The Experts below are selected from a list of 282 Experts worldwide ranked by ideXlab platform
Soren Johansen - One of the best experts on this subject based on the ideXlab platform.
-
optimal and near optimal policies for lost sales inventory models with at most one Replenishment Order outstanding
European Journal of Operational Research, 2006Co-Authors: Roger M Hill, Soren JohansenAbstract:In this paper we use policy-iteration to explore the behaviour of optimal control policies for lost sales inventory models with the constraint that not more than one Replenishment Order may be outstanding at any time. Continuous and periodic review, fixed and variable lead times, Replenishment Order sizes which are constrained to be an integral multiple of some fixed unit of transfer and service level constraint models are all considered. Demand is discrete and, for continuous review, assumed to derive from a compound Poisson process. It is demonstrated that, in general, neither the best (s, S) nor the best (r, Q) policy is optimal but that the best policy from within those classes will have a cost which is generally close to that of the optimal policy obtained by policy iteration. Finally, near-optimal computationally-efficient control procedures for finding (s, S) and (r, Q) policies are proposed and their performance illustrated.
-
production manufacturing and logistics optimal and near optimal policies for lost sales inventory models with at most one Replenishment Order outstanding
2006Co-Authors: Roger M Hill, Soren JohansenAbstract:In this paper we use policy-iteration to explore the behaviour of optimal control policies for lost sales inventory models with the constraint that not more than one Replenishment Order may be outstanding at any time. Continuous and periodic review, fixed and variable lead times, Replenishment Order sizes which are constrained to be an integral multiple of some fixed unit of transfer and service level constraint models are all considered. Demand is discrete and, for continuous review, assumed to derive from a compound Poisson process. It is demonstrated that, in general, neither the best (s, S) nor the best (r, Q) policy is optimal but that the best policy from within those classes will have a cost which is generally close to that of the optimal policy obtained by policy iteration. Finally, near-optimal computationally-efficient control procedures for finding (s, S) and (r, Q) policies are proposed and their performance illustrated.
-
The (r,q) policy for the lost-sales inventory system when more than one Order may be outstanding
2004Co-Authors: Soren Johansen, Anders ThorstensonAbstract:We study the continuous-review (r; q) system in which un_lled demands are treated as lost sales. The reOrder point r is allowed to be equal to or larger than the Order quantity q. Hence, we do not restrict our attention to the well-known case with at most one Replenishment Order outstanding, but our modeling streamlines exact analysis of that case. The cost structure is standard. We assume that demand is Poisson, that lead times are Erlangian and that Orders do not cross in time (lead times are sequential). We determine the equilibrium distribution of the inventory on hand at the delivery instants from the solution (obtained by the Gauss-Seidel method) of the equilibrium equations of a Markov chain. To optimize r and q we develop an adapted version of the algorithm suggested by Federgruen and Zheng for the backOrders model (BO). The results obtained in our numerical study show that the suggested procedure dominates standard textbook approximations. In particular, the reductions in the average cost of a simple Economic Order Quantity policy are in the range of 3-14%. Except when lead times are long and variable or when the unit cost of shortage is low, the optimal BO policy provides a fair approximation to the average cost of the best policy.
-
The (r,Q) control of a periodic-review inventory system with continuous demand and lost sales
International Journal of Production Economics, 2000Co-Authors: Soren Johansen, Roger M HillAbstract:Abstract In this paper we consider a periodic review inventory model with lost sales during a stockout and with the constraint that at most one Replenishment Order may be outstanding at any time. Demands in successive review periods are independent, identically distributed variables from a continuous distribution. The fixed lead time is an integral number of review periods. We explore control policies of the (r,Q) type – that is a Replenishment Order of size Q is placed when the inventory position (stock in hand plus stock on Order) falls to or below the re-Order level r. We use asymptotic renewal theory results to estimate the `undershoot’ of the re-Order level r and also to estimate the cycle stockholding cost (which turns out to take a relatively simple form). Based on these approximations we set out a policy improvement solution methodology and illustrate this with some numerical examples for which demand is normally distributed. These numerical examples suggest that a relatively simple approach, based on the economic Order quantity, can provide results which are very close to optimal.
