Manpower Allocation with Time Windows

Manpower Allocation with Time Windows Author(s): A. Lim, B. Rodrigues and L. Song Source: The Journal of the Operational Research Society, Vol. 55, No. 11 (Nov., 2004), pp. 1178-1186 Published by: Palgrave Macmillan Journals on behalf of the Operational Research Society Stable URL: http://www.jstor.org/stable/4101889 . Accessed: 12/10/2014 03:03 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp

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Journal of the Operational Research Society (2004) 55, I 178-1186

*(j 2004 OperationalResearchSociety Ltd.All rightsreserved. 0160-5682/04 $30.00

www.palgrave-journals.com/jors

Manpower

allocation

with

time

windows

A Lim', B Rodrigues2* and L Song3 'Hong Kong University of Science and Technology, Clearwater Bay, Hong Kong, 2Singapore Management University, Singapore; and 3National University of Singapore, Singapore In this paper, we propose a manpowerallocation model with time windows which is of practicalinterest. This model originatesfrom a real-lifeport manpowerallocation problemwhere demandis generatedfrom locations in the yard for servicemenwho are dispatchedfrom a centralpoint and where the objectivesare to minimizethe numberof servicemen used, travel distances, travel times and waiting times. We develop a tabu-embeddedsimulatedannealingalgorithmand a squeaky wheel optimization with local search algorithm for the problem. Experimentalresults are reported which show the effectivenessof our approaches. Journalof the OperationalResearchSociety,(2004) 55, 1178-1186. doi:10.1057/palgrave.jors.2601782 Publishedonline 24 June 2004 Keywords:manpower allocation; heuristics

Introduction Manpower allocation is a management problem most companies face. Depending on the size and needs of the organization,allocation and schedulingcomplexity varies, but a key concern is always the efficient and productive

utilizationof manpower.In many studies,problemformulation is encapsulated in a single integer programming problemwith the objectivebeing the minimizationof a cost function while satisfying operational constraints. In the simplestcase, the assignmentproblem,manpowerallocation can be solved by a number of well-known tools, as for example,with minimumweight matchingalgorithms.As we considermore realisticproblems,we find that a number of other factors surface naturally. Some of these are operational such as demand requirementsin servicetype, serviceman compatibilityand timings.Othersare attributessuch as individual preferences,skill levels, servicemenwith mixed skills, and staff satisfaction (see, for example, Cai and Li,1 Abboud et al2).

One importantfeaturecommon in manpowerallocationis the locational or geographic aspect where service demand can come from a diversenumber of sites and where service can only be initiated after certain specifiedtimes and must be completed before certain specified times. This is the case, for example, of companies that maintain field staff, for example, field service engineers or salesmen, who service various districts or regions. Such staff may have to service installations where demand could be around the clock with a minimum serviceman strength required at B Rodrigues,Schoolof Business,SingaporeManage-

*Correspondence.4 nent University,469 Bukit TimahRoad, Singapore259756, Singapore.

E-mail:br(asmu.edu.sg

some regions, for example. While servicemenare allocated and scheduled, unfilled on-time demand could result in expensive backfilling where travel time and other costs are penalties. In this context, this work is motivated from a study of manpower allocation needs of the Port of Singapore Authority (PSA) which is a large technology corporation located in Singapore. It manages one of the busiest ports in the world handling over 17 million 20-foot equivalent units containers (TEUs) annually representing about 9% of global container business. PSA is concerned with maximizing throughput at its ports in view of pressures derived from limited port size, high cargo transshipment volumes and limited physical facilities and equipment. A simplified description of the manpower allocation problem for the port is as follows: Different locations in the port demand varying amounts of service work to be met.

A service control centre dispatches servicemen to satisfy these demands. Each servicemanperformsone task at one location at any one time. Each location has its own demand time window, which is defined by an 'early' time and a 'late' time. A serviceman has to start a task only after the 'early' time and finish before the 'late' time, and has to wait if he arrives before the early time. We make the assumption here that servicemen have the same travel speed and work rate and can move from location to location but will eventually be required to return to the service control centre. Each demand location has a requirement for a given number of servicemen, in proportion to its work needs, to fulfill work

within its time window. The primarypurposeof this study is to develop and solve a model for this basic manpowerallocation problemwhich takes into account operational constraints. We formulate


