Inventory model involving lead time as a decision variable with a mixture of lost sales and backorders

In a recent paper, Ouyang et al. [10] proposed a (Q, r, L) inventory model with defective items in an arrival lot. The purpose of this study is to generalize Ouyang et al.?s [10] model by allowing setup cost (A) as a decision variable in conjunction with order quantity (Q), reorder point (r) and lead time (L). In this study, we first assume that the lead time demand follows a normal distribution, and then relax this assumption by only assuming that the first two moments of the lead time demand are given. For each case, an algorithm procedure of finding the optimal solution is developed.

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Reducing lost-sales rate in (T,R,L) inventory model with controllable lead time

Applied Mathematical Modelling ◽

10.1016/j.apm.2010.02.035 ◽

2010 ◽

Vol 34 (11) ◽

pp. 3465-3477 ◽

Cited By ~ 28

Author(s):

K. Annadurai ◽

R. Uthayakumar

Keyword(s):

Lead Time ◽

Inventory Model ◽

Lost Sales ◽

Controllable Lead Time

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Optimization of Inventory for Optimal Replenishment Policies and Lead-Time with Time Varying Demand

Advances in Logistics, Operations, and Management Science - Optimal Inventory Control and Management Techniques ◽

10.4018/978-1-4666-9888-8.ch010 ◽

2016 ◽

pp. 201-221

Author(s):

Kaushik Kumar ◽

Supriyo Roy

Keyword(s):

Inventory Management ◽

Lead Time ◽

Product Life Cycle ◽

Inventory Model ◽

Decision Variable ◽

Time Varying ◽

Lot Size ◽

Solution Approach ◽

Purchasing Cost ◽

Increasing Demand

Considering a single period inventory management problem used in the distribution channel to represent consumer demand for marketing/sales of a product, attempt is made to develop a deterministic inventory model with time-varying increasing demand that may be used to reflect sales in different phases of a product life cycle in the competitive market. We propose inventory model assuming replenishment cost is to be linearly dependent on lot size and purchasing cost per unit item is dependent on lead time. Lead time is taken as decision variable. Shortages are allowed to backlog and to lose partly. Our objective is to cumulatively evaluate optimal replenishment lot-size, order time and lead-time for maximization of total profit. Considering the complexities of the proposed model, we propose a heuristic solution approach by developing an ERCM Genetic Algorithm based on ranking section, elitism, whole arithmetic crossover and non-uniform mutation dependent on the age of the population. This heuristics are easy to compute and practical to implement, and perform well in numerical trials.

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Continuous review inventory model with lost sale reduction and ordering cost dependent on lead time for the mixtures of distributions

Yugoslav journal of operations research ◽

10.2298/yjor200418006s ◽

2021 ◽

pp. 6-6

Author(s):

Hardik Soni ◽

Kunal Shah

Keyword(s):

Cost Function ◽

Lead Time ◽

Capital Investment ◽

Optimal Solution ◽

Inventory Model ◽

Lost Sales ◽

Mixtures Of Distributions ◽

Continuous Review ◽

Investment Cost ◽

Mixture Of Normal Distributions

We consider a continuous review inventory system for inventory model involving lost sales reduction through capital investment cost function and the reduction of lead time further which reduces the ordering cost. To reduce the lost sales rate, two forms of capital investment cost function, viz. logarithmic and power are employed. Two relationships between ordering cost and lead time, viz. linear and logarithmic are considered. We develop four inventory models by taking different combinations of capital investment cost function and ordering cost lead time relationship. Objective of the study is to reduce the total related cost by simultaneously optimizing the order quantity, safety factor, fraction of the shortages during the stock-out period that will be lost and length of lead time. The lead time demand is assumed to follow a mixture of normal distributions. The optimal solution is derived by developing computer programs using the software MATLAB. We also provide four numerical examples to illustrate the models.

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