-
can Order policies for coordinated inventory Replenishment with erlang distributed times between Ordering
European Journal of Operational Research, 1999Co-Authors: Helle Schultz, Soren JohansenAbstract:Abstract We consider the Replenishment of items from the same supplier when the cost of each Replenishment Order is the sum of a major fixed cost and ordinary item-dependent costs. The items are coordinated by the ( s , c , S ) policy. A decomposition algorithm is developed to compute the parameters of the policy for each item. The algorithm assumes that the time between Ordering is Erlang distributed, with parameters depending on the actual policy. The algorithm is used on various examples and it performs well in comparison with other algorithms. We illustrate that this and related decomposition algorithms do not always converge and the policy identified by the algorithms is not necessarily the best one among the ( s , c , S ) policies.
Roger M Hill - One of the best experts on this subject based on the ideXlab platform.
-
optimal and near optimal policies for lost sales inventory models with at most one Replenishment Order outstanding
European Journal of Operational Research, 2006Co-Authors: Roger M Hill, Soren JohansenAbstract:In this paper we use policy-iteration to explore the behaviour of optimal control policies for lost sales inventory models with the constraint that not more than one Replenishment Order may be outstanding at any time. Continuous and periodic review, fixed and variable lead times, Replenishment Order sizes which are constrained to be an integral multiple of some fixed unit of transfer and service level constraint models are all considered. Demand is discrete and, for continuous review, assumed to derive from a compound Poisson process. It is demonstrated that, in general, neither the best (s, S) nor the best (r, Q) policy is optimal but that the best policy from within those classes will have a cost which is generally close to that of the optimal policy obtained by policy iteration. Finally, near-optimal computationally-efficient control procedures for finding (s, S) and (r, Q) policies are proposed and their performance illustrated.
-
production manufacturing and logistics optimal and near optimal policies for lost sales inventory models with at most one Replenishment Order outstanding
2006Co-Authors: Roger M Hill, Soren JohansenAbstract:In this paper we use policy-iteration to explore the behaviour of optimal control policies for lost sales inventory models with the constraint that not more than one Replenishment Order may be outstanding at any time. Continuous and periodic review, fixed and variable lead times, Replenishment Order sizes which are constrained to be an integral multiple of some fixed unit of transfer and service level constraint models are all considered. Demand is discrete and, for continuous review, assumed to derive from a compound Poisson process. It is demonstrated that, in general, neither the best (s, S) nor the best (r, Q) policy is optimal but that the best policy from within those classes will have a cost which is generally close to that of the optimal policy obtained by policy iteration. Finally, near-optimal computationally-efficient control procedures for finding (s, S) and (r, Q) policies are proposed and their performance illustrated.
-
Inventory policies for all-or-nothing demand processes
International Journal of Production Economics, 2001Co-Authors: Roger M Hill, Matthew J DomineyAbstract:Abstract When there is insufficient stock to meet a specific customer Order, a common assumption is that the remaining stock will be used to satisfy the Order partially while the balance of the Order is backOrdered or lost – this is the ‘partial backOrder’ or ‘partial lost sales’ assumption. In this paper we consider what happens when the nature of the demand process is such that Orders must be met in full or not at all – this is the ‘all-or-nothing’ demand assumption. We concentrate, for the purpose of illustration, on the context of a continuous review model, with a Poisson customer arrival rate, with a fixed lead time and for which not more than one Replenishment Order may be outstanding at any time.
