仓储能力约束和缺货下两易逝品联合采购动态批量决策
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摘要
研究了两种仓储能力约束情形下两易逝品联合采购动态批量决策问题。易逝品的特征是库存损失率及库存持有成本依赖于产品库存持有时间,在需求损失(缺货)的情况下将构建的收益最大化模型转化为成本最小化模型,成本最小化模型中包含联合启动成本,两产品单独启动成本、变动采购成本、库存持有成本和缺货成本,分析得出了最优解的结构特性,在此基础上,设计动态规划算法求解问题。同时分析了无投机性成本结构的特殊情形,设计了前向算法求解问题。
The paper analyzes the two-product dynamic lot-size problem with perishable inventory and joint ordering under two cases of inventory bounds.The stocks' deterioration rates and inventory holding costs in every period depend on the age of the stock.We transform the revenue maximization function into cost minimization function,which include joint setup costs,individual setup costs,ordering costs,inventory holding costs and stockout costs.We obtain some structural properties of the optimal solution for a T-period problem and use them to develop a dynamic programming algorithm.Finally,we also consider the case with no speculative motive in holding inventory and stockout.
The paper analyzes the two-product dynamic lot-size problem with perishable inventory and joint ordering under two cases of inventory bounds.The stocks' deterioration rates and inventory holding costs in every period depend on the age of the stock.We transform the revenue maximization function into cost minimization function,which include joint setup costs,individual setup costs,ordering costs,inventory holding costs and stockout costs.We obtain some structural properties of the optimal solution for a T-period problem and use them to develop a dynamic programming algorithm.Finally,we also consider the case with no speculative motive in holding inventory and stockout.
引文
[1]Wagner H M,Whitin T M.Dynamic version of the economic lot size model[J].Management Science,1958,5(1):89~96.
[2]Smith L A.Simultaneous inventory and pricing decisions for perishable commodities with price fluctuation constraints[J].INFOR,1975,13(1):82~87.
[3]Friedman Y,Yehuda H.A dynamic lot-size model with inventory deteriotration[J].INFOR,1978,16(2):183~188.
[4]Hsu V N.Dynamic economic lot size model with perishable inventory[J].Management Science,2000,6(8):1159~1169.
[5]Hsu V N.An economic lot size model for perishable products with age-dependent inventory and backorder costs[J].IIE Transactions,2003,(35):775~780.
[6]Chu L Y,Hsu V N,Shen Z J Max.An economic lot-sizing problem inventory and economies of scale costs:Approximation solutions and worst case analysis[J].Naval Research Logistics,2005,52(6):536~548.
[7]Peng S Y,Wee H M,Yang C C,Jou J Y T.A note on an economic lot size model for a perishable age-dependent inventory system with backorders[J].Journal of Information and Optimization Sciences,2008,29(1):191~202.
[8]Bai Q G,et al.Anapproximation solution to the ELSmodel for perishable inventory with backlogging[C]//The 7th International Symposium on Operations Research and Its Applications,Lijiang,2008:66~73.
[9]Bai Q G,et al.A note on an economic lot-sizing problem inventory and economies of scale costs:Approximation solutions and worst case analysis[J].International Journal of Automation and Computing,2010,7(1):132~136.
[10]Sargut F Z,Isik G.Dynamic economic lot size model with perishable inventory and capacity constraints[J].Applied Mathematical Modelling,2017,48:806~820.
[11]Liu X,Chu F,Chu C,Wang C.Lot sizing with bounded and inventory and lost sales[J].International Journal of Production Research,2007,45:5881~5894.
[12]Liu X.A polynomial time algorithm for production planning with bounded inventory[J].International Journal of Advanced Manufacturing Technology,2008,(39):774~782.
[13]Liu X,Tu Y L.Production planning with limited inventorycapacity and allowed stockout[J].International Journal of Production Economics,2008,(111):180~191.
[14]Hwang H C,Heuvel W V D,Wagelmans A P M.The economic lot-sizing problem with lost sales and bounded inventory[J].IIE Transactions,2013,(45):912~924.
[15]Chu F,Chu C C,Liu X.Lot sizing models with backlog and out-sourcing[J].IEEE International Conference on Systems,Man,Cybernetics,2004:4342~4347.
[16]Chu F,Chu C C.Polynomial algorithms for single item lot-sizing models with bounded inventory and backlogging,or outsourcing[J].IEEE Transactions on Automation Science and Engineering,2007,4(2):233~251.
[17]Chu F,Chu C.Single-Item dynamic lot-sizing models with bounded inventory and outsourcing[J].IEEE Transactions on Systems,Man,and Cybernetics,2008,38(1):70~77.
[18]Chu C C,etal.A polynomial algorithm for lot-sizing problem with backlogging,outsourcing and limited inventory[J].Computer and Industrial Engineering,2013,64(1):200~210.
