International Journal of Inventory Research http://www.inderscience.com/browse/index.php?journalID=178&year=2011&vol=1&issue=3/4 Inderscience Publishers Ltd en-uk International Journal of Inventory Research 1746-6962 1746-6970 © 2011 Inderscience Publishers Ltd editor@inderscience.com https://www.inderscience.com/images/files/coverImgs/ijir_scoverijir.jpg http://www.inderscience.com/browse/index.php?journalID=178&year=2011&vol=1&issue=3/4 http://www.inderscience.com/link.php?id=45383 We consider a replenishment control system in which product returns play an important role in inventory planning. We focus on the inventory of an individual item that is stored at a single location to meet a constant demand over time. We assume that the total amount of returns accumulated over a period of time can be represented by a compound Poisson process. We further assume that opportunities for inventory disposals or relocation arise occasionally in accordance with a Poisson process. We not only seek to resolve the issues of when to order and how much to order, we also consider the question of when to dispose of excess inventory and by how much. Inventory reductions occur when the opportunity for a disposal arises and the inventory position is deemed too high. After each disposal the inventory position is restored to a specified base-stock level. We develop a cost model of this system and highlight its properties through an extensive numerical study. A replenishment control system with uncertain returns and random opportunities for disposal
Ben A. Chaouch
International Journal of Inventory Research, Vol. 1, No. 3/4 (2011) pp. 221 - 247
We consider a replenishment control system in which product returns play an important role in inventory planning. We focus on the inventory of an individual item that is stored at a single location to meet a constant demand over time. We assume that the total amount of returns accumulated over a period of time can be represented by a compound Poisson process. We further assume that opportunities for inventory disposals or relocation arise occasionally in accordance with a Poisson process. We not only seek to resolve the issues of when to order and how much to order, we also consider the question of when to dispose of excess inventory and by how much. Inventory reductions occur when the opportunity for a disposal arises and the inventory position is deemed too high. After each disposal the inventory position is restored to a specified base-stock level. We develop a cost model of this system and highlight its properties through an extensive numerical study.

]]> 10.1504/IJIR.2011.045383 International Journal of Inventory Research, Vol. 1, No. 3/4 (2011) pp. 221 - 247 Ben A. Chaouch Odette School of Business, University of Windsor, Ontario N9B 3P4, Canada inventory management product returns random disposal stochastic models level-crossing theory replenishment control uncertain returns inventory planning excess inventory cost modelling. 2012-02-08T23:20:50-05:00 1 3/4 221 247 2012-02-08T23:20:50-05:00 http://www.inderscience.com/link.php?id=45384 Economic production quantities address an important problem in operations management. The objective is to determine the quantity that minimises total cost required to manufacture goods and hold inventories when production is performed incrementally during the manufacturing process. The dynamic impact of costs and demand is often neglected though parameters may vary over time. In this context, optimal control theory goes beyond the suggestion of a numerical approach and allows for an analytical interpretation of optimal solutions. This paper presents a deterministic continuous time approach minimising the net present value of production and inventory holding cost with dynamic parameters. Manufacturing cost per item, holding cost, and demand rate vary over time. Applying Pontryagin's maximum principle, the optimal policy involves intervals of production at the capacity limit with inventory build up, destocking periods, and periods of just-in-time production. A solution algorithm is presented to find the optimal manufacturing quantities and an economic interpretation of an optimal solution is provided. A continuous time dynamic optimal control manufacturing problem
Jan Arnold; Stefan Minner; Matthias Morrocu
International Journal of Inventory Research, Vol. 1, No. 3/4 (2011) pp. 248 - 261
Economic production quantities address an important problem in operations management. The objective is to determine the quantity that minimises total cost required to manufacture goods and hold inventories when production is performed incrementally during the manufacturing process. The dynamic impact of costs and demand is often neglected though parameters may vary over time. In this context, optimal control theory goes beyond the suggestion of a numerical approach and allows for an analytical interpretation of optimal solutions. This paper presents a deterministic continuous time approach minimising the net present value of production and inventory holding cost with dynamic parameters. Manufacturing cost per item, holding cost, and demand rate vary over time. Applying Pontryagin's maximum principle, the optimal policy involves intervals of production at the capacity limit with inventory build up, destocking periods, and periods of just-in-time production. A solution algorithm is presented to find the optimal manufacturing quantities and an economic interpretation of an optimal solution is provided.

