The Assignment Problem in Human Resource Project Management under Uncertainty

The assignment problem (AP) is a discrete and combinatorial problem where agents are assigned to perform tasks for efficiency maximization or cost (time) minimization. AP is a part of human resource project management (HRPM). The AP optimization model, with deterministic parameters describing agent–task performance, can be easily solved, but it is characteristic of standard, well-known projects realized in a quiet environment. When considering new (innovation or innovative) projects or projects performed in very turbulent times, the parameter estimation becomes more complex (in extreme cases, even the use of the probability calculus is not recommended). Therefore, we suggest an algorithm combining binary programming with scenario planning and applying the optimism coefficient, which describes the manager’s nature (attitude towards risk). The procedure is designed for one-shot decisions (i.e., for situations where the selected alternative is performed only once) and pure strategies (the execution of a weighted combination of several decision variants is not possible).

[1]  I. Durbach.  Outranking under uncertainty using scenarios , 2014, Eur. J. Oper. Res..

[2]  Manuel Iori,et al.  Exact and heuristic algorithms for the interval min-max regret generalized assignment problem , 2018, Comput. Ind. Eng..

[3]  Gunjan Soni,et al.  A demand aggregation approach for inventory control in two echelon supply chain under uncertainty , 2019 .

[4]  Silvano Martello,et al.  Jenő Egerváry: from the origins of the Hungarian algorithm to satellite communication , 2010, Central Eur. J. Oper. Res..

[5]  Helena Gaspars-Wieloch,et al.  A New Application for the Goal Programming—The Target Decision Rule for Uncertain Problems , 2020, Journal of Risk and Financial Management.

[6]  Helena Gaspars-Wieloch,et al.  Modifications of the Hurwicz’s decision rule , 2014, Central Eur. J. Oper. Res..

[7]  Helena Gaspars-Wieloch.  Newsvendor problem under complete uncertainty: a case of innovative products , 2017, Central Eur. J. Oper. Res..

[8]  Chi-Jen Lin,et al.  A labeling algorithm for the fuzzy assignment problem , 2004, Fuzzy Sets Syst..

[9]  A. El Mhamedi,et al.  Assignment problem under competences and preferences constraints: Modelling and resolution , 2012 .

[10]  Kalpana Dahiya,et al.  A priority based unbalanced time minimization assignment problem , 2020, OPSEARCH.

[11]  Xiao-Jun Zeng,et al.  Uncertain random assignment problem , 2018 .

[12]  Bo Zhang,et al.  Uncertain programming model for uncertain optimal assignment problem , 2013 .

[13]  Deepika Rani,et al.  A branching algorithm to solve binary problem in uncertain environment: an application in machine allocation problem , 2019 .

[14]  Project and Innovation Management: Bridging Contemporary Trends in Theory and Practice , 2016 .

[15]  Serkan Aras,et al.  Comparative study on retail sales forecasting between single and combination methods , 2017 .

[16]  Gerhard J. Woeginger,et al.  On the robust assignment problem under a fixed number of cost scenarios , 2006, Oper. Res. Lett..

[17]  Jaafar Abouchabaka,et al.  A Meta-heuristically Approach of the Spatial Assignment Problem of Human Resources in Multi-sites Enterprise , 2013, ArXiv.

[18]  Helena Gaspars Wieloch.  Scenario planning combined with probabilities as a risk management tool - analysis of pros and cons , 2021 .

[19]  Daniel Vanderpooten,et al.  Complexity of the min-max and min-max regret assignment problems , 2005, Oper. Res. Lett..

[20]  G. Locatelli,et al.  Risk, uncertainty, ignorance and myopia: Their managerial implications for B2B firms , 2020, Industrial Marketing Management.

[21]  Christoph H. Loch,et al.  On Uncertainty, Ambiguity, and Complexity in Project Management , 2002, Manag. Sci..

[22]  Anita Ravi Tailor,et al.  Genetic algorithm based hybrid approach to solve fuzzy multi-objective assignment problem using exponential membership function , 2016, SpringerPlus.

[23]  Ismail H. Toroslu,et al.  Genetic algorithm for the personnel assignment problem with multiple objectives , 2007, Inf. Sci..

[24]  V H Bajaj,et al.  Fuzzy approach with linear and some non-linear membership functions for solving multi-objective assignment problems , 2009 .

[25]  Jean-Charles Pomerol,et al.  Scenario development and practical decision making under uncertainty , 1999, Decis. Support Syst..

[26]  Dick den Hertog,et al.  Adjustable robust strategies for flood protection , 2016 .

