Solving a vendor–buyer integrated problem with rework and a specific multi-delivery policy by a two-phase algebraic approach

This paper is concerned with solving a vendor–buyer integrated inventory problem with rework and a specific multi-delivery policy by a two-phase algebraic approach. Conventional method to the problem is to use differential calculus and Hessian matrix equations to prove convexity of system cost function first before determining the optimal production–shipment policy for such a vendor–buyer integrated system (Chiu et al., 2013b). This study presents an alternative two-phase algebraic approach to derive the same optimal policy. The proposed straightforward algebraic derivations can assist practitioners who may not have sufficient knowledge of calculus in understanding with ease such a real life vendor–buyer integrated system.

[1]  Singa Wang Chiu,et al.  Alternative approach for solving replenishment lot size problem with discontinuous issuing policy and rework , 2012, Expert Syst. Appl..

[2]  Ming-Hon Hwang,et al.  Optimal common cycle time for a multi-item production system with discontinuous delivery policy and failure in rework , 2013 .

[3]  M. A. Hoque,et al.  Synchronization in the single-manufacturer multi-buyer integrated inventory supply chain , 2008, Eur. J. Oper. Res..

[4]  L. B. Schwarz,et al.  Fill-Rate Optimization in a One-Warehouse N-Identical Retailer Distribution System , 1985 .

[5]  Yuan-Shyi Peter Chiu,et al.  Replenishment run time problem with machine breakdown and failure in rework , 2012, Expert Syst. Appl..

[6]  Singa Wang Chiu,et al.  Determining production–shipment policy for a vendor–buyer integrated system with rework and an amending multi-delivery schedule , 2013 .

[7]  Arthur F. Veinott,et al.  Analysis of Inventory Systems , 1963 .

[8]  W. Shih.  Optimal inventory policies when stockouts result from defective products , 1980 .

[9]  A. G. de Kok.  Approximations for a Lost-Sales Production/Inventory Control Model with Service Level Constraints , 1985 .

[10]  S. Viswanathan,et al.  Optimal strategy for the integrated vendor-buyer inventory model , 1998, Eur. J. Oper. Res..

[11]  Ronald L. Rardin,et al.  Optimization in operations research , 1997 .

[12]  Suresh Kumar Goyal,et al.  An integrated inventory model for a single supplier-single customer problem , 1977 .

[13]  Sarada Prasad Sarmah,et al.  Buyer vendor coordination models in supply chain management , 2006, Eur. J. Oper. Res..

[14]  Ruud H. Teunter,et al.  Lot-sizing for a single-stage single-product production system with rework of perishable production defectives , 2003, OR Spectr..

[15]  Leroy B. Schwarz,et al.  A Simple Continuous Review Deterministic One-Warehouse N-Retailer Inventory Problem , 1973 .

[16]  Viliam Makis.  Optimal lot sizing and inspection policy for an EMQ model with imperfect inspections , 1998 .

[17]  Shib Sankar Sana,et al.  Optimal replenishment order for uncertain demand in three layer supply chain , 2012 .

[18]  Frederick S. Hillier,et al.  Introduction of Operations Research , 1967 .

[19]  S. Sana.  A collaborating inventory model in a supply chain , 2012 .

[20]  Robert W. Grubbström,et al.  The EOQ with backlogging derived without derivatives , 1999 .

[21]  Hong-Dar Lin,et al.  A note on optimal replenishment policy for imperfect quality EMQ model with rework and backlogging , 2008, Comput. Math. Appl..

[22]  Candace Arai Yano,et al.  The economic lot and delivery scheduling problem: The single item case , 1992 .

[23]  L. Ouyang,et al.  An integrated single-vendor single-buyer inventory system with shortage derived algebraically , 2003 .

[24]  Gyana R. Parija,et al.  An Optimal Batch Size for a Production System Operating Under a Fixed-Quantity, Periodic Delivery Policy , 1994 .

[25]  Moawia Alghalith.  The interaction among production, hedging and investment decisions , 2013 .

[26]  Jonas C. P. Yu,et al.  Optimal inventory model for items with imperfect quality and shortage backordering , 2007 .