Joint Replenishment Inventory - Can-Order Replenishment System - Thesis Example

Joint Replenishment Inventory (Can-Order Replenishment System) Table of Contents Article Review 3 Canorder 3 Canorder 2 5 Canorder 3 7 Canorder 4 9Canorder 5 11 Canorder 6 13 Canorder 7 15 Canorder 8 17 Canorder 9 19 19 Comparison of the Results 20 Conclusion to the Review 22 References 24 Article Review Canorder 1 Objectives: The prime objective of this particular article of Silver (1981) is focused on introducing and implementing an approach of lessening setup costs that are incurred based on per unit time while considering the coordination of replenishments of a specific group or a family. Apart from this, other objective of the article was identified to be assessing the coordinated control of a particular group dealing with inventoried items. The author of the article Silver (1981) paid utmost attention on diminishing the replenishment costs that imposes considerable impact on the overall performance of the replenishment groups. Aims: In relation to the above discussed objectives, the following aims of the article of Silver (1981) would be vital to take into concern for discussion: Determining persistence of exact lead time Proper evaluation of the setup costs Tracing out involved items within the replenishment group Finding appropriate cost structures Identification as well as application of a specific control system Method Used: In the provided article of Silver (1981), different systems rather than methods have been widely utilised for the purpose of lessening setup expenses incurred based on per unit time. In precise, for keeping a greater control of costs associated with replenishment in the form of decreasing the same, the author Silver (1981) considered a definite control system, which was denoted as (S,c,s) system. Apart from this, another system i.e. Compound Poisson Demand was also being used for the fulfilment of the above stated objective. Based on the article of Silver (1981), it can be found that in consideration of the above discussed two particular methods were able to fulfil the stated objective, which is discussed in the section below. Results and Conclusion: While explaining the results and drawing a suitable conclusion about how the selected control systems such as Compound Poisson Model and (S,c,s) mechanism had attained success in lessening the setup replenishment costs, it will be vital to mention that utmost focus was laid upon inventory levels. In this regard, according to the article of Silver (1981), the control system i.e. (S,c,s) mechanism was used wherein distinct inventory levels were reviewed incessantly with determining the persistent inventory positions. On the other hand, the Poisson Model was executed to enlarge the probability allocation of entire demand of a particular item, which occurs during the interval of replenishment lead time. In terms of results, the article of Silver (1981) revealed that execution of (S,c,s) mechanism is capable to diminish the setup replenishment costs by checking the execution times and developing computerised routines with satisfying specified service constraints. Thus, in conclusion, it can be affirmed that the concepts including lead time and inventory levels affect the replenishment costs to be increased or reduced by a considerable degree. In such circumstances, the methods including (S,c,s) and Compound Poisson Model are ascertained to be quite beneficial in controlling such costs to a desired level. Canorder 2 Objectives: The objectives of the article of Silver (1974) include measuring the coordination level of replenishment orders and selecting of appropriate group items. The article mainly intended to focus on attributes that have potentiality of leading into causing significant savings. Thus, Silver (1974) in the article emphasised ratifying as well as measuring coordinated replenishment mechanism in the fork of utilising varied quality as well as effective systems. In order to fulfil the above stated objectives, the article remained much concerned about identifying, determining and implementing a practical procedure based on which order-up-to-levels and must-order along with can-order points can be selected for refurbishing a coordinated control system related to synchronised inventory replenishment (Silver, 1974). Aims: By taking into concern the aforementioned objectives, the article of Silver (1974) laid down the following aims that must be attained for drawing a valid conclusion of the study: Deriving Economic Order Quantities (EOQ) Analysing methods of coordinating varied items for the purpose of replenishment Assessing the futuristic demand of the items Determining the impact of possible constraints on the economic order quantities Recognising the probable nature of demand Method Used: In relation to the article of Silver (1974), the Poisson Demand Model was used for ascertaining the fact that maximisation of replenishment orders for a particular selected item group might lead towards significant savings in the replenishment costs. While considering this model, certain suppositions were made. In this similar context, one of such assumptions was identified to be considering the demand factor as Poisson. Apart from this, the article of Silver (1974), reflected an unchanging non-zero replenishment lead time that was also assumed for fulfilling the aforesaid objective. More importantly, the author also highlighted the use of one of the efficient control strategies i.e. (S,c,s) policy in relation to the above context. Results and Conclusion: Based on the making of various assumptions, the results of the article of Silver (1974) portrayed that synchronization of replenishment orders for a selected item group is directly associated with cost savings, total expected costs and