ARTICLE IN PRESS H -F Wang, C-T. Wu/Computers 8 Operations Research i(am)Il-l regarded as the users metadata input into the analytical model, weighting parameter B, Be[o, 1], Model (11) can be transformed which has been proposed by Wang and Wu as shown in Eqs. into a single objective programming model as Model (12). while (9.1)-(9.5) Model(11) with B=l yields Model (10)for implementing maximal profit strategy; that with B=0 will emphasize the users Maximize (9.1) benefit as best service strategy: and depend on the marketing preference the suppliers adopted, B can be given by any values Subject to between 0 and 1 as win-win strategy. Note that in Model (12),c"is further normalized from c into [0, 1 to match the same scale =1,2,F,j=1,2.J sx≤B,=1,2,.F,j=1.2.J Maximize 石21.P=12…只,1=12… (94) Maximize∑>ax Subject to sxsB, f=1, 2, ., F, j=1,2,.. ∈ F,j=12,…,x∈0,1)(11) whex=bpx1=12…Ld12…D,j=12,…J fi=1,2..F,e=l if item pa is recommended to ul";otherwise, xa=0. c and s are the corresponding profit and price of pd. bis the satisfactory level requested by u, Bf is the budget limit given by Maximize +(1-B) I'.a=[ lxyp, pe to be the purchase probability measure of B",f卩=1,2,p user up on Pa. This model maximizes the profits of an EC company (9.1)when the items recommended to users satisfy their satisfactory xn≥1.f=y,2,p.j=1,2..,x∈01.(12) level as shown in constraint(9. 2); the total prices spent on the items should not exceed the budget of the user as shown in constraint (9.3). Constraint (9.4) provides a tool for strategic uses by recommending different number of items of which at least one 3.3.2. Measures of recommendation performance item should be recommended to a user at each time To evaluate the performance of information retrieval, three or different marketing strategies-the maximal profit strategy and The sures of recall, precision, and F1 are usually employed [12,471 Under the basic model, two strategies could be provide win-win strategy. When the recommending processes use only the recommendation system as well supplier viewpoint, the goal will be to maximize the profits of the oods under a set of items that satisfy the users' preferences Recall= S(user)n Rec(user)l/Rec(user)l (13) and budgets. When this is intended, denote the reduced decision- variable vector and the corresponding coefficients by""to mean that Precision= S(user) n Rec(user)//S(user) all items left for consideration are at least above the requested F1=2 x Recall x Precision/Recall+Precision, satisfactory level, namely b". Model (10)will immediately reflect such strategy. where S(user) is the actual basket for the compared user; Red(user) is the recommendation item set. Recall is the ratio of Maximize items successfully recommended, whereas precision measures he user's satisfactory degree. Fl is a leverage measure when Subject to s'x"≤B,∫=1,2,F,j=1,2,J recall and precision conflict with each other. ∑∑21,=12,p,J=12.k0 3.3.3. Summary of offline and online operation procedures After introducing the individual sub-modules of the proposed profit strategy will bring about the highest online operations procedures are categorized int from the management passively satis desires to the minimal levels and thus 3.3.3.1. Offline operatic ot a strategy to provide good services. Alternatively, the win-win Step 1. Construct user-groups through user's demographic strategy which actively takes both suppliers' profit and users features and item-groups by obtai preferences into account is proposed. Model (11) realizes such UD={u(cg)=1,2,…,Fj=1,2…Jand trategy in which the first objective function maximizes the suppliers profit as previously done: meanwhile, the second P={P(xk)d=1,2,,Dy,i=12, satisfaction.Made/ represents the maximization of the user's Step 2. Compute relative purchase priorities(w/) between user- (11)is a bi-objective programming mo groups and item-groups by Eq (3). Since there are a lot of prominent literatures discussing and Step 3. Compute similarity measures between user-groups. solving this kind of bi-criterion problems [ 1, 4,8, 13, 50] we do not Similarity function is used from common item set(Eq (6))or focus on how to solve the proposed models. In the manner non-common item set(Eq (8)). of convex combination of the two objectives: introducing a Step 4. Derive out-of-clique probability measures by Eq (4). Please cite this article as: Wang H-F, Wu C-T. A strategy-oriented operation module for recommender systems in E-com Computers and Operations Research(2010). doi: 10. 