]]> 10.1504/IJIR.2011.045384 International Journal of Inventory Research, Vol. 1, No. 3/4 (2011) pp. 248 - 261 Jan Arnold; Stefan Minner; Matthias Morrocu Camelot IDPro AG, Theodor-Heuss-Anlage 12, 68165 Mannheim, Germany. ' Department of Business, Economics, and Statistics, University of Vienna, 1210 Vienna, Austria. ' T&O Unternehmensberatung GmbH, 82205 Gilching bei München, Germany economic production quantity EPQ optimal control continuous time operations management manufacturing cost holding cost demand rate production capacity inventory build up destocking just-in-time JIT production manufacturing quantities. 2012-02-08T23:20:50-05:00 1 3/4 248 261 2012-02-08T23:20:50-05:00 http://www.inderscience.com/link.php?id=45385 When unit item costs are high and expected demand during leadtime is low, it may be desirable to implement the (0, 1) inventory policy which calls for ordering one unit when the inventory falls to zero. Under this policy, when demand arrivals constitute a renewal process it may also be desirable to delay the order release (but expedite the orders occurring during the delay period). This paper examines the (0, 1) model by focussing on its probabilistic properties. We first present explicit expressions for, 1) the probability distribution of the expedited orders; 2) the interval over which inventory is positive. Using these results, we introduce a (service-level type) chance-constraint on the number of expedited orders and determine the optimal and finite order delay. We also consider a case where the cost of expediting an order may be difficult to estimate and compute its implied value. More general models that allow non-monotone renewal density and random leadtimes are also presented and analysed. Analysis of a (0, 1) inventory system where demand follows a renewal process
Mahmut Parlar
International Journal of Inventory Research, Vol. 1, No. 3/4 (2011) pp. 262 - 287
When unit item costs are high and expected demand during leadtime is low, it may be desirable to implement the (0, 1) inventory policy which calls for ordering one unit when the inventory falls to zero. Under this policy, when demand arrivals constitute a renewal process it may also be desirable to delay the order release (but expedite the orders occurring during the delay period). This paper examines the (0, 1) model by focussing on its probabilistic properties. We first present explicit expressions for, 1) the probability distribution of the expedited orders; 2) the interval over which inventory is positive. Using these results, we introduce a (service-level type) chance-constraint on the number of expedited orders and determine the optimal and finite order delay. We also consider a case where the cost of expediting an order may be difficult to estimate and compute its implied value. More general models that allow non-monotone renewal density and random leadtimes are also presented and analysed.

]]> 10.1504/IJIR.2011.045385 International Journal of Inventory Research, Vol. 1, No. 3/4 (2011) pp. 262 - 287 Mahmut Parlar DeGroote School of Business, McMaster University, 1280 Main St. W., Hamilton, Ontario L8S 4M4, Canada stochastic inventory 0-1 order policy renewal process implied cost probability distribution order delay modelling renewal density random leadtimes. 2012-02-08T23:20:50-05:00 1 3/4 262 287 2012-02-08T23:20:50-05:00 http://www.inderscience.com/link.php?id=45386 Marketing literature has long recognised price elasticity can increase the short term mean demand by as much as 400%. In this paper, we capture this behaviour of demand using a bi-level demand function and address the related inventory management problem. The seemingly simple problem turns out to be difficult to solve optimally. We present optimal and heuristic approaches. We also reformulate this problem by making price and duration as decision variables under profit maximisation environment and present calculus-based solutions. Inventory policies for products with bi-level demand: optimal and heuristic algorithms
Parag Dhumal; P.S. Sundararaghavan; Udayan Nandkeolyar
International Journal of Inventory Research, Vol. 1, No. 3/4 (2011) pp. 288 - 321
Marketing literature has long recognised price elasticity can increase the short term mean demand by as much as 400%. In this paper, we capture this behaviour of demand using a bi-level demand function and address the related inventory management problem. The seemingly simple problem turns out to be difficult to solve optimally. We present optimal and heuristic approaches. We also reformulate this problem by making price and duration as decision variables under profit maximisation environment and present calculus-based solutions.

]]> 10.1504/IJIR.2011.045386 International Journal of Inventory Research, Vol. 1, No. 3/4 (2011) pp. 288 - 321 Parag Dhumal; P.S. Sundararaghavan; Udayan Nandkeolyar Department of Business, University of Wisconsin-Parkside, 900 Wood Road, Kenosha, WI 53141, USA. ' Information, Operations and Technology Management Department, The College of Business and Innovation, The University of Toledo, Toledo, Ohio – 43606, USA. ' Information, Operations and Technology Management Department, The College of Business and Innovation, The University of Toledo, Toledo, Ohio – 43606, USA inventory control heuristics economic order quantity EOQ ordering policy bi-level demand price elasticity demand behaviour inventory management. 2012-02-08T23:20:50-05:00 1 3/4 288 321 2012-02-08T23:20:50-05:00