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Aggregate planning in production

Aggregate planning in production. Parametric linear model. Minimize ∑ t ( C t P P t +C t W W t +C t H H t +C t L L t +C t I I t +C t B B t ) Subject to P t ≤ n t W t Production-capacity constraints

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Aggregate planning in production

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  1. Aggregate planning in production

  2. Parametric linear model

  3. Minimize ∑t (CtPPt+CtWWt+CtHHt+CtLLt+CtIIt+CtBBt) Subject to Pt ≤ ntWt Production-capacity constraints Wt = Wt-1+Ht-Lt Work-force constraints It-Bt = It-1-Bt-1+Pt-Dt Inventory-balance constraints Pt , Wt , Ht , Lt , It , Bt ≥ 0

  4. T: periods (constant) & t : index of periods (constant) Dt: demand in period t (constant) nt: number of units that can be made by one worker in period t (constant) CtP: cost to produce one unit for period t (constant) CtW: cost for one worker in period t (constant) CtH: cost to hire one worker in period t (constant) CtL: cost to lay off one worker in period t (constant)

  5. CtI: cost to hold one unit in inventory for period t (constant) CtB: cost to backorder one unit for period t (constant) Pt: number of units produced in period t (variable) Wt: number of workers available in period t (variable) Ht: number of workers hired in period t (variable) Lt: number of workers laid off in period t (variable) It: number of units held in inventory at the end of period t (variable) Bt: number of units backordered at the end of period t (variable)

  6. CtW= (wage in a day)*(number of working days in period t) nt= (number of units that each worker produce in a day) *(working days in period t)

  7. Numerical example

  8. Required Data & information

  9. Production: 4 units/worker/day Wage: $120 worker/day Hiring cost: $450 /worker (CtH) Firing cost: $600 /worker (CtL) Holding cost: $5 /unit/month (CtI) Backorder cost: 0 /unit

  10. Because production costs don’t change over the periods, we don’t consider them. So CtP= 0 Also we consider no backorder and we have: CtH= 450 , CtL= 600 , CtI= 5 for all periods(t) For example: C1W= 120 * 21 = 2520 n1= 4 * 21 = 84

  11. Final Linear Model

  12. Minimize 0P1+0P2+0P3+0P4+0P5+0P6 +2520W1+2400W2+2760W3 +2520W4+2640W5+2640W6 +450H1+450H2+450H3+450H4 +450H5+450H6 +600L1+600L2+600L3 +600L4+600L5+600L6 +5I1+5I2+5I3+5I4+5I5+5I6 Objective Function

  13. P1 ≤ 84W1 P2 ≤ 80W2 P3 ≤ 92W3 P4 ≤ 84W3 P5 ≤ 88W5 P6 ≤ 88W6 Production-capacity constraints

  14. W1= 35+H1-L1 W2= W1+H2-L2 W3= W2+H3-L3 W4= W3+H4-L4 W5= W4+H5-L5 W6= W5+H6-L6 Work-force constraints

  15. I1= P1-2760 I2= I1+P2-3320 I3= I2+P3-3970 I4= I3+P4-3540 I5= I4+P5-3180 I6= I5+P6-2900 Inventory-balance constraints

  16. And P1, P2, …, P6, W1, W2, …, W6 , H1, H2, …, H6, L1, L2, …, L6 , I1, I2, …, I6 ≥ 0

  17. Solving the model inlingo

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