Two-warehouse partial backlogging inventory model with ramp type demand rate, three-parameter Weibull distribution deterioration under inflation and permissible delay in payments

Abstract Decay or deterioration of physical goods while in stock is a natural phenomenon in many inventory systems. The three-parameter Weibull distribution is an excellent generalization of exponential decay, which can be used for items with any initial value of the rate of deterioration and for items which starts deteriorating only after a certain period of time. To reduce the amount of deterioration and the limited storage facility in own warehouse (OW) the retailer’s is moving their excess items to store in a rented warehouse (RW). Generally it is seen that for any new brand of consumer goods coming to the market, the demand rate increases with time up to a certain period and then ultimately stabilize and becomes constant. This kind of stabilization has been termed as ’ramp-type’ demand rate. So, in this paper, we have developed two warehouse inventory models with ramp type demand rate and three-parameter Weibull distribution deterioration (ThPWD) under inflationary conditions, where permissible delay in payment is available for retailer if outstanding amount is compensated within the given credit period. Since, not all customers are willing to wait for backlogged during the shortage period, in this investigation shortages are also allowed and partially backlogged. The purpose of this study is not only to find retailer’s optimal replenishment policies but also to minimize the total average cost. Finally, a numerical example is presented to illustrate the proposed model and sensitivity analysis of the optimal solutions with respect to major parameters is carried out using the Mathematica-8.0 software.

[1]  K. Sarma.  A deterministic order level inventory model for deteriorating items with two storage facilities , 1987 .

[2]  Jinn-Tsair Teng,et al.  Supply chain models for deteriorating products with ramp type demand rate under permissible delay in payments , 2011, Expert Syst. Appl..

[3]  Bhaba R. Sarker,et al.  Optimal payment time under permissible delay in payment for products with deterioration , 2000 .

[4]  Jui-Jung Liao,et al.  A deterministic inventory model for deteriorating items with two warehouses and trade credit in a supply chain system , 2013 .

[5]  George C. Philip,et al.  A Generalized EOQ Model for Items with Weibull Distribution Deterioration , 1974 .

[6]  R. Uthayakumar,et al.  Optimal replenishment policies of an EOQ model for non-instantaneous Weibull deteriorating items with ramp-type of demand under shortages , 2015, Int. J. Math. Oper. Res..

[7]  Po-Chung Yang,et al.  An integrated multi-lot-size production inventory model for deteriorating item , 2003, Comput. Oper. Res..

[8]  Kun-Jen Chung.  A theorem on the determination of economic order quantity under conditions of permissible delay in payments , 1998, Comput. Oper. Res..

[9]  Ali Akbar Shaikh,et al.  Investigation of two-warehouse inventory problems in interval environment under inflation via particle swarm optimization , 2016 .

[10]  Dipankar Chakraborty,et al.  Multi-item integrated supply chain model for deteriorating items with stock dependent demand under fuzzy random and bifuzzy environments , 2015, Comput. Ind. Eng..

[11]  Yong-Wu Zhou,et al.  A two-warehouse inventory model for items with stock-level-dependent demand rate , 2005 .

[12]  Uttam Kumar Bera,et al.  An EPQ model for two-warehouse in unremitting release pattern with two-level trade credit period concerning both supplier and retailer , 2016, Appl. Math. Comput..

[13]  Jinn-Tsair Teng,et al.  Optimal Ordering Policy for Deteriorating Items with Partial Backlogging under Permissible Delay in Payments , 2006, J. Glob. Optim..

[14]  Lakdere Benkherouf,et al.  Inventory models with ramp type demand rate, partial backlogging and general deterioration rate , 2013, Appl. Math. Comput..

[15]  A. K. Pal,et al.  Order level inventory system with ramp type demand rate for deteriorating items , 1998 .

[16]  Samarjit Kar,et al.  A multi-warehouse partial backlogging inventory model for deteriorating items under inflation when a delay in payment is permissible , 2014, Annals of Operations Research.

[17]  G. S. Mahapatra,et al.  A production inventory model for deteriorating item with ramp type demand allowing inflation and shortages under fuzziness , 2015 .

[18]  Jinn-Tsair Teng,et al.  On the economic order quantity under conditions of permissible delay in payments , 2002, J. Oper. Res. Soc..

[19]  Hark Hwang,et al.  Management of Deteriorating Inventory under Inflation , 1983 .

[20]  Samarjit Kar,et al.  Improving production policy for a deteriorating item under permissible delay in payments with stock-dependent demand rate , 2010, Comput. Math. Appl..

[21]  Swati Agrawal,et al.  A two-warehouse inventory model for items with three-parameter Weibull distribution deterioration, shortages and linear trend in demand , 2008, Int. Trans. Oper. Res..

[22]  Kun-Shan Wu.  An EOQ inventory model for items with Weibull distribution deterioration, ramp type demand rate and partial backlogging , 2001 .

[23]  Liang-Yuh Ouyang,et al.  A study on an inventory model for non-instantaneous deteriorating items with permissible delay in payments , 2006, Comput. Ind. Eng..

