Discrete Particle Swarm Optimization with Scout Particles for Library Materials Acquisition

Table 1

Notations.

Variable	Description
𝑛	Number of materials
𝑚	Number of departments
𝑞	Number of categories
𝑟	Number of languages
𝑝𝑖𝑗	Preference for material i recommended by department 𝑗, for 1≤𝑖≤𝑛 and 1≤𝑗≤𝑚
𝑐𝑖	Cost of material i, for 1≤𝑖≤𝑛
𝐵𝑗	Budget limit of department j, for 1≤𝑗≤𝑚
𝐿𝑈𝑙	Upper bound on the number of materials in language l, for 1≤𝑙≤𝑟
𝐿𝐿𝑙	Lower bound on the number of materials in language l, for 1≤𝑙≤𝑟
𝑎𝑖𝑙	𝑎𝑖𝑙=1 if material i is in language q; 𝑎𝑖𝑙=0 otherwise, for 1≤𝑖≤𝑛 and 1≤𝑙≤𝑟
𝐶𝑈𝑘	Upper bound on the number of materials in category k, for 1≤𝑘≤𝑞
𝐶𝐿𝑘	Lower bound on the number of materials in category k, for 1≤𝑘≤𝑞
𝑏𝑖𝑘	𝑏𝑖𝑘=1 if material i belongs to category k; 𝑏𝑖𝑘=0 otherwise, for 1≤𝑖≤𝑛 and 1≤𝑙≤𝑟
𝑥𝑖𝑗	Decision variable: 𝑥𝑖𝑗=1 if material i is acquired for department j from which the cost will be charged; 𝑥𝑖𝑗=0 otherwise, for 1≤𝑖≤𝑛 and 1≤𝑗≤𝑚
𝑧𝑖	Auxiliary variable: 𝑧𝑖=1, if ∑^𝑚𝑗=1𝑥𝑖𝑗>0; otherwise 𝑧𝑖=0, for 1≤𝑖≤𝑛 (𝑧𝑖 reveals whether material i is acquired or not)
𝑒𝑖𝑗	Actual expenses of material i by department j, for 1≤𝑖≤𝑛 and 1≤𝑗≤𝑚