estimated service levels among others. With regards to the article of Silver (1974), it can be ascertained that cost comparisons with inclusion of effective along with quality independent strategy do affect substantial savings by averaging 18.8% through the approach of coordination. This denotes the prevalence of direct connection between coordinated inventory replenishment and best independent control strategy (Silver, 1974). In terms of conclusion, it is to be affirmed that the article developed a practical process for calculating control parameters’ values within a coordinated replenishment structure. While testing varied numerical based examples, it can be ascertained that average savings in relation to replenishment as well as carrying expenditures were recorded at 18.8%. This denotes the percentage of cost savings in the background of a well-coordinated inventory replenishment system. In precise, the results that were highlighted in the article represented the fact that substantial savings can be witnessed through coordination means. Canorder 3 Objectives: This particular article of Thompstone & Silver (1975) has relevance with that of the article of Silver (1974). This can be acceptable with reference to the fact that the article of Thompstone & Silver (1975) focused on explaining the role-play by coordination of replenishment items towards making significant level of savings in the replenishment costs. With this concern, the article intended to take into concern different variables based on which substantial savings can be made by making better coordination of replenishment based items as well as costs. This could be regarded as one of the major objectives of the article. Aims: With regards to the above depicted objectives, the prime aims of the article have been portrayed hereunder. Understanding the circumstances wherein coordination of a single or a group of items might result into causing extensive level of cost savings Identifying and applying an effective control system towards measuring the level of such cost savings Examining the situations wherein the approach of coordination may prove to be quite advantageous Developing methods of effective control system Demonstrating about how control variables may get selected in the stated purpose Method Used: It has been earlier mentioned that the article of Thompstone & Silver (1975) is deemed to be much parallel with the article of Silver (1974). In this regard, the technique or the system used in the above stated two articles was found to be similar for attaining the set objectives. In the context of the article concerning Thompstone & Silver (1975), it has been ascertained that the Poisson Demand Model was used for ascertaining the rise in savings of replenishment costs. Apart from this model, a (S,c,s) based control system was also used for fulfilling the stated objective with ease. Results and Conclusion: In order to determine the extent up to which the replenishment costs are increased by forming better coordination amid the replenishment items, the association persisting between the projected cost savings of coordinated control and varied features of replenishment group of items was assessed and controlled. By determining such relationship, the results highlighted the fact of increasing substantial savings by forming effective coordination of replenishments with zero lead time. In this particular article of Thompstone & Silver (1975), the average value was recorded at 15.9%, which was quite low as compared to that of the article of Silver (1974) that estimated the same at 18.8%. Thus, in conclusion, it can be stated that the control system of (S,c,s) and Poisson Demand Model were able to determine the role play by several items of replenishment on making huge amount of savings in the replenishment costs with the consideration of zero lead time. From the article, it is clear to understand that there lay certain situations wherein better coordination amid the group items of replenishment might result into making increased level of cost savings. In this regard, one of such circumstances was reckoned to be decreased lead time and superior command over the increasing costs of replenishment. Canorder 4 Objectives: One of the chief objectives of this article “Coordinated Replenishments in a Multi-Item Inventory System with Compound Poisson Demands” of Federgruen & et. al. (1984) include conducting continuous review of multi-item inventory system with consideration to the procedure of Compound Poisson Demand. Apart from this, the other objectives of the above stated article were reckoned to be verifying whether excess demands of replenishment items were backlogged also identifying whether such items require lead time to raise the demand of the same. Aims: With regards to the above stated objectives, the following aims were broadly considered by the author of the article: Determining particular setup expenses of individual item to be entailed in the replenishment procedure Working over the potential impacts laid down by service-level constraints specifically on the existing inventory bases Providing solutions towards addressing as well as mitigating any sort of issue persisting within the replenishment system Presenting an effective heuristic algorithm for ensuring coordinated control rule Making better allocation of replenishment based items Method Used: Based on the observation made in the article of Federgruen & et. al. (1984), certain quality methods were used to attain the aforesaid objectives as well as aims. In this context, two of the useful methods encompassing zero lead time and Poisson Demand Distribution Model were used. These models emphasised viewing as well as analysing the dimensionality of the replenishment costs as well as items, determining whether methods of