published year is the issue number. (b) References [7] and [14] read "to appear" -have any of them been published in the meanwhile, so that we could update the information? [7] is published and is given below. ...
Article
Full-text available
In this paper, we develop two novel pricing methods for solving an integer program. We demonstrate the methods by solving an integrated commercial fishery planning model (IFPM). In this problem, a fishery manager must schedule fishing trawlers (determine when and where the trawlers should go fishing, and when the trawlers should return the caught fish to the factory). The manager must then decide how to process the fish into products at the factory. The objective is to maximise profit. The problem may be modelled as a single integer program, with both the trawler scheduling and production planning parts integrated. Inventory constraints connect the two parts of the problem. Production planning alone would result in an easy linear program, but due to the trawler scheduling aspect, the IFPM is a hard integer program in the sense that traditional solution methods result in computation times that are far too long to be practical. The two pricing methods developed in this paper are a decomposition-based O'Neill pricing method and a reduced cost-based pricing method. We demonstrate the methods by means of numerical examples for different planning horizons, corresponding to differently sized problems.
... Although not explicitly applied to equipment readiness, optimization has been applied to training readiness for an Army tank battalion [10] and a Navy "Prowler" ...
Article
The U.S. Army has undergone unprecedented change in the last decade, completing an organizational transformation and redesigning its deployment policies. These changes and other factors have resulted in an increase of 107% in equipping requirements between 2003 and 2011, forcing the Army to update its equipping policies. We develop the multi-period optimal readiness allocation model (MPORAM) to maximize unit equipment readiness across the force over several years. MPORAM extends an earlier single-period model to account for the dynamic nature of unit priorities, budget, and other factors that vary over the planning horizon. Using a small test case, we observe that MPORAM distributes and/or transfers equipment in anticipation of future demand needs. For example, if one unit cannot improve its readiness in one time period, MPORAM focuses on improving other units ratings, if possible, regardless of their priorities. Using two realistically-sized cases, we observe that the multi-period solution does not differ notably from the single-period solution. Thus, we cannot make any strong conclusions about the added value of MPORAM in these cases. However, these results are strongly influenced by a large gap between supply and demand, and we expect MPORAM to improve the single-period solution in more balanced cases.
... used DBP in a column generation and branch-and-bound method for cutting stock problem for the general integer variables, not restricted to be binary.Raffensperger and Schrage (2006) used DBP with a scheduling model for a tank battalion. We apply DBP for solving our mixed integer IFPM. In DBP, the subproblems are identical to the subproblems of DWD, but the DWD master is replaced by a version of the original problem with all of the original rows and a subset of original columns, termed the restricted master. As with ...
Article
Full-text available
A quota-based integrated commercial fishery owns fishing trawlers, processing plants, and fish quotas. Such a fishery must decide how to schedule trawlers for fishing and landing, how to schedule processing of products, how to schedule labour for processing, and how to plan inventory of raw materials and products. This problem is of great economic significance to New Zealand, whose economy depends to a large extent on the fishery industry. To assist the fishery manager, we develop a mixed integer linear program (MILP) for optimal scheduling of fishing trawlers, production planning (processing) and labour allocation for a quota-based integrated fishery of New Zealand. The model decides when and where each trawler should go for fishing, how much fish each trawler should land, and how much product to produce in each period. Since the fishery is a private farm, its main objective will be profit maximization (or cost minimization if its demand is on contract). The government manages the conservation of fish through the quota allocation. In this thesis the objective of the fishery model is to maximise the total profit. We demonstrate our model with examples based on data from a major New Zealand fishery. We investigate ways to manage the uncertainties involved in trawler scheduling and production planning of the fishery. To manage end-of-planning-horizon effects in the fishery, we develop a simple safety stock approach. We also analyse the workability of a rolling horizon approach to solve the longer planning horizon models and to deal with the end-of-planning horizon effects. We investigate the effect of initial and final position of the trawlers on the profit. We also investigated many different challenging data sets to observe the impact on the effectiveness of our IFPM. The second objective of this thesis is to develop an efficient solution procedure for the MILP, named integrated fishery planning model (IFPM). The IFPM consists of a fishing subproblem, a processing subproblem, and complicating side constraints. We have tried techniques including LP relaxation, Lagrangean relaxation (LR), Dantzig-Wolfe decomposition (DWD) and decomposition-based pricing (DBP). We develop a new DBP method to solve the IFPM. It gives excellent computation times. We also develop a decomposition-based O'Neill pricing (DBONP) method to improve the solution obtained from DBP procedure. It improves the DBP solutions but takes longer time to solve the IFPM. Finally, we develop a simple and efficient reduced cost-based pricing (RCBP) method. It takes less time to solve the IFPM and yields excellent results. The initial formulations for several planning horizons are solved using the AMPL modelling language and CPLEX with branch and bound. Relevant results and computational difficulties are reported.
