Calhoun: The NPS Institutional Archive Theses and Dissertations Thesis Collection 1992-03 Optimization models for underway replenishment of a dispersed carrier battle group Wu, Tzu-li Monterey, California. Naval Postgraduate School http://hdl.handle.net/10945/30607 NAVAL POSTGRADUATE SCHOOL Monterey , California THESIS OPTIMIZATION MODELS FOR UNDERWAY REPLENISHMENT OF A DISPERSED CARRIER BA,TTLE GROUP by I Wu, Tzu-Li March 1992 Thesis Co-Advisor: Robert Dell Thesis Co-Advisor: Siriphong Lawphongpanich Approved for public release; distribution is unlimited. Thesis + W9315 c!2 SECURITY CLASSIFICATION OF THIS PAGE REPORT DOCUMENTATION PAGE la. REPORT SECURITY CLASSIFICATION 1b. RESTRICTIVE MARKINGS JNCLASSFIED 2a. SECURITY CLASSIFICATION AUTHORITY 3. DISTRIBUTION/AVAILABlLlTYOF REPORT Approved for public release; distribution is unlimited. 2b. DECLASSIFICATION/DOWNGRADlNGSCHEDULE 4. PERFORMING ORGANIZATION REPORT NUMBER(S) 5. MONITORING ORGANIZATION REPORT NUMBER(S) 6a NAME OF PERFORMING ORGANIZATION 6b OFFICE SYMBOL 7a. NAME OF MONITORING ORGANIZATION Naval Postgraduate School (If a~~licable) Naval Postgraduate School 55 6c. ADDRESS (City, State, and ZIP Code) 7b. ADDRESS (City, State, andZlPCode) Monterey, CA 93943-5000 Monterey, CA 93943-5000 8a. NAME OF FUNDING/SPONSORING 8b. OFFICE SYMBOL 9 PROCUREMENT INSTRUMENT IDENTIFICATION NUMBER ORGANIZATION (If applicable) I 8c ADDRESS (City, State, andZlP Code) 10 SOURCE OF FUNDING NUMBERS Program Element No Project No I I&.No Vvorl, Unn Access~ori Number 1 1 TITLE (Include Security Classification) OI'TIMIZATION MODELS FOR UNDERWAY REPLENISHMENT OF A DISPERSED CARRIER-BATTLE GROUP 12 PERSONAL AUTHOR(S) Wu, Tzu-1.i 13a TYPE OF REPORT 13b TIME COVERED 14 DATE OF REPORT (year, month, day) 15 PAGE COUNT Master's Thesls From lo 92 March 20 9 5 16. SUPPLEMENTARY NOTATION The views expressed in this thesisare thuse of the autlltrr do not reflect the official policy or position of he Departn~rl~~d'Ijrltnse ihc. tl.S 17 COSATI CODES 18 SUBJECT TERMS (continue on reverse if necessary andidentify by block number) FIELD 1 GROUP I SUBGROUP Optlmizatlon, Integer Programmlng,Traveling Salesman Problem I 19 ABSTRACT (contrnue on reverse if necessary and tdentrfy by block number) This thesis presents a classification ofbasic optimization models for planning underway replenishment of'a battle group. In part~culu~-,tills thesis focuses on two scenarios, routine and reormming, and considers three replenishment tactics: circuit rider, delivery boy and gas ataciun. Some ofthe models presented can be classified as (standard)traveling salesman, generalized traveling salesman or orieultwri~~g~)rublerr~. However, several models are further generalization ofthese problems which have not been previously considered. Computation expt:rimt.n~s using Sour formations frotn the literature and con~merciallyavailable software identifj. problems that are dificult to sulve iind/c,t require specialized algorithms , 20 DISTRIBUTION/AVAILABlLlTY OF ABSTRACT I 21 ABSTRACT SECURITY CLASSIFICATION I UNCLASSIFIED~UNLIMITLL, >AME 45~;~0k7 DTIC USERS UNCLASSFlED 22a NAME OF RESPONSIBLE INDIVIDUAL 122b TELEPHONE (Indi~deArea code) 122~3FFICE SYMBOL Robert Dell; Smphong Lawphongpanlch 1 408-646-2583;408-646-2106 1 <b&Lk!, ()W~.[J I DD FORM 1473.84 MAR 83 APR edltlon may be used untll exhausted SECURITY CLASSIFICATIONOF TYlS PAGt All other editions are obsolete UNCLASSFIEI) Approved for public release; distribution is unlimited. Optimization Models for Underway Replenishment of a Dispersed Carrier Battle Group Tzu-li/)Vu Lieutenant , R.O.C. Navy B.S., Chinese Naval Academy, 1985 Submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN OPERATIONS RESEARCH from the NAVAL POSTGRADUATE SCHOOL March 1992 Author: Approved by: Robert Dell, Thesis Co-Advisor sirip%n; Lawphongpanich, Thesis Co-advisor Peter Purdue, Chairman Department of Operations Research ABSTRACT This thesis presents a classification of basic optimization models for planning underway replenishment of a battle group. In particular, this thesis focuses on two scenarios, routine and rearming, and considers three replenishment tactics: circuit rider, delivery boy and gas station. Some of the models presented can be classified as a (standard) traveling salesman, generalized traveling salesman or orienteering problem. However, several models are further generalizations of these problems which have not been previously considered. Computational experiments using four formations from the literature and commercially available software identify problems that are diffkult to solve and/or require specialized algorithms. DISCLAIMER The views expressed in this thesis are those of the author and do not reflect the official policy or position of the Department Defense or the U.S. Government. The reader is cautioned that computer programs developed in this research may not have been exercised for all cases of interest. While every effort has been made, within the time available, to ensure that the programs are free of computational and logic errors, they cannot be considered validated. Any application of these programs without additional verification is at the risk of the user. TABLE OF CONTENTS I. INTRODUCTION ....................................... 