infinite planning horizon
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2021 ◽  
Vol 36 ◽  
pp. 04002
Author(s):  
Ivan Yeo

In this paper, we study an inventory system over an infinite planning horizon where a time-varying demand is satisfied by process cycles that consist of a production batch followed by a recovery batch. Our model considers three types of inventory—returned items, serviceable items, and raw material. Furthermore, our model considers two recovery channels—recovery into serviceable items and recovery into raw material. Serviceable items are thus sourced from two inputs—direct recovery and production from raw material. These raw materials can be salvaged from returned items, as well as bought from external sources whenever required. We propose an expression for the unit time total cost as well as a numerical method to find the optimal policy. The properties of the model are studied through numerical experiments, in particular, the feasible situations where hybrid policies are better than pure policies.


2020 ◽  
Vol 37 (02) ◽  
pp. 2050001
Author(s):  
Hong-Qiao Chen ◽  
Xiao-Song Ding ◽  
Ji-Hong Zhang ◽  
Hua-Yi Li

This paper studies a periodic-review production-inventory control model under an energy buy-back program over an infinite planning horizon, in which a fixed setup cost and compensation levels corresponding to various market states are involved. The objective is to identify the manufacturer’s optimal production-inventory policy that can minimize his total discounted cost or long-run average cost. By using Veinott’s conditions, it is shown that such a state dependent optimal policy is of either an [Formula: see text], or partly an [Formula: see text] type.


2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Lixia Zhang ◽  
Lili Han

This paper discusses the inventory mechanism with backordering and with the infinite planning horizon consisting of two stages wherein the demand rate in the first stage is strictly greater than that in the second stage. To minimize the retailer’s inventory cost, we establish a lot sizing decision model. On the basis of the inventory cost analysis, we present a closed-form solution to the model and provide an optimal replenishment and stocking strategy to the retailer. The given numerical experiments show the validity of the model.


Author(s):  
Hans Fehr ◽  
Fabian Kindermann

In this chapter we apply the principles of dynamic programming to some standard macroeconomic models. For now we stay in the world of infinite horizon models, which are characterized by the fact that they are populated by one or several households with an infinite planning horizon, similar to the previous chapter. There are several justifications for such an assumption. Beneath simplicity, altruism is probably the most famous argument in favour of infinite horizon models. Assume that in a period t there is one generation that dies with certainty after this period.The utility of this generation from its own consumption is u(·). Yet, each generation is altruistic towards its descendants. Consequently, total utility of the generation is Ut = u(·) + βUt+1 where β ≤ 1 can be interpreted as the degree of altruism. All generations together then form a dynasty.


2017 ◽  
Vol 1 (2) ◽  
pp. 211-224
Author(s):  
Ezhari Asfa’ani

We discuss about Nash equilibria for the linear quadratic differential game for an infinite planning horizon. We consider an open-loop information structure. In the standard literature this problem is solved under the assumption and provide both necessary and sufficient conditions for existence of Nash equilibria for this game under the assumption that the system as a whole is stabilizable.      Keywords: linear quadratic differential games, open-loop information structure


2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Himani Dem ◽  
Leena Prasher

This paper derives a reverse logistic inventory model with imperfect production, stock-dependent demand, flexible manufacturing, and shortages over infinite planning horizon. The objective is to determine the joint policy for optimal production, amount of remanufacturing, collection of reusable items, and collection as well as disposal of defective items which minimizes the total cost of the inventory system under consideration. To make the model more realistic, both of the cases of linear and nonlinear holding costs have been discussed. The results are discussed with a numerical example to illustrate the theory.


2013 ◽  
Vol 23 (4) ◽  
pp. 473-493
Author(s):  
Muhammad Wakhid Musthofa ◽  
Jacob C. Engwerda ◽  
Ari Suparwanto ◽  

Abstract In this paper the feedback saddle point equilibria of soft-constrained zero-sum linear quadratic differential games for descriptor systems that have index one will be studied for a finite and infinite planning horizon. Both necessary and sufficient conditions for the existence of a feedback saddle point equilibrium are considered


Author(s):  
Huachun Xiong ◽  
Jinxing Xie ◽  
Bo Niu

This paper deals with the two-warehouse partial backlogging inventory problems under inflation for a deteriorating product with a constant demand rate over an infinite horizon. In contrast to the traditional model in which each replenishment cycle starts with an instant replenishment and ends with shortages, an alternative model is proposed in recent literature in which each cycle starts with shortages. It is proven to be less expensive to operate than the traditional model in terms of the present value of the cost per unit time. The present paper points out that the criteria of minimizing the cost per unit time is unreasonable when the inflationary effect is taken into consideration, and instead, the criteria of minimizing the present value of the total cost over the whole infinite planning horizon should be used. The objective functions of these two models are changed and proved that the model with shortages at the start of the cycle is less expensive to operate than the traditional model in terms of the present value of the total cost, but the optimal solutions of the models minimizing the cost per unit time indicate significantly higher total costs.


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