Article
We present an efficient and exact algorithm for timetabling military training — a novel integration of Knuth’s efficient Dancing Links indexing scheme with A∗ search that allows us to simultaneously schedule and optimally assign military trainees to classes while respecting domain constraints. We show that our Simultaneous Sequencing and Assignment Solver (SSAS) is able to handle cohort sizes appropriate to the requirements of the Australian Defence Force under a complex prerequisite structure for the courses. Comparisons using real-life parameters with the best known integer programming approach (a column generation-based heuristic) has showed a significant computational benefit from using SSAS. We further tested our method on larger problem instances that might arise in larger training schools. Our SSAS was able to optimally solve such larger-scale problems or prove the problem infeasible in a reasonable computation time.
Article
In this paper, we study a unique, rich combinatorial optimization problem that arose from helicopter aircrew training for the Royal Australian Navy. Each pilot trainee (student) has to complete a syllabus. A syllabus is a sequence of courses (commonly known as subjects), and each course is associated with a pass rate. A pre-requisite structure exists amongst some courses. Each course has a number of repeated sessions, each spanning the same amount of time, but occupying a different set of (possibly overlapping) time slots. A feasible schedule is a sequence of course sessions such that each course in the syllabus is covered by exactly one session, and that all pre-requisite requirements are observed. The optimization problem is to simultaneously assemble course sessions to form feasible schedules, allocate students to these schedules with an objective to minimize the total time-span in completing the syllabus, while ensuring that the class size limits for each course session is not exceeded. The problem is different from the school or university time tabling family of problems due to the assembly component required. This paper is to serve as a pilot study: we derive a number of mixed-integer linear programming models and investigate their performance using test instances provided for us by our industry partner. For each of these models, we propose a number of solution strategies as topics for future research papers. From our numerical testing, it appears that the Column Generation-based approach is computationally the most promising method.
Article
The authors develop a mathematical programming method to make a weekly flight schedule for the ASW helicopter SH-60J in a squadron of the Japan Maritime Self-Defense Force (JMSDF). The targets of the scheduling are four missions: skill training, emergency ready, maintenance of skill, and the assignment of instructor or support crew on training flights. The schedule determines flight mission, crew members as trainee, instructor or other duties, and seat of the crew in the real flight and the simulator training. In many JMSDF squadrons, some specialists spend much time to achieve a feasible and equitable schedule. The proposed method would approximately decrease the workload of them by one-thirtieth.
Article
Full-text available
National census data contain information on place of residence and place of work. It is possible to combine this information and create journey-to-work flows. The process of establishing these flows are presented in this paper. The intramax method is explained and used to identify functional regions based upon these flows. Interesting applications, such as the demarcation of regions in South Africa are considered and solutions to disputed areas are put forward. The process of the creation of the current provincial boundaries are discussed. New boundaries, based on the intramax analysis of the journey-to-work data are proposed for four or five new provinces. Results compare favourably with those from a principal component and cluster analysis, which has previously been used to demarcate the South African space economy into a hierarchy of development regions.
Article
Full-text available
We propose and test a new pricing procedure for solving large-scale structured linear programs. The procedure interactively solves a relaxed subproblem to identify potential entering basic columns. The subproblem is chosen to exploit special structure, rendering it easy to solve. The effect of the procedure is the reduction of the number of pivots needed to solve the problem. Our approach is motivated by the column-generation approach of Dantzig-Wolfe decomposition. We test our procedure on two sets of multicommodity flow problems. One group of test problems arises in routing telecommunications traffic and the second group is a set of logistics problem which have been widely used to test multicommodity flow algorithms.
Article
This paper describes an attempt to solve the one-dimensional cutting stock problem exactly, using column generation and branch-and-bound. A new formulation is introduced for the one-dimensional cutting stock problem that uses general integer variables, not restricted to be binary. It is an arc flow formulation with side constraints, whose linear programming relaxation provides a strong lower bound. In this model, a cutting pattern, which corresponds to a path, is decomposed into single arc variables. The decomposition serves the purpose of showing that it is possible to combine the branch-and-bound method with variable generation. Computational times are reported for one-dimensional cutting stock instances with a number of orders up to 30.