[27]  H. W. Kuhn,et al.  Variants of the hungarian method for assignment problems , 1956 .

[28]  Theodor J. Stewart,et al.  Integrating multicriteria decision analysis and scenario planning—Review and extension , 2013 .

[29]  H. Kuhn.  The Hungarian method for the assignment problem , 1955 .

[30]  Shweta Singh.  A Comparative Analysis of Assignment Problem , 2012 .

[31]  Helena Gaspars-Wieloch,et al.  Spare parts quantity problem under uncertainty - the case of entirely new devices with short life cycle , 2019, Multiple Criteria Decision Making.

[32]  Jaafar Abouchabaka,et al.  A Hybrid Heuristic Method to Solve an Assignment Problem of Human Resource , 2015 .

[33]  C. Derman,et al.  A Sequential Stochastic Assignment Problem , 1972 .

[34]  Ying Zhang,et al.  Managing uncertain tasks in technology‐intensive project environments: A multi‐method study of task closure and capacity management decisions , 2020 .

[35]  Panos M. Pardalos,et al.  Random assignment problems , 2009, Eur. J. Oper. Res..

[36]  Helena Gaspars-Wieloch.  Propozycja hybrydy reguł Hurwicza i Bayesa w podejmowaniu decyzji w warunkach niepewności , 2014 .

[37]  Helena Gaspars-Wieloch.  Modifications of the Omega ratio for decision making under uncertainty , 2015 .

[38]  Ian N. Durbach,et al.  Modeling uncertainty in multi-criteria decision analysis , 2012, Eur. J. Oper. Res..

[39]  D. Ellsberg.  Decision, probability, and utility: Risk, ambiguity, and the Savage axioms , 1961 .

[40]  Helena Gaspars-Wieloch.  Critical analysis of classical scenario-based decision rules for pure strategy searching , 2020 .

[41]  George Wright,et al.  Future‐focussed thinking: combining scenario planning with decision analysis , 1999 .

[42]  J.-C. Panayiotopoulos,et al.  The General Problem of m Persons and n Positions for Short- and Long-Term Decision-Making , 1979 .

[43]  Jan H. Kwakkel,et al.  Systemic Flood Risk Management: The Challenge of Accounting for Hydraulic Interactions , 2019, Water.

[44]  Sibo Ding,et al.  Uncertain random quadratic bottleneck assignment problem , 2019, Journal of Ambient Intelligence and Humanized Computing.

[45]  P. Schoemaker.  Scenario Planning: A Tool for Strategic Thinking , 1995 .

[46]  Hong Wang,et al.  Study on solution models and methods for the fuzzy assignment problems , 2012, Expert Syst. Appl..

[47]  Christian Hugo Hoffmann.  Strengths and Weaknesses of Scenario Planning as a Risk Management Tool , 2017 .

[48]  Pankaj Gupta,et al.  A fuzzy approach to multicriteria assignment problem using exponential membership functions , 2012, International Journal of Machine Learning and Cybernetics.

[49]  Guido Reger,et al.  Advantages and Disadvantages of Scenario Approaches for Strategic Foresight , 2005 .

[50]  Maria Grazia Speranza,et al.  The locomotive assignment problem: a survey on optimization models , 2014, Int. Trans. Oper. Res..

[51]  Joachim Kasten,et al.  Wind Turbines on German Farms—An Economic Analysis , 2019, Energies.

[52]  Lin Lin,et al.  Choosing suitable project control modes to improve the knowledge integration under different uncertainties , 2019, International Journal of Project Management.

[53]  J. Abouchabaka,et al.  A MULTIPLE KNAPSACK APPROACH FOR ASSIGNMENT PROBLEM OF HUMAN RESOURCES , 2016 .

[54]  Liang-Hsuan Chen,et al.  An extended assignment problem considering multiple inputs and outputs , 2007 .

[55]  Rosshairy Abd Rahman,et al.  An Assignment Problem and Its Application in Education Domain: A Review and Potential Path , 2018, Adv. Oper. Res..

[56]  John C. Panayiotopoulos,et al.  Personnel Assignment with a Budget Constraint , 1981 .

[57]  Stephen M. Millett,et al.  Should Probabilities Be Used with Scenarios , 2009 .

[58]  Fan Liu,et al.  Multicriteria ABC Inventory Classification Using the Social Choice Theory , 2019 .

[59]  D. Samson.  Operations/supply chain management in a new world context , 2020, Operations Management Research.

[62]  Seweryn Spałek,et al.  Innovative vs. Innovation Projects in Organisations , 2016 .