1016/j. cor. 2010.03.011 mmerce.ARTICLE IN PRESS regarded as the user’s metadata input into the analytical model, which has been proposed by Wang and Wu as shown in Eqs. (9.1)–(9.5): Maximize X J j ¼ 1 XFj fj ¼ 1 cxfj , ð9:1Þ Subject to afj xfj Zbfj , fj ¼ 1j ,2j , ... ,Fj , j ¼ 1,2, ... ,J, ð9:2Þ sxfj rBfj , fj ¼ 1j ,2j , ... ,Fj , j ¼ 1,2, ... ,J, ð9:3Þ XI i ¼ 1 XDi di ¼ 1 x fj idi Z1, fj ¼ 1j ,2j , ... ,Fj , j ¼ 1,2, ... ,J, ð9:4Þ x fj idi Af0,1g, ð9:5Þ where xfj ¼ ½x fj di P i Di1, i ¼ 1,2, ... ,I, di Af1,2, ... ,Di g, j ¼ 1,2, ... ,J, fj ¼ 1j ,2j , ... ,Fj , xfj di ¼ 1 if item pdi is recommended to ufj ; otherwise, x fj di ¼ 0. c and s are the corresponding profit and price of pdi . bfj is the satisfactory level requested by ufj ; Bfj is the budget limit given by ufj . aj ¼ ½@ ufj pdi 1 P i Di , @ ufj pdi to be the purchase probability measure of user ufj on pdi . This model maximizes the profits of an EC company (9.1) when the items recommended to users satisfy their satisfactory level as shown in constraint (9.2); the total prices spent on the items should not exceed the budget of the user as shown in constraint (9.3). Constraint (9.4) provides a tool for strategic uses by recommending different number of items of which at least one item should be recommended to a user at each time. Under the basic model, two strategies could be provided for different marketing strategies—the maximal profit strategy and win–win strategy. When the recommending processes use only the supplier viewpoint, the goal will be to maximize the profits of the goods under a set of items that satisfy the users’ preferences and budgets. When this is intended, denote the reduced decision￾variable vector and the corresponding coefficients by ‘‘0 ’’ to mean that all items left for consideration are at least above the requested satisfactory level, namely bfj . Model (10) will immediately reflect such strategy. Maximize X J j ¼ 1 XFj fj ¼ 1 c0 xfj 0 Subject to s0 xfj 0 rBfj , fj ¼ 1j ,2j , ... ,Fj , j ¼ 1,2, ... ,J XI i ¼ 1 XDi di0 ¼ 1 xfj idi 0 Z1, fj ¼ 1j ,2j , ... ,Fj , j ¼ 1,2, ... ,J, xfj idi 0 Af0,1g ð10Þ Although maximal profit strategy will bring about the highest income to the suppliers, from the management viewpoint, it only passively satisfies users’ desires to the minimal levels and thus is not a strategy to provide good services. Alternatively, the win–win strategy which actively takes both suppliers’ profit and users’ preferences into account is proposed. Model (11) realizes such strategy in which the first objective function maximizes the supplier’s profit as previously done; meanwhile, the second objective function represents the maximization of the user’s satisfaction. Model (11) is a bi-objective programming model. Since there are a lot of prominent literatures discussing and solving this kind of bi-criterion problems [1,4,8,13,50] we do not focus on how to solve the proposed models. In the manner of convex combination of the two objectives: introducing a weighting parameter b, bA½0,1, Model (11) can be transformed into a single objective programming model as Model (12). While Model (11) with b¼1 yields Model (10) for implementing maximal profit strategy; that with b¼0 will emphasize the users’ benefit as best service strategy; and depend on the marketing preference the suppliers adopted, b can be given by any values between 0 and 1 as win–win strategy. Note that in Model (12), c00 is further normalized from c0 into [0, 1] to match the same scale with aj 0 . Maximize X J j ¼ 1 XFj fj ¼ 1 c0 xfj 0 Maximize X J j ¼ 1 XFj fj ¼ 1 aj 0 xfj 0 Subject to s0 xfj 0 rBfj , fj ¼ 1j ,2j , ... ,Fj , j ¼ 1,2, ... ,J XI i ¼ 1 XDi di 0 ¼ 1 x fj idi 0 Z1, fj ¼ 1j ,2j , ... ,Fj , j ¼ 1,2, ... ,J, x fj idi0 Af0,1g ð11Þ Maximize b 0 @X J j ¼ 1 XFj fj ¼ 1 c 00 xfj 0 1 Aþ ð1bÞ X J j ¼ 1 XFj fj ¼ 1 aj 0 xfj 0 Subject to s0 xfj 0 rBfj , fj ¼ 1j ,2j , ... ,Fj , j ¼ 1,2, ... ,J XI i ¼ 1 XDi di 0 ¼ 1 x fj idi 0 Z1, fj ¼ 1j ,2j , ... ,Fj , j ¼ 1,2, ... ,J, x fj idi0 Af0,1g, ð12Þ 3.3.2. Measures of recommendation performance To evaluate the performance of information retrieval, three measures of recall, precision, and F1 are usually employed [12,47]. They are defined as follows and will be used to evaluate our recommendation system as well. Recall ¼ jSðuserÞ \ RecðuserÞj=jRecðuserÞj, ð13Þ Precision ¼ jSðuserÞ \ RecðuserÞj=jSðuserÞj, ð14Þ FI ¼ 2 Recall Precision=RecallþPrecision, ð15Þ where S(user) is the actual basket for the compared user; Rec(user) is the recommendation item set. Recall is the ratio of items successfully recommended, whereas precision measures the user’s satisfactory degree. F1 is a leverage measure when recall and precision conflict with each other. 3.3.3. Summary of offline and online operation procedures After introducing the individual sub-modules of the proposed RS, we would summarize the operation procedures for the proposed RS. The procedures are categorized into offline and online operations. 3.3.3.1. Offline operation procedures. Step 1. Construct user-groups through user’s demographic features and item-groups by item attributes to obtain Uj ¼ fufjðogÞjfj ¼ 1j ,2j , ... ,Fj ,j ¼ 1,2, ... ,Jg and Pi ¼ fpdiðakÞjdi ¼ 1i ,2i , ... ,Di ,i ¼ 1,2, ... ,Ig. Step 2. Compute relative purchase priorities ðwj i Þ between user￾groups and item-groups by Eq. (3). Step 3. Compute similarity measures between user-groups. Similarity function is used from common item set (Eq. (6)) or non-common item set (Eq. (8)). Step 4. Derive out-of-clique probability measures by Eq. (4). 8 H.-F. Wang, C.-T. Wu / Computers & Operations Research ] (]]]]) ]]]–]]] Please cite this article as: Wang H-F, Wu C-T. A strategy-oriented operation module for recommender systems in E-commerce. Computers and Operations Research (2010), doi:10.1016/j.cor.2010.03.011