-
The (r,Q) control of a periodic-review inventory system with continuous demand and lost sales
International Journal of Production Economics, 2000Co-Authors: Soren Johansen, Roger M HillAbstract:Abstract In this paper we consider a periodic review inventory model with lost sales during a stockout and with the constraint that at most one Replenishment Order may be outstanding at any time. Demands in successive review periods are independent, identically distributed variables from a continuous distribution. The fixed lead time is an integral number of review periods. We explore control policies of the (r,Q) type – that is a Replenishment Order of size Q is placed when the inventory position (stock in hand plus stock on Order) falls to or below the re-Order level r. We use asymptotic renewal theory results to estimate the `undershoot’ of the re-Order level r and also to estimate the cycle stockholding cost (which turns out to take a relatively simple form). Based on these approximations we set out a policy improvement solution methodology and illustrate this with some numerical examples for which demand is normally distributed. These numerical examples suggest that a relatively simple approach, based on the economic Order quantity, can provide results which are very close to optimal.
-
On the suboptimality of (S-1, S) lost sales inventory policies
International Journal of Production Economics, 1999Co-Authors: Roger M HillAbstract:Abstract This paper considers Replenishment policies for the continuous review inventory model with Poisson demand, a fixed lead time on Replenishment and lost sales during a stockout. There is a time-dependent stockholding cost and a cost per unit of sale lost but there is no (or negligible) cost associated with placing a Replenishment Order. The standard policy is to specify a maximum stock level, S, and place a Replenishment Order whenever a demand occurs and is met. This is commonly referred to as an (S−1, S) policy. It is shown that there are other Replenishment policies which give lower-cost solutions. In fact it is demonstrated that an (S−1, S) policy can never be optimal if S⩾2.
Ka Fai Cedric Yiu - One of the best experts on this subject based on the ideXlab platform.
-
Analysis of optimal opportunistic Replenishment policies for inventory systems by using a (s,S) model with a maximum issue quantity restriction
European Journal of Operational Research, 2005Co-Authors: K. L. Mak, K. K. Lai, W. C. Ng, Ka Fai Cedric YiuAbstract:The analysis of optimal inventory Replenishment policies for items having lumpy demand patterns is difficult, and has not been studied extensively although these items constitute an appreciable portion of inventory populations in parts and supplies types of stockholdings. This paper studies the control of an inventory item when the demand is lumpy. A continuous review (s,S) policy with a maximum issue quantity restriction and with the possibility of opportunistic Replenishment is proposed to avoid the stock of these items being depleted unduly when all the customer Orders are satisfied from the available inventory and to reduce Ordering cost by coordinating inventory Replenishments. The nature of the customer demands is approximated by a compound Poisson distribution. When a customer Order arrives, if the Order size is greater than the maximum issue quantity w, the Order is satisfied by placing a special Replenishment Order rather than from the available stock directly. In addition, if the current inventory position is equal to or below a critical level A when such an Order arrives, an opportunistic Replenishment Order which combines the special Replenishment Order and the regular Replenishment Order will be placed, in Order to satisfy the customer's demand and to bring the inventory position to S. In this paper, the properties of the cost function of such an inventory system with respect to the control parameters s, S and A are analysed in detail. An algorithm is developed to determine the global optimal values of the control parameters. Indeed, the incorporation of the maximum issue quantity and opportunistic Replenishment into the (s,S) policy reduces the total operating cost of the inventory system. © 2004 Elsevier B.V. All rights reserved.
Rommert Dekker - One of the best experts on this subject based on the ideXlab platform.
-
an efficient optimal solution method for the joint Replenishment problem with minimum Order quantities
European Journal of Operational Research, 2006Co-Authors: Eric Porras, Rommert DekkerAbstract:We study the joint Replenishment problem (JRP) for M items under deterministic demand, with a minimum Order quantity constraint for each item in the Replenishment Order. We derive bounds on the basic cycle time and we propose an efficient global optimisation procedure to solve the JRP with constraints. Moreover, we also consider the case where a correction is made for empty Replenishment occasions. The algorithms are tested with data from a real case and some additional numerical experiments are also presented.
