A Heuristic Algorithm for Resource Allocation/Reallocation Problem

Algorithm 1

DPH algorithm for MMKP.

Notation:

   𝑧^∗: current objective function value

   𝑧: new objective function value

   𝑥^∗: current solution vector

   𝑥: new solution vector

initial value:

   𝑥,𝑥^∗: zero valued vectors

   𝑧,𝑧^∗: zero

   k: 1 (iteration)

Step  1: For 𝑔=1 to 𝑛 do begin

    𝑡=argmin_{1≤𝑗≤𝑙𝑔}{∑𝑟_𝑔𝑖𝑗},𝑖=1to𝑚,

   𝑥_𝑔𝑡=1,

   𝑧=𝑧+𝑝_𝑔𝑡

   end for

do begin

 𝑘=𝑘+1,𝑧^∗=𝑧,𝑥^∗=𝑥

Step  2: For our convenience convert

   𝑝_𝑖𝑗into𝑐_𝑗,𝑗=∑𝑙_𝑖,

   𝑟_𝑘𝑖𝑗into𝑎_𝑖𝑗,𝑖=1to𝑚,

   𝑗=∑𝑙_𝑖

For 𝑔=1 to 𝑛 do begin

Step  3: Intercept matrix 𝑑_𝑖𝑗={^{𝑏𝑖/𝑎𝑖𝑗,𝑎𝑖𝑗>0,}_{𝑀(alargevalue)otherwise}

Step  4: Redundant variables 𝑟𝑣

   𝑟𝑣=arg_{1≤𝑗≤𝑛}{𝑑_𝑖𝑗<1),𝑖=1,…,𝑚,

   𝑎_𝑖𝑟𝑣=0,∀𝑖,

   𝑥_𝑟𝑣=0

Step  5: Dominant variable s

   total_𝑗=∑𝑑_𝑖𝑗,𝑖=1,…,𝑚,𝑗=1,…,𝑙_𝑔,

   𝑠=argmax{total_𝑗∗𝑐_𝑗},∀𝑗

   if 𝑥_𝑠=0and𝑝_𝑠>𝑝_𝑗∗(𝑗^∗---thevariablewhichisalreadyinthesolution)

   then

   𝑥_𝑠=1,

   𝑧=𝑧−𝑝_𝑗∗+𝑝_𝑠,

   𝑏_𝑖=𝑏_𝑖−𝑎_𝑖𝑠+𝑎_𝑖𝑗^∗,∀𝑖

   else

   𝑧=𝑧+𝑝_𝑗∗,

   𝑏_𝑖=𝑏_𝑖−𝑎_𝑖𝑗^∗,∀𝑖

   end if

end for

while (𝑧^∗<𝑧and𝑘≤10)

Display 𝑥 and 𝑧.