An EOQ inventory model with nonlinear stock dependent holding cost, nonlinear stock dependent demand and trade credit

Abstract This paper deals with an economic order quantity (EOQ) inventory model under both nonlinear stock dependent demand and nonlinear holding cost. This inventory model is developed from retailer’s point of view, where the supplier offers a trade credit period to the retailer. In this paper, we relax the traditional assumption of zero ending inventory level to a non-zero ending inventory level. Consequently, the ending inventory level can be positive, zero or negative. When the ending inventory level is negative means that the shortages are permitted and partially backlogged with a constant backlogging rate. Basically, two inventory models are developed: (i) an inventory model with shortage and (ii) an inventory model without shortage. The primary objective of both inventory models is to determine the optimal ordering quantity and the ending inventory level which maximizes the retailer’s total profit per unit time. In order to obtain the optimal solution, lemmas, and theorems are derived along with a solution procedure. The proposed inventory models are a general framework as several previously published inventory models are particular cases of the inventory models derived in this paper. Some numerical examples and a sensitivity analysis are conducted to illustrate the findings of the inventory models and some observations are also discussed.

[1]  U. Spiegel,et al.  Optimal inventory policy for a perishable item with demand function sensitive to price and time , 2013 .

[2]  Luis A. San-José,et al.  Optimal lot-size policy for deteriorating items with stock-dependent demand considering profit maximization , 2018, Comput. Ind. Eng..

[3]  K. S. Chaudhuri,et al.  On an inventory model with two levels of storage and stock-dependent demand rate , 1998, Int. J. Syst. Sci..

[4]  Chung-Yuan Dye,et al.  An inventory model for deteriorating items under stock-dependent demand and controllable deterioration rate , 2012, Comput. Ind. Eng..

[5]  M. Goh,et al.  Joint pricing and inventory model for deteriorating items with expiration dates and partial backlogging under two-level partial trade credits in supply chain , 2018, International Journal of Production Economics.

[6]  Ruihai Li,et al.  Pricing and lot-sizing decisions for perishable goods when demand depends on selling price, reference price, product freshness, and displayed stocks , 2018, Eur. J. Oper. Res..

[7]  C. V. Balan,et al.  An order-level lot size inventory model with inventory-level dependent demand and deterioration , 1997 .

[8]  Ali Akbar Shaikh,et al.  An inventory model under price and stock dependent demand for controllable deterioration rate with shortages and preservation technology investment , 2017, Ann. Oper. Res..

[9]  S. R. Singh,et al.  Optimal trade-credit policy for perishable items deeming imperfect production and stock dependent demand , 2014 .

[10]  Timothy L. Urban,et al.  A Deterministic Inventory System with an Inventory-Level-Dependent Demand Rate , 1988 .

[11]  A. Roy,et al.  AN INVENTORY MODEL FOR DETERIORATING ITEMS WITH PRICE DEPENDENT DEMAND AND TIME VARYING HOLDING COST , 2008 .

[12]  Kun-Jen Chung,et al.  The EPQ model under conditions of two levels of trade credit and limited storage capacity in supply chain management , 2013, Int. J. Syst. Sci..

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

[14]  Edieal J. Pinker,et al.  An EOQ model for perishable goods with age-dependent demand rate , 2017, Eur. J. Oper. Res..

[15]  J. Sicilia,et al.  Analysis of an EOQ inventory model with partial backordering and non-linear unit holding cost , 2015 .

[16]  Jiang Wu,et al.  Optimal credit period and lot size for deteriorating items with expiration dates under two-level trade credit financing , 2014, Eur. J. Oper. Res..

[17]  Wansheng Tang,et al.  Optimal dynamic pricing and replenishment policy for perishable items with inventory-level-dependent demand , 2016, Int. J. Syst. Sci..

[18]  Tsu-Pang Hsieh,et al.  Optimal dynamic pricing for deteriorating items with reference price effects when inventories stimulate demand , 2017, Eur. J. Oper. Res..

[19]  Hesham K. Alfares,et al.  Inventory model with stock-level dependent demand rate and variable holding cost , 2007 .

[20]  Yong-Wu Zhou,et al.  An EPQ model for deteriorating items with inventory-level-dependent demand and permissible delay in payments , 2012, Int. J. Syst. Sci..

[21]  Kun-Jen Chung.  The integrated inventory model with the transportation cost and two-level trade credit in supply chain management , 2012, Comput. Math. Appl..

[22]  K. Chaudhuri,et al.  An EOQ model with stock-dependent demand, shortage, inflation and time discounting , 1997 .

[23]  L. Ouyang,et al.  An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and partial backlogging , 2006 .

[24]  B. Sarkar,et al.  An inventory model with time dependent demand and shortages under trade credit policy , 2013 .

[25]  A. Bhunia,et al.  A two-warehouse inventory model for deteriorating item under permissible delay in payment via particle swarm optimisation , 2016 .

[26]  I. N. Kamalabadi,et al.  Joint pricing and inventory control for non-instantaneous deteriorating items with partial backlogging and time and price dependent demand , 2012 .

