```! The Holt-Modigliani-Muth-Simon-Hanssmann-Hess (HanssmannHess.lng) production planning model. Given a fluctuating demand forecast for each period in a planning horizon, what combination of: carrying inventory, backlogging, using overtime, and changing workforce level from period to period is the best way of meeting this demand? ; ! Keywords: Holt-Modigliani, Hanssmann-Hess, Production planning, Workforce scheduling; SETS: period: w, p, invp, invn, chgup, chgdn, ovt, dem; ENDSETSDATA: cr = 80; ! Cost of regular time; ch = 60; ! Cost of hiring; cf = 40; ! Cost of firing/layoffs; co = 120; ! Cost of overtime; ci = 130; ! cost of inventory; cs = 150; ! cost of shortage; k = 2; ! workforce needed/unit production; w0 = 100; ! initial workforce level; inv0 = 50;! initial inventory; ! Demand forecast over planning horizon; dem = 90 95 110 120 150 115 120 120 115 100 95 90; ENDDATA ! Parameters: dem(t) = demand in period t, k = workforce level required per unit production, Variables w(t) = workforce level in period t, invp(t) = positive inventory in period t, invn(t) = negative inventory(backlog) in t, chgup(t) = change up of workforce in t, chgdn(t) = change down of workforce in t, ovt(t) = overtime in period t ; ! minimize sum of the various cost types; min = crtot + chtot + cftot + cotot + citot + cstot; ! Total regular time cost; crtot = cr*@SUM( period( t): w(t)); ! Total hiring cost; chtot = ch*@SUM( period( t): chgup(t)); ! Total firing cost; cftot = cf*@SUM( period( t): chgdn(t)); ! Total overtime cost; cotot = co*@SUM( period( t): ovt(t)); ! Total cost of positive inventory; citot = ci*@SUM( period( t): invp(t)); ! Total cost of backlogging; cstot = cs*@SUM( period( t): invn(t)); ! First period is special; ! Inventory balance equation; inv0 + p(1) = invp(1) - invn(1) + dem(1); ! Workforce change; chgup(1) - chgdn(1) = w(1) - w0; ! Overtime to cover excess of production beyond regular time; ovt(1) >= k*p(1) - w(1); ! For subsequent periods; @FOR( period(t) | t #gt# 1: ! Inventory balance; invp(t-1) - invn(t-1) + p(t) = invp(t) - invn(t) + dem(t); ! Workforce change; chgup(t) - chgdn(t) = w(t) - w(t-1); ! Overtime; ovt(t) >= k*p(t) - w(t); ); ! At the end of the planning horizon, you may wish to put some constraints on ending inventory level and workforce level; ```