[19]Zhong J H,Chu F,Chu H B,Yang S L.Polynomial dynamic programming algorithms for lot sizing models with bounded inventory and stockout and or backlogging[J].Journal of Systems Science and Systems Engineering,2016,25(3):370~397.
[20]Sandbothe R A,Thompson G L.A forward algorithm for the capacitated lot size model with stockouts[J].Operations Research,1990,38(3):474~486.
[21]Sandbothe R A,Thompson G L.Decision horizons for the capacitated lot size model with inventory bounds and stockouts[J].Computers&Operations Research,1993,20(5):455~465.
[22]Aksen D,Altnkemer K,Chand S.The single-item lot-sizing problem with immediate lost sales[J].European Journal of Operational Research,2003,147(3):558~566.
[23]Aksen D.Loss of customer goodwill in the uncapacitated lot-sizing problem[J].Computer and Operations Research,2007,34(9):2805~2823.
[24]Berk E,Toy A O,Hazir O.Single item lot-sizing problem for a worm/cold process with immediate lost sales[J].European Journal of Operational Research,2008,187(3):1251~1267.
[25]Absi N,Sidhoum S K.The multi-item capacitated lot-sizing problem with setup times and shortage costs[J].European Journal of Operational Research,2008,185(3):1351~1374.
[26]Absi N,et al.Uncapacitated lot-sizing problem with production time window,early production,backlog and lost sale[J].International Journal of Production Research,2011,49:2551~2566.
[27]Wang N,He Z W,Sun J C,Xie H Y,Shi W.Asingle-item uncapacitated lot-sizing problem with remanufacturing and outsourcing[J].Procedia Engineering,2011,15(5):5170~5178.
[28]Narenji M,Ghomi,S M T F,Nooraie S V R.Grouping in decomposition method for multi-item capacitated lot-szing problem with immediate lost sales and joint and item-dependent setup cost[J].International Journal of System Science,2011,42(3):489~498.
[29]Gayon J P,Massonnet G,Rapine C,Satuffer G.Constant approximation algorithms for the one warehouse multiple retailers problem with backlog or lost-sales[J].European Journal of Operational Research,2016,250(1):155~163.
[30]黄玲,钟金宏,杨善林.考虑延期交货、转包和非减库存能力约束的单产品批量模型[J].系统工程理论与实践,2007,27(9):87~95.
[31]黄玲,钟金宏,倪志伟,杨善林.允许缺货和转包的受限批量模型的多项式算法[J].系统仿真学报,2008,20(11):2800~2805.
[32]钟金宏,黄玲.带外包受限批量模型的启发式遗传算法[J].系统仿真学报,2011,23(12):2623~2628.
[33]王能民,孙青林,孙林岩.考虑外包的单产品再制造批量决策[J].运筹与管理,2011,20(5):162~168.
[34]徐娟,汪小京,刘志学.不同顾客环境下生产及外包的动态批量问题[J].系统工程,2014,32(10):63~70.
[35]李建军,周熙登,张东梅.需求依赖支付期限的的易逝品库存最优策略[J].系统工程,2016,34(1):96~101.
[36]彭扬,陈金叶,傅培华.时变需求下基于部分预付策略的易腐品库存控制[J].系统工程,2016,34(3):20~24.
[37]林峰,贾涛,李然.基于改进C-W算法的易腐品一体化库存路径问题研究[J].系统工程,2016,34(8):100~107.
[2]Smith L A.Simultaneous inventory and pricing decisions for perishable commodities with price fluctuation constraints[J].INFOR,1975,13(1):82~87.
[3]Friedman Y,Yehuda H.A dynamic lot-size model with inventory deteriotration[J].INFOR,1978,16(2):183~188.
[4]Hsu V N.Dynamic economic lot size model with perishable inventory[J].Management Science,2000,6(8):1159~1169.
[5]Hsu V N.An economic lot size model for perishable products with age-dependent inventory and backorder costs[J].IIE Transactions,2003,(35):775~780.
[6]Chu L Y,Hsu V N,Shen Z J Max.An economic lot-sizing problem inventory and economies of scale costs:Approximation solutions and worst case analysis[J].Naval Research Logistics,2005,52(6):536~548.
[7]Peng S Y,Wee H M,Yang C C,Jou J Y T.A note on an economic lot size model for a perishable age-dependent inventory system with backorders[J].Journal of Information and Optimization Sciences,2008,29(1):191~202.
[8]Bai Q G,et al.Anapproximation solution to the ELSmodel for perishable inventory with backlogging[C]//The 7th International Symposium on Operations Research and Its Applications,Lijiang,2008:66~73.
[9]Bai Q G,et al.A note on an economic lot-sizing problem inventory and economies of scale costs:Approximation solutions and worst case analysis[J].International Journal of Automation and Computing,2010,7(1):132~136.
[10]Sargut F Z,Isik G.Dynamic economic lot size model with perishable inventory and capacity constraints[J].Applied Mathematical Modelling,2017,48:806~820.