Article
We describe a model for making decisions concerning the proper mix of TADSS (training aids, devices, simulators and simulations) and conventional training resources, and the best modes of using them to maintain soldier and unit proficiency. Given the proficiency standards, the model determines the resources needed, the training methods for using them, and the frequency with which each method needs to be repeated, in order to maintain the standards at minimum cost (sum of equipment procurement costs and operational costs). The model is illustrated with an example problem dealing with the analysis of training systems in a battalion training strategy. Our model has much wider applicability: it can be used for evaluating and determining minimum cost training strategies for other combined arms elements, higher level units and other training scenarios under a variety of circumstances.
Article
While educational programs and professional journals typically devote much of their resources to exact, mathematically elegant methods for the solution of small or modest size problems, the practitioner often encounters large-scale or massive problems for which such exact methods hold little promise. This study discusses this phenomena and presents some thoughts as to the incorporation of guidelines through which large-scale problems may be solved by means of efficient heuristic techniques. Further, these heuristics are classified and related to a fundamental set of base heuristics.
Article
Current measures of military readiness are inadequate. Their only incentive is more is better. They are subject to gaming between subordinates and superiors. They can mislead planners even when they are accurate. They do not tell precisely when a unit can be ready, nor which units to send to a conflict. They give no information about how much readiness we can buy with another dollar.We propose a new paradigm with the potential to give operational readiness information that can inform and guide defense decision-making and policy, from the lowest level to the highest. Our methods rely heavily on operations research analysis. It is already possible to measure accurately the readiness of a small unit such as a tank battalion, but soon it will also be possible to measure accurately the readiness of a large unit such as a divisionin dollars. Furthermore, it may be possible to prescribe optimal levels of readiness.
Article
In this paper an effective search-type heuristic algorithm for the problems of scheduling activities under resource and precedence constraints is presented. Such problems are typically massive in size and combinatorially explosive. The algorithm to solve these problems consists of two phases (both of which are heuristic). Phase I develops a “good” initial solution. Phase II then employs the solution derived in Phase I as a starting point; attempting to manipulate this schedule so as to reduce the project completion time via suitable reshuffles, or rearrangements of the activities while maintaining feasibility. A random problem generator and a random active schedule generator were prepared and utilized to evaluate the performance of the algorithm.
Article
An efficient heuristic for the generalized job shop scheduling problem, with or without multiple parallel machines, is herein presented. This heuristic, in a somewhat more general form, was explained in some detail in our earlier work in project scheduling; and we now suggest that, through this approach, problems in the areas of job shop scheduling and project scheduling may be viewed as elements of the same class. Given an initial feasible solution, the algorithm seeks to improve on this schedule through reduction of makespan by effectively identifying rearrangement opportunities. The quality of the final schedule appears to be, in general, directly correlated to the quality of the starting solution. However, it is recommended that the process be initiated with a reasonably good randomly-generated schedule, rather than a better one produced through rule-based scheduling (such as the Longest Processing Time rule), owing to the fact that such better schedules actually tend to offer less opportunity for rearrangement. The heuristic produces results which compare favorably with those obtained through branch-and-bound techniques for benchmark scheduling problems of the single machine type, and does so in significantly less CPU time. Since the heuristic makes inherent allowance for their inclusion, this approach is equally applicable to job shop scheduling problems with multiple parallel machines
Article
The U.S. Navy Prowler aircraft is designed for electronic surveillance and countermeasures. In this paper, we describe the problem of scheduling Prowler crew training, and we present two integer programming models to solve it. The first model maximizes the number of aviators trained above 75% in each mission area, subject to the available number of flights, over a single month. The second model distinguishes peacetime from mobilization, and minimizes the number of flights done in mobilization subject to the available number of flights in peacetime. Our models distinguish different types of crew and allow more than one qualification to be earned on a given flight. We give numerical results using real data, comparing our results to the actual readiness of a squadron. We found that crew readiness of Prowler squadrons can be increased by 10%, simply by better scheduling. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 289–305, 2003.
Article
This paper reports computational experience with the codesDecompsx andLift which are built on IBM's MPSX/370 LP software for large-scale structured programs.Decompsx is an implementation of the Dantzig-Wolfe decomposition algorithm for block-angular LP's.Lift is an implementation of a nested decomposition algorithm for staircase and block-triangular LP's. A diverse collection of test problems drawn from real applications is used to test these codes, including multinational energy models and global economic models.
