A (<i>Q,R</i>) inventory model with lost sales and erlang‐distributed lead times

Buchanan, David J.; Love, Robert F.

doi:10.1002/nav.3800320407

Cited by 21 publications

(11 citation statements)

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“…[8] investigate an (r, Q) inventory system with lost sales and Erlang-distributed lead times, where customer demands are satisfied without any loss of time. Their result for the special case of exponentially distributed lead times coincides with the marginal distribution of the inventory process of our system.…”

Section: M/m/1/∞-system With (R Q)-policymentioning

confidence: 99%

“…E.g. these models apply to cases such as essential spare parts where one must go to the outside of the normal ordering system when a stockout occurs ( [8] p. 605). The essential spare part problem is central for many repair procedures, where broken down units arrive at a repair station, queue for repair, and are repaired by substituting a failed part by a spare part from the inventory.…”

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confidence: 99%

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M/M/1 Queueing systems with inventory

Schwarz¹,

Sauer²,

Daduna³

et al. 2006

Queueing Syst

146

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We derive stationary distributions of joint queue length and inventory processes in explicit product form for various M/M/1-systems with inventory under continuous review and different inventory management policies, and with lost sales. Demand is Poisson, service times and lead times are exponentially distributed. These distributions are used to calculate performance measures of the respective systems. In case of infinite waiting room the key result is that the limiting distributions of the queue length processes are the same as in the classical M/M/1/∞-system.

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Section: M/m/1/∞-system With (R Q)-policymentioning

confidence: 99%

mentioning

confidence: 99%

M/M/1 Queueing systems with inventory

Schwarz¹,

Sauer²,

Daduna³

et al. 2006

Queueing Syst

146

View full text Add to dashboard Cite

show abstract

“…A brief look at the existing literature (Feeny and Sherbrooke [7], Burgine and Norman [6], Smith [11], Archibald [1], Buchanan and Love [5], Kalpakam and Arivarignan [10], and Johansen and Thorstenson [9], among others) indicates that the analytic treatment of continuous-review inventory systems with lost sales has only been made possible through a series of assumptions such as base stock policies [i.e., ( S 0 1, S) or (s, Q Å 1) policies] or zero lead time or no more than one order allowed to be outstanding at any time. Moreover, in the case of stochastic lead times, it is usually assumed (excluding the models involving a base stock policy) that demands are unit sized, and are often generated by a Poisson process.…”

Section: Introductionmentioning

confidence: 98%

A continuous-review inventory system with lost sales and variable lead time

Mohebbi

Posner

1998

Naval Research Logistics

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“…If x > 0, the optimal demand rate (price) is obtained by solving the optimization problem (3). It states that, if there is no inventory on hand, x = 0, the seller will choose the highest price, p, so that the demand rate is lowest, which incurs a constant lost-sales cost rate λπ.…”

Section: Discounted Profit Criterionmentioning

confidence: 99%

Coordinated Pricing and Inventory Control With Batch Production and Erlang Leadtimes

Pang¹,

Chen²

2014

Prob. Eng. Inf. Sci.

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This paper addresses a joint pricing and inventory control problem for a batch production system with random leadtimes. Assume that demand arrives according to a Poisson process with a price-dependent arrival rate. Each replenishment order contains a single batch of a fixed lot size. The replenishment leadtime follows an Erlang distribution, with the number of completed phases recording the delivery state of outstanding orders. The objective is to determine an optimal inventory-pricing policy that maximizes total expected discounted profit or long-run average profit. We first show that when there is at most one order outstanding at any point in time and that excess demand is lost, the optimal reorder policy can be characterized by a critical stock level and the optimal pricing decision is decreasing in the inventory level and delivery state. We then extend the analysis to mixed-Erlang leadtime distribution which can be used to approximate any random leadtime to any degree of accuracy. We further extend the analysis to allowing three outstanding orders where the optimal reorder point becomes state-dependent: the closer an outstanding order is to its arrival or the more orders are outstanding, the lower selling price is charged and the lower reorder point is chosen. Finally, we address the backlog case and show that the monotone pricing structure may not be true when the optimal reorder point is negative. 530Z. Pang and F.Y. Chen challenges intrinsic to problems with dynamically controllable prices (Federgruen and Heching [13]). In standard inventory models with fully backordering and exogenous prices (hence exogenous random demand), the impact of current inventory positions (= inventory levels + outstanding orders − backorders) is evaluated on the basis of the present value of expected inventory cost one order leadtime later. However, in the presence of positive leadtime, with dynamically controllable prices, these future costs depend on the pricing decisions of future periods during the leadtime, and they are therefore unspecified in the current period. An exact formulation requires a multi-dimensional state space to record the inventory levels on hand and on order, and is therefore very difficult to analyze. Pang, Chen, and Feng [31] represent the early effort to provide some partial characterization of the optimal policy structure for periodic-review systems. Our paper attempts to continue their effort to address the continuous-review systems.Furthermore, the literature on inventory-pricing control has also confined itself to models with arbitrary ordering sizes (i.e., lot-for-lot sizes), whereas in supply chains, materials often flow in fixed batch sizes. For example, consumer packaged goods typically arrive at stores in cartons or case packs, finished goods may be transported in full containers or truckloads, and work-in-process (WIP) is usually processed in some convenient lot sizes (Kapuscinski et al. [22]). In addition, a batch production system can serve as an approximation of a capacitated inventory s...

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A (Q,R) inventory model with lost sales and erlang‐distributed lead times

Cited by 21 publications

References 1 publication

M/M/1 Queueing systems with inventory

M/M/1 Queueing systems with inventory

A continuous-review inventory system with lost sales and variable lead time

Coordinated Pricing and Inventory Control With Batch Production and Erlang Leadtimes

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