[11]Liu X,Chu F,Chu C,Wang C.Lot sizing with bounded and inventory and lost sales[J].International Journal of Production Research,2007,45:5881~5894.
[12]Liu X.A polynomial time algorithm for production planning with bounded inventory[J].International Journal of Advanced Manufacturing Technology,2008,(39):774~782.
[13]Liu X,Tu Y L.Production planning with limited inventorycapacity and allowed stockout[J].International Journal of Production Economics,2008,(111):180~191.
[14]Hwang H C,Heuvel W V D,Wagelmans A P M.The economic lot-sizing problem with lost sales and bounded inventory[J].IIE Transactions,2013,(45):912~924.
[15]Chu F,Chu C C,Liu X.Lot sizing models with backlog and out-sourcing[J].IEEE International Conference on Systems,Man,Cybernetics,2004:4342~4347.
[16]Chu F,Chu C C.Polynomial algorithms for single item lot-sizing models with bounded inventory and backlogging,or outsourcing[J].IEEE Transactions on Automation Science and Engineering,2007,4(2):233~251.
[17]Chu F,Chu C.Single-Item dynamic lot-sizing models with bounded inventory and outsourcing[J].IEEE Transactions on Systems,Man,and Cybernetics,2008,38(1):70~77.
[18]Chu C C,etal.A polynomial algorithm for lot-sizing problem with backlogging,outsourcing and limited inventory[J].Computer and Industrial Engineering,2013,64(1):200~210.
[19]Zhong J H,Chu F,Chu H B,Yang S L.Polynomial dynamic programming algorithms for lot sizing models with bounded inventory and stockout and or backlogging[J].Journal of Systems Science and Systems Engineering,2016,25(3):370~397.
[20]Sandbothe R A,Thompson G L.A forward algorithm for the capacitated lot size model with stockouts[J].Operations Research,1990,38(3):474~486.
[21]Sandbothe R A,Thompson G L.Decision horizons for the capacitated lot size model with inventory bounds and stockouts[J].Computers&Operations Research,1993,20(5):455~465.
[22]Aksen D,Altnkemer K,Chand S.The single-item lot-sizing problem with immediate lost sales[J].European Journal of Operational Research,2003,147(3):558~566.
[23]Aksen D.Loss of customer goodwill in the uncapacitated lot-sizing problem[J].Computer and Operations Research,2007,34(9):2805~2823.
[24]Berk E,Toy A O,Hazir O.Single item lot-sizing problem for a worm/cold process with immediate lost sales[J].European Journal of Operational Research,2008,187(3):1251~1267.
[25]Absi N,Sidhoum S K.The multi-item capacitated lot-sizing problem with setup times and shortage costs[J].European Journal of Operational Research,2008,185(3):1351~1374.
[26]Absi N,et al.Uncapacitated lot-sizing problem with production time window,early production,backlog and lost sale[J].International Journal of Production Research,2011,49:2551~2566.
[27]Wang N,He Z W,Sun J C,Xie H Y,Shi W.Asingle-item uncapacitated lot-sizing problem with remanufacturing and outsourcing[J].Procedia Engineering,2011,15(5):5170~5178.
[28]Narenji M,Ghomi,S M T F,Nooraie S V R.Grouping in decomposition method for multi-item capacitated lot-szing problem with immediate lost sales and joint and item-dependent setup cost[J].International Journal of System Science,2011,42(3):489~498.
[29]Gayon J P,Massonnet G,Rapine C,Satuffer G.Constant approximation algorithms for the one warehouse multiple retailers problem with backlog or lost-sales[J].European Journal of Operational Research,2016,250(1):155~163.
[30]黄玲,钟金宏,杨善林.考虑延期交货、转包和非减库存能力约束的单产品批量模型[J].系统工程理论与实践,2007,27(9):87~95.
[31]黄玲,钟金宏,倪志伟,杨善林.允许缺货和转包的受限批量模型的多项式算法[J].系统仿真学报,2008,20(11):2800~2805.
[32]钟金宏,黄玲.带外包受限批量模型的启发式遗传算法[J].系统仿真学报,2011,23(12):2623~2628.
[33]王能民,孙青林,孙林岩.考虑外包的单产品再制造批量决策[J].运筹与管理,2011,20(5):162~168.
[34]徐娟,汪小京,刘志学.不同顾客环境下生产及外包的动态批量问题[J].系统工程,2014,32(10):63~70.
[35]李建军,周熙登,张东梅.需求依赖支付期限的的易逝品库存最优策略[J].系统工程,2016,34(1):96~101.
[36]彭扬,陈金叶,傅培华.时变需求下基于部分预付策略的易腐品库存控制[J].系统工程,2016,34(3):20~24.
[37]林峰,贾涛,李然.基于改进C-W算法的易腐品一体化库存路径问题研究[J].系统工程,2016,34(8):100~107.