ALim eta/-Manpower allocation1179

this problemas a multi-objectiveproblemwherethe primary objective is to minimizethe number of servicemenused in satisfyingall servicedemands,while the secondaryobjective is to minimizethe total travel distancefor such a schedule. Other tertiary objectives aim to minimize total worker scheduledtime and total waiting times at servicepoints. Our model is closely related to the well-known vehicle routing problem with time windows (VRPTW) (see, eg, Pardalosand Resende3).It is, however, essentiallydifferent from the latter in that the demand (or customer points) require a fixed number of servicemen whereas in the VRPTW there is no such requirement.Furthermore, a location may have more than one demand that overlap in time. Because of the closeness of the manpower allocation model with the VRPTW,we cite referencesto work done on the latter as the most relevantto our manpowerallocation model. Savelsbergh4showed the VRPTW to be NP-hard. Much work has been done to derive exact algorithms to solve the problem. In general,more recent researchon the VRPTW can be divided into optimization and heuristic approaches.Results obtained recentlyby heuristicscan be found in Rochat and Taillard,s Chiang and Russell,6 Taillard et al,7 Thangiah,8 Homberger and Gehring,9 Cordeau et al,'0 Backer et al," Rousseau et a112and Li and Lim.'13

heuristicsfor the problem using these mechanisms.To test the algorithms, we conducted experiments and provide results.In the last section, we suggestpossible futurework. Problem statement and formulation The manpower allocation problem with time windows (MAPTW) is described as follows: We are given enough servicemento meet servicedemand from N+ 1 demand or customer points that include a service centre. Typically, a servicemanwill traverse a route that starts at the service centre, moves to a customer, and then to other customers before returningto the servicecentre. A travel distance c, and a travel time tqjare costs incurredas the serviceman travels from customers i to j. Each customer in the route demandsd, numbersof servicemenwho must provideservice within the time window specifiedfor the customerlocation which is given by an earliestand a latest time. Servicemenwho arrive early are required to wait. The multi-objectivemodel for the MAPTW is given as follows: Decision variables: is 1 if serviceman k travels from customer i to xi?-k customer j, and 0 otherwise, ifij, i, j= 0,1,...,N;

ti

wi M

Complexity and objectives The manpower allocation model is clearly NP-hard. It suffices to consider the minimum travel distance objective with the demands at locations set to unity without time windows to see that this problemhas largercomplexitythan that for the travelling salesman problem. Solution approaches to related problems such as the VRPTW include constructionheuristics,improvementheuristicsand composite heuristics. In particular,route construction heuristics build feasible solutions by inserting an unrouted location into a currentpartialrouteuntil all locationsare routed.The sequential insertion algorithm proposed by Solomonl4 belongs to the class of construction heuristics. Route improvement heuristics modify a solution by performing local searches for better solutions in neighbourhoods generated by node/edge-swappingoperators. A composite heuristic usually mixes route construction and route improvementprocedures. The objective of this study is to find an efficientway to solve the manpower allocation problem with time windowsusing heuristics.We implementeda tabu-embedded simulated annealing algorithm and used the relatively new 'squeaky wheel optimization' (SWO) technique for this problem. This work is organizedas follows. In the next section, we describe the model. Following this, we develop basic neighbourhoodgeneratingmechanisms, and then develop

k= 1...,M arrivaltime at node i waiting time at node i total numberof servicemen

Parameters: N

total numberof demand nodes (customers) c1j distancecost betweennode i and j travel time cost betweennodes i and j ti demand in numbersof servicemenat node i di ei earliestarrivaltime at node i li latest arrivaltime at node i si servicetime at node i mk total shift time of servicemank Objectives: minimizeM N

N

M

minimize i=0 j=0 k=l

N

(2.1)

for i ij

(2.2)

for i#j

(2.3)

wxilk for i j

(2.4)

ciixik

NM

minimizeSS

t1xk

i=0 j=0 k=l

N

N

M

minimize55 i=0 j=O k=l


Vol.55, No.11 Research oftheOperational 1180 Journal Society

subjectto M

N

forj

=Ed,

Sxik k=l i=0O

t-i + si + = k 1,... IM

Xijk(ti +

wi)

•

(2.5)

0,1,...,N

t for i = 0,

1,... ,N,

j = 1,... N (2.6)

to = 1wo= S = 0

(2.7)

fori= 0,1,...,N + ei