1 I1 . BACKGROUND ........................................ 4 A. UNDERWAY REPLENISHMENT PLANNING ............ 4 B . TRAVELING SALESMAN PROBLEM .................. 8 1. Multiple Traveling Salesman Problem (M-TSP) ....... 9 2 . Generalized Traveling Salesman Problem (GTSP) ..... 9 3 . Prize Collecting Traveling Salesman Problem (PCTSP) . 10 C. PRIOR STUDIES ON UNDERWAY REPLENISHMENT .... 11 I11 . BASIC MODELS FOR UNREP OPERATION ................. 13 A . MODEL ASSUMPTIONS ............................ 14 B. DELIVERY BOY MODELS ........................... 15 C. CIRCUIT RIDER MODELS .......................... 23 D . GAS STATION MODELS ............................ 29 1. Limited number of ships off-station ................ 30 2 . Unlimited number oPsliips-off.,.t~t,i~~?~............. 33 IV. COMPUTATIONAL EXPERIENCE ......................... 41 A. ROUTINE SCENARIO .............................. 44 B . REARMING SCENARIO ............................. 47 IV. CONCLUSION ........................................ 52 APPENDIX A. ALTERNATE GAS STATION MODEL WITH LIMITED NUMBER OF SHIPS OFF-STATION RESTRICTION .......... 54 APPENDIX B. FOUR BATTLE GROUPS FORMATION LAYOUT .... 55 A. FORMATION 1 .................................... 55 B . FORMATION2 .................................... 56 C. FORMATION 3 .................................... 57 D . FORMATION4 .................................... 58 APPENDIX C. UNREP GAMS MODELS ........................ 59 A. DELIVERY BOY TACTIC WITH MINIMUM TOTAL UNREP TIME OBJECTIVE FUNCTION ...................... 59 B. DELIVERY BOY TACTIC WITH MAXIMUM COMBAT VALUE OBJECTIVE FUNCTION ........................... 61 C. CIRCUIT RIDER TACTIC WITH MINIMUM TOTAL UNREP TIME OBJECTIVE FUNCTION ...................... 63 D. CIRCUIT RIDER TACTIC WITH MAXIMUM COMBAT VALUE OBJECTIVE FUNCTION ..................... 65 E. GAS STATION TACTIC WITH MINIMUM TOTAL UNREP TIME OBJECTIVE FUNCTION, TWO TRANSFERSTATIONS AND LIMITED NUMBER OF SHIPS OFF-STATION ...... 67 F. GAS STATION TACTIC WITH MAXIMUM COMBAT VALUE OBJECTIVE FUNCTION, TWO TRANSFER STATIONS AND LIMITED NUMBER OF SHIPS OFF-STATION .......... 70 G. GAS STATION TACTIC WITH MINIMUM TOTAL UNREP TIME OBJECTIVE FUNCTION, TWO TRANSFERSTATIONS AND UNLIMITED NUMBER OF SHIPS OFF-STATION ... 73 H. GAS STATION TACTIC WITH MAXIMUM COMBAT VALUE OBJECTIVE FUNCTION, TWO TRANSFER STATIONS AND UNLIMITED NUMBER OF SHIPS OFF-STATION ........ 77 LIST OF REFERENCES ..................................... 81 INITIAL DISTRIBUTION LIST ............................... 85 vii I. INTRODUCTION Carrier battle groups have the unique capability to deploy military striking power anywhere in the world. They can operate in international water without relying upon the support or cooperation of other governments. This capability is essential to carrying out the strategy of forward engagement, i.e., the strategy of waging war in the enemy's backyard instead of our own. During peace time, the mobility and flexibility of carrier battle groups also provide the ability to project relatively unobtrusive 'over the horizon' presence which is indispensable for responding to and, perhaps deterring, crises and low intensity conflicts around the globe. One of the most important factors in insuring the effectiveness and survivability of carrier battle groups is sustainability. Battle groups must be capable of carrying the fight to the enemy as well as sustaining combat operations for an extended period of time. Certainly, the degree of sustainability depends on the level of logistic support. One way to insure a high level of such support involves a three-step process. The first step is to locate 'advanced logistics support bases' (ALBSs) close to areas of potential conflict. In the second step, supplies and materiel are transported from ALBSs to battle groups by 'shuttle' ships. Finally, assets such as station ships and helicopters distribute the needed supplies and materiel to other ships in the battle group. The distribution of supply and materiel by a station ship is often referred to as 'underway replenishment' or simply 'unrep'. To avoid confusion, this thesis refers to a station ship as a supply ship. The tactical disposition of ships in a carrier battle group has changed over the last forty years