Referee s report on the Ph.D. thesis Applications of Combinatorial Optimization for Online Shopping by Jędrzej Musiał

Transcription

1 Adam Janiak, D.Sc., Ph.D., M.Eng., Full Professor, Institute of Computer Engineering, Control and Robotics Wrocław University of Technology Janiszewskiego 11/ Wrocław Poland Wroclaw, February 8, 2013 Referee s report on the Ph.D. thesis Applications of Combinatorial Optimization for Online Shopping by Jędrzej Musiał 1. Research background We can say that electronic commerce (e-commerce) is one of the fastest developing parts of the computing science (based on operational research, combinatorial optimization). However, it is worth noticing that e-commerce is a giant hybrid built in additional areas such as logistics, economy and social sciences. E-commerce is an industry, which focuses on selling and buying products with a support of an electronic system (the Internet!). Internet purchases are within the interest of a huge number of people, and this number is constantly growing at a fast rate. There are many reasons for online shopping. We can just point a few more important ones such as: lower prices, a wide choice of products, a wide choice of sellers, home shopping comfort, buying from abroad. Motivated by the problem of buying multiple products from different e- commerce web sites, the author of the Ph.D. thesis proposed a combinatorial optimization problem where we have a set of products and a consumer who wishes to buy all products in from a set of Internet stores at the minimum final price, subject to the price, availability, and discount constraints at each store. For, let denote the decision variable that corresponds to the subset of products selected by the consumer from store. The corresponding 1

2 optimization problem, which the author refers to as the ISOP (Internet Shopping Optimization Problem), is given by: ( ) where for, denotes the delivery price from store and denotes the setof products available at store. Moreover, for each and, denotes the price of product in store. The function denotes the discount function associated with store (which is a function of the delivery and total price of the products). During his research Mr. Musiał examined different versions (specializations) of the ISOP. All of them are described in detail in the refereed thesis. The main stress was placed on the most complicated version of the problem (furthermore, the most realistic at the same time) where we deal with the discounting functions for every store. Overall, I find the topic of the thesis interesting and well motivated. Finding the cheapest way to buy products from multiple web sites subject to product availability and discount constraints is an interesting problem faced by many consumers. Furthermore, the problem is mathematically defined (mathematical formulation) and proved to be NP-hard. This issue makes it an interesting scientific problem that is for sure worth conducting research on it. 2. Thesis and its contribution 116 numbered pages of the thesis are written in English (good quality of language, clear and without mistakes). The work is clear and the proportions of the following chapters are well balanced. Following the Introduction there is nomenclature and abbreviation description in Chapter 2. Chapter 3 contains basic definitions combinatorial optimization primer. Some of actually working support systems for online shopping are described in the fourth chapter. Moreover, the author proposed 2

3 new decision aid system for online shopping with self pick-up. Chapter 5 defines Internet Shopping Optimization Problem with its mathematical formulation and the NP-hardness proof. A few different versions of the ISOP problem are defined within this chapter. The most important version is the one with the discounting function. The following chapter contains information about possible reductions. Chapter 7 and 8 describe new, original heuristic algorithms that are developed by Mr. Musiał. Moreover, the model of the computational experiment is described. The author uses an enormous amount of well-planned tests to provide and comment on the results. The last chapter concludes the thesis. Moreover, the author added bibliography, a list of his original publications (appendix A) and two more additional appendices: appendix B with tables, and appendix C with database scheme optimization for online application problem description. The main contributions of the thesis are the following: Mathematical formulation of the Internet Shopping Optimization Problem (ISOP). Providing the proof that the ISOP problem is NP-hard by a polynomial transformation from the Exact Cover by 3-Sets (X3C), which is a well-known NP-complete problem. Detailed literature analysis with a special attention paid to Facility Location and Knapsack Problems. Algorithm design Mr. Musiał proposed 5 new algorithms (one exact and four heuristics) for solving the problem in question. Extensive computational experiments done for a wide range of problem parameters. They proved the value and quality of the algorithms. Design of the support system for online shopping with self pick-up. 3. Remarks and comments There are some misprints (mainly Polish accent issues) in Polish Abstract (wysylki->wysyłki;związanych->związany; odrębnych->odrębny; odleglych- >odległych; zostalo->zostało) [page 4]. On page 20, Appendix A should be Appendix B and B should be C, respectively. 3

4 It seems that the sentences are sometimes too long. Dividing them into shorter ones could improve the overall clarity. World working model will be a little bit better when using real data instead of a designed model (therefore the model is very sophisticated and based on real research, observations and experience) [page 58]. Subsection could be enhanced for better explanation of the proposed metrics [page 37]. In subsection abbreviation ISOP is used without explanation reference should be added [page 30]. There are different types of quotation mark that Mr. Musiał uses around the thesis. The best will be to use British or US quotation marks. Virtual Pharmacist test web-page application could be accessible for use [page 42]. Sentence Stratila [SoTORC09] studied a concave cost facility location problem whose mathematical program can be written as [ ] and the following equation are doubled on two pages [pages 56-57]. Figure 7.2 should be clearer (colored or patterned) [page 62]. Algorithm pseudo-codes could be printed as an additional Appendix [pages 68, 70, 71, 72, 75]. During computational tests the author could consider the use of validity measure. It would have strengthened test formulation. The above mentioned are merely shortcomings and do not substantially affect the quality of the work. 4. Conclusion Overall, I find the topic of the thesis interesting and well motivated. The author provides a detailed description and mathematical formulation of the problem, and characterizes its complexity properly. He later proposes new algorithms and correctly implements them. The computational tests verified high quality of the algorithms. The refereed thesis and research work of Jędrzej Musiał should be perceived as high quality work having a substantial potential in the connection with Internet applications. A partial publication of the obtained results in such journals as, Applied Mathematics and Computer Science, 4OR - A Quarterly Journal of Operations 4

5 Research, Lecture Notes in Computer Science, Foundations of Computing and Decision Sciences justifies this judgment. To sum up, I consider the thesis entitled Applications of Combinatorial Optimization for Online Shopping by Jędrzej Musiał to meet the conditions imposed by the current doctoral dissertation law. 5