Worker Scheduling Algorithm

Question

The Problem

Here\'s the essence of the problem I want to solve. We have workers taking care of children in a nursery for set times during the weekend. There\'s 16 diff

Answer 1

The "hospitals/residents problem" could indeed work but it depends of your constraints :

• Hospital have a maximum capacity and will order the resident (most wanted to less wanted).
• Residents will order hospitals.
• No other constraints possible.

In your case the hospitals are workers and the residents are slots.

• Slots can order workers (maybe you prefer experimented ones in the morning...).
• Workers can order slots.
• But you can't have other constraints such as : "I've worked in the morning, I don't want to work the same day in the evening".

If that's ok for you then you have to possibilities :

• you want to advantage workers : "hospital oriented case".

  You will try to assign workers to their preferred slot(s).

• you want to advantage slots : "resident oriented case"

  Each slot will have their preferred workers.

I had to code it last year, here is the code.

/* 
RO : needed for Resident-Oriented version
HO : needed for Hospital-Oriented version
*/
const int MAX_R = 1000;
const int MAX_H = 1000;
const int INF = 1000*1000*1000;

You need to fill the input variables. Everything is straightforward :

• R_pref and H_pref are the list of preferences for residents/hospitals
• H_rank[h][r] is the rank of r in H_pref[h] : the position of r in the preference list of h

That's all.

// Input data
int R, H;                   // Number of Residents/Hospitals
int C[MAX_H];               // Capacity of hospitals
vector R_pref[MAX_R], H_pref[MAX_H]; // Preferences : adjency lists
/*RO*/int H_rank[MAX_H][MAX_R];   // Rank : rank of r in H_pref[h]
/*HO*/int R_rank[MAX_R][MAX_H];   // Rank : rank of h in R_pref[r]

No need to touch below.

// Internal data
int RankWorst[MAX_H];   // Rank of the worst r taken by h
/*RO*/int BestH[MAX_R];       // Indice of the best h in R_pref the r can get
/*HO*/int BestR[MAX_H];       // Indice of the best r in H_pref the h can get
int Size[MAX_H];        // Number of residents taken by h

// Output data
int M[MAX_R];

void stable_hospitals_RO()
{
    for(int h = 0 ; h < H ; h++)
      RankWorst[h] = H_pref[h].size()-1;
    fill_n(BestH, R, 0);
    fill_n(Size, H,0);
    fill_n(M,R,INF);
    for (int i = 0; i < R; i++)
        for (int r = i; r >= 0;)
        {
        if(BestH[r] == int(R_pref[r].size()))
            break;
            const int h = R_pref[r][BestH[r]++];
            if(Size[h]++ < C[h])
            {
                M[r] = h;
                break;
            }
            int WorstR = H_pref[h][RankWorst[h]];
            while(WorstR == INF || M[WorstR] != h) // Compute the worst
                WorstR = H_pref[h][--RankWorst[h]];
            if(H_rank[h][r] < RankWorst[h])        // Ranked better that worst
            {
                M[r] = h;
                M[r = WorstR] = INF;    // We have eliminate it, he need to put it somewhere
            }
        }
}
void stable_hospitals_HO()
{
    fill_n(BestR, H, 0);
    fill_n(Size, H,0);
    fill_n(M,R,INF);
    vector SH;
    for (int h = 0; h < H; h++)
        SH.push_back(h);
    while(!SH.empty())
    {
        int h = SH.back();
        if(Size[h] == C[h] || BestR[h] == int(H_pref[h].size())) // Full or no r available
        {
            SH.pop_back();
            break;
        }
    const int r = H_pref[h][BestR[h]++];
    // r is unassigned or prefer h to current hospital
        if(M[r] == INF || R_rank[r][h] < R_rank[r][M[r]]) 
        {
            if(++Size[h] == C[h]) // Will be full
                SH.pop_back();
            if(M[r] != INF) // Delete from M[r]
            {
                Size[M[r]]--;
                SH.push_back(M[r]);
            }
            M[r] = h;
        }
    }
}

Example of use to show how to build rank from prefs. (In that case the preference lists were on the stdin).

int main()
{
    scanf("%d%d",&R,&H);
    int num;
    // put inf

    for(int r = 0 ; r < R ; r++)
    {
        scanf("%d",&num);
        R_pref[r].resize(num);
        for(int h = 0 ; h < num ; h++)
        {
            scanf("%d",&R_pref[r][h]);
            R_rank[r][R_pref[r][h]] = h;
        }
    }
    for(int h = 0 ; h < H ; h++)
    {
        scanf("%d",&C[h]);
        scanf("%d",&num);
        H_pref[h].resize(num);
        for(int r = 0 ; r < num ; r++)
        {
            scanf("%d",&H_pref[h][r]);
            H_rank[h][H_pref[h][r]] = r;
        }
    } 
    stable_hospitals_RO();
    printf("\n\n\n\n");
    stable_hospitals_HO();
    return 0;
}

On an example : Hospitals 1 to 3, 6 résidents.

H_pref :

• 1 -> 2 5 6 1 (prefers 2 then 5 then 6 then 1)
• 2 -> 4 2 1 6 3 5
• 3 -> 1 2

R_pref :

• 1 -> 1 2 3
• 2 -> 3 1
• 3 -> 2 1
• 4 -> 1 3 2
• 5 -> 3 2 1
• 6 -> 3

H_rank :

• 1 -> 4 1 INF INF 2 3 (1 is in position 4 in H_pref[1], 3 is not theree)
• 2 -> 3 2 5 1 6 4
• 3 -> 1 2 INF INF INF INF

Similar for R_rank.

Hospital don't have to rank everyone et can also rank less people than their capacity.