A polynomial time algorithm for the single-item lot sizing problem with capacities, minimum order quantities and dynamic time windows

This paper deals with the single-item capacitated lot sizing problem with concave production and storage costs, considering minimum order quantity and dynamic time windows. The frequency constraints on the production lots are modeled by dynamic time windows. Between two consecutive production lots, there are at least Q periods and at most R periods. This paper presents an optimal algorithm in O ( ( T - Q ) 2 ( R - Q ) T 4 Q 3 ) , which is bounded by O ( T 7 ) .

[1]  G. Bitran,et al.  Computational Complexity of the Capacitated Lot Size Problem , 1982 .

[2]  Stéphane Dauzère-Pérès,et al.  Capacitated Multi-Item Lot-Sizing Problems with Time Windows , 2006, Oper. Res..

[3]  Bernard Penz,et al.  Comparison of just-in-time and time window delivery policies for a single-item capacitated lot sizing problem , 2011 .

[4]  Stéphane Dauzère-Pérès,et al.  Single item lot sizing problems , 2006, Eur. J. Oper. Res..

[5]  Bernard Penz,et al.  Corrigendum to "A polynomial time algorithm to solve the single-item capacitated lot sizing problem with minimum order quantities and concave costs" [Eur. J. Oper. Res. (2012) 10-16] , 2013, Eur. J. Oper. Res..

[6]  Albert P. M. Wagelmans,et al.  An $O(T^3)$ algorithm for the economic lot-sizing problem with constant capacities , 1993 .

[7]  M. Florian,et al.  DETERMINISTIC PRODUCTION PLANNING WITH CONCAVE COSTS AND CAPACITY CONSTRAINTS. , 1971 .

[8]  Laurence A. Wolsey,et al.  Lot-sizing with production and delivery time windows , 2005, Math. Program..

[9]  Knut Richter,et al.  An O(T3) algorithm for the capacitated lot sizing problem with minimum order quantities , 2011, Eur. J. Oper. Res..

[10]  Bernard Penz,et al.  A polynomial time algorithm to solve the single-item capacitated lot sizing problem with minimum order quantities and concave costs , 2012, Eur. J. Oper. Res..

[11]  Safia Kedad-Sidhoum,et al.  Uncapacitated lot-sizing problem with production time windows, early productions, backlogs and lost sales , 2011 .

[12]  Chung-Yee Lee,et al.  Inventory replenishment model: lot sizing versus just-in-time delivery , 2004, Oper. Res. Lett..

[13]  Bernard Penz,et al.  Stability contracts between supplier and retailer: a new lot sizing model , 2015 .

[14]  Hark-Chin Hwang.  Dynamic lot-sizing model with production time windows , 2007 .

[15]  Rommert Dekker,et al.  An efficient optimal solution method for the joint replenishment problem with minimum order quantities , 2003, Eur. J. Oper. Res..

[16]  M. Katehakis,et al.  Effective control policies for stochastic inventory systems with a minimum order quantity and linear costs , 2007 .

[17]  Suresh P. Sethi,et al.  Forecast, Solution, and Rolling Horizons in Operations Management Problems: A Classified Bibliography , 2001, Manuf. Serv. Oper. Manag..

[18]  Albert P. M. Wagelmans,et al.  Four equivalent lot-sizing models , 2008, Oper. Res. Lett..

[19]  Albert P. M. Wagelmans,et al.  A comparison of methods for lot-sizing in a rolling horizon environment , 2005, Oper. Res. Lett..

[20]  Chung-Yee Lee,et al.  A Dynamic Lot-Sizing Model with Demand Time Windows , 2001 .

[21]  Diego Klabjan,et al.  Single Item Lot-Sizing Problem with Minimum Order Quantity , 2011 .