Joint replenishment policy with backordering and special sale

In this paper, an inventory control model with a joint replenishment policy and a temporary discount is developed. We assume that shortage is allowed and buyer uses an economic order quantity inventory control model. Different cases based on ordering policies for the first joint replenishment if the special order is not taken, and coincidence of a special period length with a positive or negative inventory level of the last regular period length, are investigated. Furthermore, several theorems are proved through which closed-form solutions are obtained. At the end, two numerical examples illustrate the different situations that the buyer may face and sensitivity analyses for both examples are reported.

[1]  Richard J. Tersine,et al.  Economic purchasing strategies for temporary price discounts , 1995 .

[2]  Saeed Zolfaghari,et al.  An inventory model with random discount offerings , 2011 .

[3]  Prakash L. Abad.  Buyer's response to a temporary price reduction incorporating freight costs , 2007, Eur. J. Oper. Res..

[4]  Nirmal Kumar Mandal,et al.  Multi-item imperfect production lot size model with hybrid number cost parameters , 2006, Appl. Math. Comput..

[5]  E. Silver.  A Simple Method of Determining Order Quantities in Joint Replenishments Under Deterministic Demand , 1976 .

[6]  Meir J. Rosenblatt,et al.  An Improvement of Silver's Algorithm for the Joint Replenishment Problem , 1983 .

[7]  Nita H. Shah,et al.  Retailer's pricing, credit and inventory policies for deteriorating items in response to temporary price/credit incentives , 2003 .

[8]  Ata Allah Taleizadeh,et al.  Constraint multiproduct joint-replenishment inventory control problem using uncertain programming , 2011, Appl. Soft Comput..

[9]  S. T. A. Niaki,et al.  Multiproduct EPQ model with single machine, backordering and immediate rework process , 2011 .

[10]  W. Hsu,et al.  EOQ model for imperfective items under a one-time-only discount , 2009 .

[11]  Elisa Luciano,et al.  Capital structure and inventory management:: The temporary sale price problem , 1999 .

[12]  T. M. Whitin.  Inventory Control in Theory and Practice , 1952 .

[13]  Tsung-Hui Chen,et al.  The multi-item replenishment problem in a two-echelon supply chain: the effect of centralization versus decentralization , 2005, Comput. Oper. Res..

[14]  Faruk Güder,et al.  Fixed cycle ordering policies for capacitated multiple item inventory systems with quantity discounts , 2000 .

[15]  Bhaba R. Sarker,et al.  Optimal inventory system with two backlog costs in response to a discount offer , 2011 .

[16]  Richard J. Tersine,et al.  Composite lot sizing with quantity and freight discounts , 1995 .

[17]  Prakash L. Abad,et al.  Optimal price and lot size when the supplier offers a temporary price reduction over an interval , 2003, Comput. Oper. Res..

[18]  S. Goyal.  Determination of Optimum Packaging Frequency of Items Jointly Replenished , 1974 .

[19]  B. Sarker,et al.  Optimal ordering policies in response to a discount offer , 2006 .

[20]  Ata Allah Taleizadeh,et al.  Multi products single machine economic production quantity model with multiple batch size , 2011 .

[21]  Alireza Ardalan.  Optimal prices and order quantities when temporary price discounts result in increase in demand , 1994 .

[22]  Francisco J. Arcelus,et al.  A retailer's decision process when anticipating a vendor's temporary discount offer , 2009, Comput. Ind. Eng..

[23]  Leopoldo Eduardo Cárdenas-Barrón.  Optimal ordering policies in response to a discount offer: Corrections , 2009 .

[24]  W. C. Benton,et al.  A classification of literature on determining the lot size under quantity discounts , 1996 .

[25]  Richard J. Tersine.  Economic replenishment strategies for announced price increases , 1996 .

[26]  G. E. Martin.  Note on an EOQ model with a temporary sale price , 1994 .

[27]  Yu-Chung Tsao,et al.  Managing multi-echelon multi-item channels with trade allowances under credit period , 2010 .

[28]  Yu-Chung Tsao,et al.  Effects of Joint Replenishment Policy on Company Cost under Permissible Delay in Payments , 2010 .

[29]  Rhonda L. Aull-Hyde.  A Backlog Inventory Model During Restricted Sale Periods , 1996 .

[30]  Frank T. Shu.  Economic Ordering Frequency for two Items Jointly Replenished , 1971 .

[31]  Leopoldo Eduardo Cárdenas-Barrón,et al.  OPTIMAL ORDER SIZE TO TAKE ADVANTAGE OF A ONE-TIME DISCOUNT OFFER WITH ALLOWED BACKORDERS , 2010 .

[32]  Ata Allah Taleizadeh,et al.  Multiproduct single-machine production system with stochastic scrapped production rate, partial backordering and service level constraint , 2010, J. Comput. Appl. Math..

[33]  Hui-Ming Wee,et al.  Multi-product production quantity model with repair failure and partial backordering , 2010, Comput. Ind. Eng..

[34]  Nita H. Shah,et al.  Retailer's response to special sales: price discount vs. trade credit , 2001 .

[35]  Francisco J. Arcelus,et al.  Costing partial order cycles in the temporary sale price problem , 1998 .

[36]  Francisco J. Arcelus,et al.  Special sales with guaranteed minimum duration but uncertain termination date , 2003 .

[37]  David W. Pentico,et al.  A survey of deterministic models for the EOQ and EPQ with partial backordering , 2011, Eur. J. Oper. Res..

[38]  S. K. Goyal.  A comment on Martin's: Note on an EOQ model with a temporary sale price , 1996 .

[39]  Suresh Goyal,et al.  A review of the joint replenishment problem literature: 1989-2005 , 2008, Eur. J. Oper. Res..

[40]  Shunji Osaki.  Optimal ordering policies , 1978, Advances in Applied Probability.

[41]  Mohamad Y. Jaber,et al.  A note on: Optimal ordering policies in response to a discount offer , 2006 .

[42]  Suresh Kumar Goyal.  Economic ordering policy during special discount periods for dynamic inventory problems under certainty , 1990 .

[43]  L. Cárdenas-Barrón,et al.  Multi products single machine EPQ model with immediate rework process , 2012 .

[44]  J. Bookbinder,et al.  Discount Pricing for a Family of Items: The Supplier's Optimal Decisions , 2012 .

[45]  Horng-Jinh Chang,et al.  Closed-form solutions for Wee's and Martin's EOQ models with a temporary price discount , 2011 .

[46]  Suresh Kumar Goyal,et al.  Joint replenishment inventory control: Deterministic and stochastic models , 1989 .

[47]  Amir Abbas Najafi,et al.  ECONOMIC PRODUCTION QUANTITY MODEL WITH SCRAPPED ITEMS AND LIMITED PRODUCTION CAPACITY , 2010 .

[48]  Jonas C. P. Yu,et al.  A deteriorating inventory model with a temporary price discount , 1997 .