[27]  Hesham K. Alfares,et al.  Inventory and pricing model with price-dependent demand, time-varying holding cost, and quantity discounts , 2016, Comput. Ind. Eng..

[28]  R. Higgins,et al.  Inventory Policy and Trade Credit Financing , 1973 .

[29]  Ioannis Konstantaras,et al.  Optimal ordering quantities for substitutable products with stock-dependent demand , 2015 .

[30]  Leopoldo Eduardo Cárdenas-Barrón,et al.  Retailer's decision for ordering and credit policies for deteriorating items when a supplier offers order-linked credit period or cash discount , 2015, Appl. Math. Comput..

[31]  K. S. Chaudhuri,et al.  Deterministic models of perishable inventory with stock-dependent demand rate and nonlinear holding cost , 1998, Eur. J. Oper. Res..

[32]  Kun-Jen Chung,et al.  The simplified solution procedure for deteriorating items under stock-dependent demand and two-level trade credit in the supply chain management , 2013 .

[33]  Chih-Te Yang.  An inventory model with both stock-dependent demand rate and stock-dependent holding cost rate , 2014 .

[34]  Liang-Yuh Ouyang,et al.  An EOQ model for perishable items under stock-dependent selling rate and time-dependent partial backlogging , 2005, Eur. J. Oper. Res..

[35]  Ford W. Harris,et al.  How Many Parts to Make at Once , 1990, Oper. Res..

[36]  Mark Goh,et al.  Two-warehouse inventory model for non-instantaneous deteriorating items with stock-dependent demand and inflation using particle swarm optimization , 2017, Ann. Oper. Res..

[37]  Ali Akbar Shaikh,et al.  An application of PSO in a two-warehouse inventory model for deteriorating item under permissible delay in payment with different inventory policies , 2015, Appl. Math. Comput..

[38]  T. Datta,et al.  A Note on an Inventory Model with Inventory-level-dependent Demand Rate , 1990 .

[39]  R. Uthayakumar,et al.  Designing a new computational approach of partial backlogging on the economic production quantity model for deteriorating items with non-linear holding cost under inflationary conditions , 2011, Optim. Lett..

[40]  B. Mandal,et al.  An Inventory Model for Deteriorating Items and Stock-dependent Consumption Rate , 1989 .

[41]  H. Weiss.  Economic order quantity models with nonlinear holding costs , 1982 .

[42]  Leopoldo Eduardo Cárdenas-Barrón,et al.  Celebrating a century of the economic order quantity model in honor of Ford Whitman Harris , 2014 .

[43]  R. Levin.  Production/Operations Management: Contemporary Policy for Managing Operating Systems , 1983 .

[44]  M. Goh.  EOQ models with general demand and holding cost functions , 1994 .

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

[46]  A. Bhunia,et al.  A memo on stock model with partial backlogging under delay in payments , 2015 .

[47]  Hark Hwang,et al.  An optimal procurement policy for items with an inventory level-dependent demand rate and fixed lifetime , 2000, Eur. J. Oper. Res..

[48]  David Alcaide López de Pablo,et al.  An inventory system with demand dependent on both time and price assuming backlogged shortages , 2018, Eur. J. Oper. Res..

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

[50]  A. Goswami,et al.  A deterministic inventory model for deteriorating items with stock-dependent demand rate , 1993 .

[51]  Sunil Tiwari,et al.  Inventory and credit decisions for deteriorating items with displayed stock dependent demand in two-echelon supply chain using Stackelberg and Nash equilibrium solution , 2018, Ann. Oper. Res..

[52]  Luis A. San-José,et al.  Maximizing profits in an inventory model with both demand rate and holding cost per unit time dependent on the stock level , 2012, Comput. Ind. Eng..

[53]  Sumon Sarkar,et al.  Lot-sizing policies for defective and deteriorating items with time-dependent demand and trade credit , 2017 .

[54]  R. P. Tripathi,et al.  Inventory model with different demand rate and different holding cost , 2013 .

[55]  J. Sicilia,et al.  An economic lot-size model with non-linear holding cost hinging on time and quantity , 2013 .

[56]  Kun-Jen Chung,et al.  An inventory model with non-instantaneous receipt and exponentially deteriorating items for an integrated three layer supply chain system under two levels of trade credit , 2014 .

[57]  G. Padmanabhan,et al.  EOQ models for perishable items under stock dependent selling rate , 1995 .

[58]  L. Cárdenas-Barrón,et al.  Optimal pricing and lot-sizing policy for supply chain system with deteriorating items under limited storage capacity , 2018, International Journal of Production Economics.

[59]  Luis A. San-José,et al.  Optimal policy for profit maximising in an EOQ model under non-linear holding cost and stock-dependent demand rate , 2012, Int. J. Syst. Sci..

[60]  L. Cárdenas-Barrón,et al.  An EOQ model for perishable product with special sale and shortage , 2013 .

[61]  Biswajit Sarkar,et al.  An EMQ model with price and time dependent demand under the effect of reliability and inflation , 2014, Appl. Math. Comput..