Optimal strategies for an inventory system with cost functions of general form

Daduna, Hans; Knopov, P. S.; Tur, L. P.

doi:10.1007/bf02835856

Cited by 17 publications

(8 citation statements)

References 10 publications

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“…The weak continuity of the transition probabilities follows directly from their definition [2]. The measure m concentrated at the point 0 with weight F M F Q ( ) ( ) -satisfies the following conditions:…”

Section: Proof Letmentioning

confidence: 99%

A control model for an insurance company

Derieva

2004

Cybern Syst Anal

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The activity of an insurance company with a reinsurance condition system is modeled on an infinite time interval. Payment times and sums insured are random. The amount of money replenished is selected as a control parameter. The task is to minimize the average insurance payment per unit time, thus optimizing investments.Let us consider a model of an insurance company with continuous insurance premiums. Naturally, the company is interested in the maximum investment of this money. However, it should have a reserve for immediate payments. The reserve can be replenished continuously and is bounded from above by Q.Insurance claims arrive at random times, and in premium rate y n the nth claim has a distribution function F. The company has reinsurance conditions. Premium payments greater than M are not paid and are transferred to a reinsuring company. The company's resources are checked before payment, and then, depending on the result of the check x, a decision on replenishment is made. We believe that the reserve is replenished immediately by the necessary value a with probability p or is not replenished with probability ( ) 1-p (for example, when replenishment involves money that cannot be withdrawn immediately, i.e., when the company operates under the conditions of unstable market). Then premium is paid, and the system remains in this state during a period t n , which is a random variable with distribution function F( / , , ) × x y a , until a new claim arrives.We believe that all the random variables of the model are defined on a probability space ( , , ) W J P . Denote by r t x a ( / , )losses of the system that is in a state x during a period t if a decision a was made at the beginning of this period. The model accounts for the following losses: r a 1 ( )-reserve replenishment costs (i.e., the sum lost due to withdrawal of money invested), r Q R 1 0 :[ , ] ® + ; r x 2 ( ) -costs of failed premium payment x because of a lack of reserved money, r R R 2 : + + ®; r x 3 ( ) -costs of maintaining the reserve per unit time (i.e., profit lost because the reserved money have not been invested), r Q R 3 0 :[ , ] ® + ; r 4 -rate of premium payment to the reinsuring company per unit time.The functions r i , i = 1 2 3 , , , are monotonic, non-negative, and non-decreasing, r r xd Fx 2 2 0 0 0 ( ) , ( ) ( ) = < ¥ ¥ ò .

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Section: Proof Letmentioning

confidence: 99%

A control model for an insurance company

Derieva

2004

Cybern Syst Anal

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“…The authors of [2][3][4][5] established the existence conditions for j-and y b -optimal determined strategies of the above inventory control problem and showed that the solution for the y b -criterion can be obtained by the method of successive approximations. They also presented conditions for the optimal strategy to have a threshold structure are presented.…”

Section: Models With a Continuous Set Of States And Controls Case 1mentioning

confidence: 99%

“…Note that if the set of states and controls is finite, then deriving optimal strategies is reduced to a linear programming problem [6]. If the set of states and controls is countable or compact, then the threshold value of the functional can be found by stochastic programming methods [2,3,7].…”

Section: Case 2 a Concave Costmentioning

confidence: 99%

Some Approaches to Solving Inventory Control Problems

Knopov

Tur

2005

Cybern Syst Anal

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“…The first one was proposed by Scarf in 1960, who studied a dynamic system which models inventory management and demonstrates that the optimal operating strategy is (R, Q) class. After Scarf, other authors followed him and demonstrated for different dynamic systems that the optimal strategy remains being (R, Q) ( [4], [5], [11] and [12]).…”

Section: Introductionmentioning

confidence: 99%

Inventory control policies for a polyester company

Blancas-Rivera

Cruz−Suárez

Tajonar-Sanabria

et al. 2019

JIO

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In this paper, we study an inventory control model, which is analyzed by means of a difference equation. This model is applied to study the stock of a polyester company. In this company, two types of polyester are manufactured, and it is considered a stochastic demand. In the paper, an optimal policy of production is determined, which minimizes the total expected discounted cost. The one-step cost function is integrated with the following components: production, storage and sale lost. The methodology consists on applied the dynamic programming approach and some results of convex analysis to determine a (R, Q)-optimal policy, where R and Q are positive numbers. R represents the maximum level of production and Q is the minimum stock. Finally, with a company database of monthly sales, we adjust a probability distribution and present a numerical implementation of the optimal. Furthermore, simulations to observe the asymptotic behavior of the stock are illustrated.

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Optimal strategies for an inventory system with cost functions of general form

Cited by 17 publications

References 10 publications

A control model for an insurance company

A control model for an insurance company

Some Approaches to Solving Inventory Control Problems

Inventory control policies for a polyester company

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