Abstract
The newsvendor model is the cornerstone of most periodic inventory models; however, it distorts the correct timing of inventory costs and thus misses the optimal solution of the inventory system. This work presents a modification of the classical newsvendor model that considers the holding cost according to the stock-levels within the selling period rather than according to the stock-level at the end of it. The selling period (for example, a season) is divided into equal-time epochs (for example, one-day epochs), where demands are not necessarily identical across epochs or independently distributed. A mathematical model is formulated to find the optimal order quantity which maximizes the expected profit. We show: 1) that the profit function is concave; 2) that the structure of the optimality equation is similar to that of the classical newsvendor model; 3) how to attain the real tradeoff between the expected profit and the service level. Finally, we propose three heuristics to approximate the optimal order quantity and two bounds on its value, which are easy to implement in practice, and evaluate their performances using extensive numerical examples in a factorial experimental design.
Highlights
In contrast to deterministic demand models, such as the economic order quantity (EOQ), which assume continuous accounting of inventory costs, most stochastic periodic-review inventory models assume that inventory costs are calculated according to the inventory level at the end of the replenishment period
Avinadav newsvendor problem assumes only overage and underage costs and the optimal policy is obtained when the probability of not stocking out in a review cycle is equal to cu. It seems that developers of stochastic models use this cost accounting approach as a means of increasing their models’ mathematical tractability
Our formulations of the first two elements do not diverge from those of the standard newsvendor model: the purchase cost is cQ, and the expected revenue, which includes revenue from units that are sold within the selling period, as well as the salvage value of the remaining units, is REV (Q) =∑ (rj + s (Q − j)) Pn ( j) + rQ ∑ Pn ( j) =(r − s) ∑ jPn ( j) + sQ∑ Pn ( j) + rQ ∑ Pn ( j)
Summary
In contrast to deterministic demand models, such as the economic order quantity (EOQ), which assume continuous accounting of inventory costs, most stochastic periodic-review inventory models assume that inventory costs are calculated according to the inventory level at the end of the replenishment period. Rudi et al [1] show that, in a full backlogging system in which both holding and shortage costs are accounted for continuously, the optimal policy is obtained when the fill rate (referred to as the type 2 service level) is equal to cu (co + cu ) This result does not hold in the case of lost sales, in which only the holding cost is duration dependent, whereas the cost of a stock-out predominantly depends on the stock-out quantity. A common assumption, which is assumed here, is that unsatisfied demand is lost, so that shortage leads to a loss of profits, which depends only on the stock-out quantity (and not on the duration) Such a model was suggested as a direction for future research by Rudi et al [1], who analyzed a full backlogging inventory system, and it is applicable to many inventory systems of perishable items, such as supermarkets and fashion stores.
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