-
an efficient optimal solution method for the joint Replenishment problem with minimum Order quantities
Econometric Institute Research Papers, 2003Co-Authors: Porras E Musalem, Rommert DekkerAbstract:textabstractWe study the joint Replenishment problem (JRP) for M items under deterministic demand, with a minimum Order quantity constraint for each item in the Replenishment Order. We first study an iterative procedure that proves to be not efficient in this case. Further, we derive bounds on the basic cycle time and propose an efficient global optimisation procedure to solve the JRP with constraints. Moreover, we also consider the case where a correction is made for empty Replenishment occasions. The algorithms are tested in a real case.
W. C. Ng - One of the best experts on this subject based on the ideXlab platform.
-
Analysis of optimal opportunistic Replenishment policies for inventory systems by using a (s,S) model with a maximum issue quantity restriction
European Journal of Operational Research, 2005Co-Authors: W. C. NgAbstract:Abstract The analysis of optimal inventory Replenishment policies for items having lumpy demand patterns is difficult, and has not been studied extensively although these items constitute an appreciable portion of inventory populations in parts and supplies types of stockholdings. This paper studies the control of an inventory item when the demand is lumpy. A continuous review (s,S) policy with a maximum issue quantity restriction and with the possibility of opportunistic Replenishment is proposed to avoid the stock of these items being depleted unduly when all the customer Orders are satisfied from the available inventory and to reduce Ordering cost by coordinating inventory Replenishments. The nature of the customer demands is approximated by a compound Poisson distribution. When a customer Order arrives, if the Order size is greater than the maximum issue quantity w, the Order is satisfied by placing a special Replenishment Order rather than from the available stock directly. In addition, if the current inventory position is equal to or below a critical level A when such an Order arrives, an opportunistic Replenishment Order which combines the special Replenishment Order and the regular Replenishment Order will be placed, in Order to satisfy the customer's demand and to bring the inventory position to S. In this paper, the properties of the cost function of such an inventory system with respect to the control parameters s, S and A are analysed in detail. An algorithm is developed to determine the global optimal values of the control parameters. Indeed, the incorporation of the maximum issue quantity and opportunistic Replenishment into the (s,S) policy reduces the total operating cost of the inventory system.
-
Analysis of optimal opportunistic Replenishment policies for inventory systems by using a (s,S) model with a maximum issue quantity restriction
European Journal of Operational Research, 2005Co-Authors: K. L. Mak, K. K. Lai, W. C. Ng, Ka Fai Cedric YiuAbstract:The analysis of optimal inventory Replenishment policies for items having lumpy demand patterns is difficult, and has not been studied extensively although these items constitute an appreciable portion of inventory populations in parts and supplies types of stockholdings. This paper studies the control of an inventory item when the demand is lumpy. A continuous review (s,S) policy with a maximum issue quantity restriction and with the possibility of opportunistic Replenishment is proposed to avoid the stock of these items being depleted unduly when all the customer Orders are satisfied from the available inventory and to reduce Ordering cost by coordinating inventory Replenishments. The nature of the customer demands is approximated by a compound Poisson distribution. When a customer Order arrives, if the Order size is greater than the maximum issue quantity w, the Order is satisfied by placing a special Replenishment Order rather than from the available stock directly. In addition, if the current inventory position is equal to or below a critical level A when such an Order arrives, an opportunistic Replenishment Order which combines the special Replenishment Order and the regular Replenishment Order will be placed, in Order to satisfy the customer's demand and to bring the inventory position to S. In this paper, the properties of the cost function of such an inventory system with respect to the control parameters s, S and A are analysed in detail. An algorithm is developed to determine the global optimal values of the control parameters. Indeed, the incorporation of the maximum issue quantity and opportunistic Replenishment into the (s,S) policy reduces the total operating cost of the inventory system. © 2004 Elsevier B.V. All rights reserved.