Article
This paper investigates the impact of problem formulation on Dantzig—Wolfe decomposition for the multicommodity network flow problem. These problems are formulated in three ways: origin-destination specific, destination specific, and product specific. The path-based origin-destination specific formulation is equivalent to the tree-based destination specific formulation by a simple transformation. Supersupply and superdemand nodes are appended to the tree-based product specific formulation to create an equivalent path-based product specific formulation. We show that solving the path-based problem formulations by decomposition results in substantially fewer master problem iterations and lower CPU times than by using decomposition on the equivalent tree-based formulations. Computational results on a series of multicommodity network flow problems are presented.
Article
One of the most difficult, as well as one of the most important problems faced in military training is that of the determination of a “best” schedule for the performance of training activities, subject to limited resources, precedence and contingency constraints. Such problems are typically massive in size and combinatorically explosive; leading to the need to employ a heuristic methodology. In this paper, we present the results of an actual study of such a problem. Specifically, we address the scheduling of training activities for (army) battalions as located at a typical training base. The approach used to solve this problem consists of two phases (both of which are heuristic). Phase I develops a “good” initial solution. Phase II then employs the solution derived in Phase I as a starting point; attempting to manipulate this schedule so as to reduce the total makespan via suitable reshuffles, or rearrangements of the tasks— while all the while maintaining feasibility. Results for problems of actual sizes are presented and discussed.
Article
Thesis (Ph. D.)--University of Chicago Graduate School of Business, March 1997. Includes bibliographical references.
Article
The problem of selecting and scheduling projects to maximize the scientific, military or commercial value of a space mission has been the subject of ongoing studies for several years. The typical outcome of such studies, even after many man-years of effort, is a heuristic solution with no comparison to optimality. We depart from the traditional, knowledge-based systems, approach and describe a machine scheduling model for the problem. The problem, which is similar to a longest path problem with time windows, is NP-complete in the strong sense. A number of heuristic methods are described, and computational tests reveal that they routinely deliver very close to optimal solutions. We describe two upper bounding procedures, based upon a preemptive relaxation of the problem, and upon the use of Lagragean relaxation. The heuristics and bounding procedures are incorporated into a dynamic programming algorithm, which can solve to optimality randomly generated problem instances with one hundred or more projects. We further demonstrate how, if problems are too large to be solved optimally, a limited-enumeration version of this algorithm can be used to provide very accurate heuristic solutions. We also examine some special cases and variants of the problem.
A framework for characterization of military unit training status
  • Moore Sc
  • Hanser Lm
  • Bd
  • Holroyd
  • Sm
  • Fernandez
  • Jc
Moore SC, Hanser LM, Rostker BD, Holroyd SM, Fernandez JC. A framework for characterization of military unit training status, Technical report, National Defense Research Institute, RAND Corporation, Santa Monica, CA, 1995.
Base scheduling and resource estimation for the Army battalion training model
  • Ignizio
  • Jp
  • Van
  • Ja Eijk
  • Yang
Ignizio JP, van der Eijk JA, Yang T. Base scheduling and resource estimation for the Army battalion training model. Technical report DABT 60-80-C-0049, United States Army, 1981.
Battle Focused Training: Battalion and Company Soldiers, Leaders, and Units. FM 25-101, Headquarters, Department of the Army
  • U S Army
U.S. Army, Battle Focused Training: Battalion and Company Soldiers, Leaders, and Units. FM 25-101, Headquarters, Department of the Army, September 1990.
Maximizing the value of a space mission Working paper series, no. WPS 91-60
  • Hall Ng Magazine
  • Mj
Hall NG, Magazine MJ. Maximizing the value of a space mission. Working paper series, no. WPS 91-60, College of Business, The Ohio State University, September 1991.
Scheduling prowler training. Naval Research Logistics
  • J F Raffensperger
  • S Swords
An exchange heuristic for project scheduling with limited resources. Engineering Optimization. v14
  • T Yang
  • J Ignizio
Base scheduling for a battalion training model under resource and precedence constraints The Pennsylvania State University, 1982. Dr. Yang indicated that this reference supersedes Ignizio
  • T Yang
A framework for characterization of military unit training status
  • S C Moore
  • L M Hanser
  • B D Rostker
  • S M Holroyd
  • J C Fernandez
Base scheduling and resource estimation for the Army battalion training model
  • J P Ignizio
  • J A Van Der Eijk
The Pennsylvania State University, 1982. Dr. Yang indicated that this reference supersedes Ignizio, van der Eijk and
  • T Yang
The army training mix model
  • Murty