! The simplest possible work staffing model in LINGO (StaffPatSimp.lng); ! Keywords: Staff scheduling, Workforce scheduling, Covering, Scheduling, Chart, Graph, Bar chart, ChartBar; SETS: ! The generic data structures; PERIOD: REQUIRED, SUPPLIED; WORKPAT: NUM2RUN, COST; WXD( WORKPAT, PERIOD): ONRNOT; ENDSETS DATA: ! The circular week staffing problem; ! The names for the periods; PERIOD = MON TUE WED THU FRI SAT SUN; ! Number folks required on duty each period; REQUIRED= 19 17 15 19 17 14 12; ! The possible work patterns. ONRNOT(i,j) = 1 if workpattern i has someone on duty in period j; ONRNOT = 1 1 1 1 1 0 0 ! 5 days/week; 0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 1 ; ! Cost per unit of each work pattern; ! COST = 1 1 1 1 1 1 1; ! Make SAT and SUN slightly less attractive; COST = 1 1.01 1.05 1.05 1.05 1.05 1.04; ! Make SUN more attractive; ! COST = 1 1 0.999 0.999 0.999 0.999 0.999; ENDDATA SUBMODEL STAFFIT: ! Minimize cost of people used over all patterns; MIN = OBJ; OBJ= @SUM( WORKPAT( i): COST(i)*NUM2RUN( i)); ! For each period j, patterns used must cover that period; @FOR( PERIOD( j): SUPPLIED( j) = @SUM( WORKPAT( i): ONRNOT(i,j)*NUM2RUN(i)); SUPPLIED( j) >= REQUIRED( j); ! Meet demand; ); ! Can only hire integer people; @FOR(WORKPAT( j): @GIN( NUM2RUN( j))); ENDSUBMODEL CALC: @SOLVE(STAFFIT); ! Write a lil report; @FOR( WORKPAT(i) | NUM2RUN #GT# 0: @WRITE(' Put ', NUM2RUN(i),' people on the work pattern:', @NEWLINE(1)); @FOR(PERIOD(j): @WRITE(' ',ONRNOT(i,j))); @WRITE( @NEWLINE(2)); ); ! Generate a bar chart of Required vs. Supplied; @CHARTBAR('Staff Required vs. Supplied: Multi-Bar Chart, Cost= ' +@FORMAT(OBJ,'6.1f'),! Title of chart; 'Day of week', ! X axis label; '# People on duty', ! Y axis label; 'Required', REQUIRED, ! Quantity 1; 'Supplied', SUPPLIED); ! Quantity 2; ENDCALC