Price discount facility in an EOQ model for deteriorating items with stock‐dependent demand and partial backlogging

Abstract

All-units discount facilities are one of the attractive features in the competitive business situation. Due to the globalization of the marketing policy, all-units discount facilities play an important role in the competitive business. Typical economic order quantity (EOQ) models are cloistered by considering as constant not only the purchase cost (irrespective of the order size of the product) but also the carrying cost during the entire cycle period. However, the unit purchase cost has an antagonistic relationship with the order size, and the carrying cost has a commensurate relationship with the storage time-period of the product, that is, the higher the order size, the lower the unit purchase cost, and the longer the storage time-period, the greater carrying cost per unit. Also deterioration is another imperative issue in inventory analysis as it has a huge impact on profit or cost of the inventory system. Considering all of the above-mentioned factors, we study two different inventory models, namely (a) inventory model for zero-ending case and (b) inventory model for shortages case. The demand for both models is considered as price and stock dependent, whereas shortages are partially backlogged at a rate with the length of the waiting time to the arrivals of the next lot. The existence and uniqueness of the optimal solution for both models are examined theoretically and the solution procedures are discussed along with two proposed algorithms for minimizing the total cost. Finally, we perform sensitivity analyses for both models and make a fruitful conclusion regarding the proposed work.

Coordination of Pricing and Order Quantity for Two Replaceable and Seasonal Products

“…Finally, the last term shows the transportation cost of the products to the firm. Equations (5) and (6) indicate the constraints of the problem, so that the former one is related to the nonnegativity of demand and the latter one indicates the upper bound of periods. About Equation 5, as the demand is decreasing during time, it reaches to the minimum amount at the end of each period.…”

“…Pricing or order quantity in the supply chain has been considered separately for a long time [1,2,3], while nowadays dynamic pricing and inventory decisions are mentioned simultaneously by many researchers as the most important factors towards the success of a business. Dynamic pricing is applied by the researchers for the products whose demand and price change during the time like perishable products [4,5] and seasonal products. One of the researches in the field of pricing for seasonal goods is done by Aviv and Pazgal.…”

Effect of Price Concession Strategy and Preservation Technology on Inventory Model for Decaying Products with Partial Backlogging and Price-Stock-Dependent Demand

“…Alfares and Ghaithan [20] developed an inventory model for no shortage case under price discount facility. Shaikh et al [21] modified Alfares and Ghaithan's [20] model considering shortages.…”

The effect of advance payment with discount facility on supply decisions of deteriorating products whose demand is both price and stock dependent

“…Recently, Shaikh et al. () developed an EOQ inventory model for deteriorating items with stock‐dependent demand and partial backlogging considering price discount facility. Considering two substitutable products in a two‐echelon supply chain, Taleizadeh et al.…”

“…Shaikh et al. () introduced an EOQ model with price discount inventory model for deteriorating items. Taleizadeh et al.…”