[24]  S. Saha.  Optimal order quantity of retailer with quadratic ramp-type demand under supplier trade credit financing , 2014 .

[25]  Chandra K. Jaggi,et al.  Supply chain model for deteriorating items with stock-dependent consumption rate and shortages under inflation and permissible delay in payment , 2010, Int. J. Math. Oper. Res..

[26]  Hui-Ling Yang,et al.  A two-warehouse partial backlogging inventory model for deteriorating items with permissible delay in payment under inflation , 2013 .

[27]  S. Aggarwal,et al.  Credit financing in economic ordering policies of deteriorating items , 1994 .

[28]  Hark Hwang,et al.  Joint price and lot size determination under conditions of permissible delay in payments and quantity discounts for freight cost , 1996 .

[29]  K. S. Chaudhuri,et al.  Production, Manufacturing and Logistics An EOQ model with ramp type demand rate, time dependent deterioration rate, unit production cost and shortages , 2006 .

[30]  Jui‐Jung Liao.  ON AN EPQ MODEL FOR DETERIORATING ITEMS UNDER PERMISSIBLE DELAY IN PAYMENTS , 2007 .

[31]  R. Misra,et al.  Optimum production lot size model for a system with deteriorating inventory , 1975 .

[32]  Kheng Joo Heng,et al.  An order-level lot-size inventory model for deteriorating items with finite replenishment rate , 1991 .

[33]  S. Goyal.  Economic Order Quantity under Conditions of Permissible Delay in Payments , 1985 .

[34]  Chuanxu Wang,et al.  Pricing for seasonal deteriorating products with price- and ramp-type time-dependent demand , 2014, Comput. Ind. Eng..

[35]  L. Cárdenas-Barrón,et al.  Retailer’s economic order quantity when the supplier offers conditionally permissible delay in payments link to order quantity , 2014 .

[36]  Gerhard-Wilhelm Weber,et al.  An inventory model for non-instantaneous deteriorating items with partial backlogging, permissible delay in payments, inflation- and selling price-dependent demand and customer returns , 2015, Ann. Oper. Res..

[37]  Swati Agrawal,et al.  Inventory model with deteriorating items, ramp-type demand and partially backlogged shortages for a two warehouse system , 2013 .

[38]  Maw-Sheng Chern,et al.  Deterministic inventory lot-size models under inflation with shortages and deterioration for fluctuating demand , 2001 .

[39]  Kun-Jen Chung.  The EOQ model with defective items and partially permissible delay in payments linked to order quantity derived analytically in the supply chain management , 2013 .

[40]  Yanlai Liang,et al.  A two-warehouse inventory model for deteriorating items under conditionally permissible delay in payment , 2011 .

[41]  Chin-Hsiung Lin,et al.  An EOQ inventory model with ramp type demand rate for items with Weibull deterioration , 1999 .

[42]  Hark Hwang,et al.  Retailer's pricing and lot sizing policy for exponentially deteriorating products under the condition of permissible delay in payments , 1997, Comput. Oper. Res..

[43]  Xu-Ren Luo.  Analysis of inventory models with ramp type demand , 2017 .

[44]  L. Cárdenas-Barrón,et al.  Impact of trade credit and inflation on retailer's ordering policies for non-instantaneous deteriorating items in a two-warehouse environment , 2016 .

[45]  K. S. Chaudhuri,et al.  Economic Order Quantity model with Weibull deterioration distribution, shortage and ramp-type demand , 2003, Int. J. Syst. Sci..

[46]  Hui-Ling Yang.  Two-warehouse partial backlogging inventory models with three-parameter Weibull distribution deterioration under inflation , 2012 .

[47]  D. Jana,et al.  A three-layer supply chain inventory model for non-instantaneous deteriorating item with inflation and delay in payments in random fuzzy environment , 2017 .

[48]  George C. Philip,et al.  An EOQ Model for Items with Weibull Distribution Deterioration , 1973 .

[49]  Hui-Ling Yang.  Two-warehouse partial backlogging inventory models for deteriorating items under inflation , 2006 .

[50]  Hui-Ling Yang,et al.  Two-warehouse inventory models for deteriorating items with shortages under inflation , 2004, Eur. J. Oper. Res..

[51]  Peter Chu,et al.  Economic order quantity of deteriorating items under permissible delay in payments , 1998, Comput. Oper. Res..

[52]  Ioannis Konstantaras,et al.  Inventory models with ramp type demand rate, partial backlogging and Weibull deterioration rate , 2009, Eur. J. Oper. Res..

[53]  Ioannis Ganas,et al.  Two-Warehouse Inventory Systems for Seasonal Deteriorating Products with Permissible Delay in Payments , 2017 .

[54]  S. Aggarwal,et al.  Ordering Policies of Deteriorating Items under Permissible Delay in Payments , 1995 .

[55]  J. Buzacott.  Economic Order Quantities with Inflation , 1975 .

[56]  S. Kar,et al.  An inventory model for a deteriorating item with displayed stock dependent demand under fuzzy inflation and time discounting over a random planning horizon , 2009 .