Department of Economics and Business Economics

A heuristic for computing a new value-based stationary policy for the stochastic joint replenishment problem

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@techreport{bc7103442aac4485a8d76115c5272f3e,
title = "A heuristic for computing a new value-based stationary policy for the stochastic joint replenishment problem",
abstract = "A stationary control policy is constructed for the mulit-item stochastic joint replenishment problem. The cornerstone in the construction is a policy-iteratin improvement step which assumes that there is a single possibility for making a joint order and thus deviate from the rule that the items are governed by independent, re-order and order-up-to, (s, S) polities. However this policy-iteration improvement step is done repeatedly at each demand epoch. For the policy-iteration step it is only required the development of one-dimensional functions of relative values where in general these must be multi-dimensional. Knowledge about good order-op.to values is important. So in order to secure that these order-up-to values are hit when making a joint order, an allocated order cost is constructed for each item. Furthermore, a relaxation parameter α is introducted such that one can, if convenient, make it easier or more difficult to issue a joint order when following the policy-iteration step. Also, a vector of can-orders is employed, in case a joint order is made, to include additional items. The policy is denoted a (c, S, α ) policy. Numerical results show that is performs almost as well as the Q (s, S) policy and contrary to the Q(s, S) policy, it is stationary. Also some of the peculiarities of the Q (s, S) that can appear for a constructed data set may be better handled by the (c, S, α) policy. Numerical results also indicate that given a can-order policy one can always constuct a better (c,S, α) policy",
keywords = "Inventory, Stochastic demand, Joint replenishment, Control policies",
author = "Christian Larsen",
note = "Paper haves p{\aa} AU Library, Fuglesangs alle: AU Research 2014 / Paper is available in print at AU Library, Fuglesangs alle: AU Research 2014",
year = "2014",
month = dec,
day = "19",
language = "English",
pages = "1--16",
type = "WorkingPaper",

}

RIS

TY - UNPB

T1 - A heuristic for computing a new value-based stationary policy for the stochastic joint replenishment problem

AU - Larsen, Christian

N1 - Paper haves på AU Library, Fuglesangs alle: AU Research 2014 / Paper is available in print at AU Library, Fuglesangs alle: AU Research 2014

PY - 2014/12/19

Y1 - 2014/12/19

N2 - A stationary control policy is constructed for the mulit-item stochastic joint replenishment problem. The cornerstone in the construction is a policy-iteratin improvement step which assumes that there is a single possibility for making a joint order and thus deviate from the rule that the items are governed by independent, re-order and order-up-to, (s, S) polities. However this policy-iteration improvement step is done repeatedly at each demand epoch. For the policy-iteration step it is only required the development of one-dimensional functions of relative values where in general these must be multi-dimensional. Knowledge about good order-op.to values is important. So in order to secure that these order-up-to values are hit when making a joint order, an allocated order cost is constructed for each item. Furthermore, a relaxation parameter α is introducted such that one can, if convenient, make it easier or more difficult to issue a joint order when following the policy-iteration step. Also, a vector of can-orders is employed, in case a joint order is made, to include additional items. The policy is denoted a (c, S, α ) policy. Numerical results show that is performs almost as well as the Q (s, S) policy and contrary to the Q(s, S) policy, it is stationary. Also some of the peculiarities of the Q (s, S) that can appear for a constructed data set may be better handled by the (c, S, α) policy. Numerical results also indicate that given a can-order policy one can always constuct a better (c,S, α) policy

AB - A stationary control policy is constructed for the mulit-item stochastic joint replenishment problem. The cornerstone in the construction is a policy-iteratin improvement step which assumes that there is a single possibility for making a joint order and thus deviate from the rule that the items are governed by independent, re-order and order-up-to, (s, S) polities. However this policy-iteration improvement step is done repeatedly at each demand epoch. For the policy-iteration step it is only required the development of one-dimensional functions of relative values where in general these must be multi-dimensional. Knowledge about good order-op.to values is important. So in order to secure that these order-up-to values are hit when making a joint order, an allocated order cost is constructed for each item. Furthermore, a relaxation parameter α is introducted such that one can, if convenient, make it easier or more difficult to issue a joint order when following the policy-iteration step. Also, a vector of can-orders is employed, in case a joint order is made, to include additional items. The policy is denoted a (c, S, α ) policy. Numerical results show that is performs almost as well as the Q (s, S) policy and contrary to the Q(s, S) policy, it is stationary. Also some of the peculiarities of the Q (s, S) that can appear for a constructed data set may be better handled by the (c, S, α) policy. Numerical results also indicate that given a can-order policy one can always constuct a better (c,S, α) policy

KW - Inventory

KW - Stochastic demand

KW - Joint replenishment

KW - Control policies

M3 - Working paper

SP - 1

EP - 16

BT - A heuristic for computing a new value-based stationary policy for the stochastic joint replenishment problem

ER -