standard solution are intractable in a computational manner and working over the setup costs that is likely to measure the increase in cost savings. By utilising Poisson Demand Distribution Model and zero lead time as the chief elements, an attempt has been made towards ensuing greater optimisation of coordinated control rule in the context of multi-item inventory system (Federgruen & et. al. 1984). Results and Conclusion: From the results depicted in this article analysed above reflect that an extensive level of savings can be made by the procedure of merging numerous items in a single order. In this similar context, such items, as per the article of Federgruen & et. al. (1984), can be reckoned as replenishment cost structure, service-level constraints, inventory levels, cost savings and independent control. The results of the above stated article depicted that the replenishment costs in a multi-item inventory method with the inclusion of the model concerning Compound Poisson Model can be worked out and likewise can also be changed by effective utilisation of coordinated based control algorithm and better evaluation of the quantities of interest. In conclusion, it can be affirmed that the practical independency of certain crucial factors including lead time and service-level constraints certainly leads towards generating better as well as positive results in ascertaining appropriate replenishment costs specifically in a multi-item inventory system. By taking into concern the results depicted in the article, it is apparent that an extensive level of cost savings can be attained by proper usage of suboptimal coordinated control rather than considering best coordinated control. Canorder 5 Objectives: The identification and analysis of reasons that lead to the problem of joint-replenishment are the prime objectives of the article propounded by Kayis & et. al. (2008). Apart from this, the stated article intended to determine the prevailing standard cost structures, working upon economies of scale and evaluating inventory positions for recognising the problems persisted within joint-replenishment. Similar to the articles of Thompstone & Silver (1975) and Silver (1974), this particular article is also identified to consider certain significant aspects for identifying as well as mitigating varied problems persisted within joint-replenishment. In this similar context, such aspects can be reckoned as lead time, inventory levels and replenishment costs or replenishment based cost structures among others (Kayis & et. al., 2008). Aims: By taking into concern, the above discussed objectives laid down under the article of Kayis & et. al. (2008), certain aims can be derived from the same that have been depicted in the following: To acquire a brief understanding about the notion of joint-replenishment To ascertain the situations based on which problems are likely to be occurred in joint-replenishment To identify the reasons for which joint-replenishment problems mainly erupt To assess the impacts of problems of joint-replenishment particularly on lead time, inventory levels and replenishment cost structure To work upon inventory positions in accordance with replenishment cost structure and savings Method Used: In the article of Kayis & et. al. (2008), certain methods were adopted as well as implemented for ascertaining the problems persistent within joint-replenishment that impose extensive level of impact on inventory levels, lead time and replenishment cost structure or savings as well. In this regard, such methods were reckoned as adopting along with following semi-Markov decision procedure and considering three particular parameters that entail can-order level denoted as cj, reorder level represented as the symbol of sj and order-up-to level signified as Sj (Kayis & et. al. 2008). Apart from the above discussed methods, in relation to modelling context, a two-item inventory system was also considered for finding out joint-replenishment problems. It can be apparently observed in this similar concern that in terms of modelling factor, demand specifically for the item 1 was mainly generated by the inclusion of a Poisson procedure with rating the same as λ. On the other hand, the demand for the item 2 was created by a Poisson procedure with rating the similar context as µ. More importantly, alongside with considering such modelling items, the inventory levels were also reviewed on a periodic manner (Kayis & et. al. 2008). Results and Conclusion: The results depicted in the article of Kayis & et. al. (2008) clearly evidences the fact of causing joint-replenishment problem with having a special note on the factor of can-order policy. Specially mentioning, with the changes noted in the aspect of can-order policy, significant differences in the joint-replenishment costs can be witnessed. In addition, the decomposition assumption is also noted to be contributed in making greater differences in the problems persistent within joint-replenishment that is caused by can-order class (Kayis & et. al. 2008). Based on the overall analysis of the article, it can be ascertained that the factor concerning can-order policy contributes in making significant differences in the structure of joint-replenishment, which eventually results in minimising long-run average costs per unit time and complicating the assumption pattern. Canorder 6 Objectives: In accordance with the article of Fung & et. al. (2001), the prime intent can be reckoned as determining whether extensive reductions in cost could be attained through the incorporation of an inventory system and by execution of (T,S) policy. It can be apparently observed that this particular article has duly considered a coordinated ‘periodic-review, order-up-to-level’ policy named (T,S) policy for determining multi-item inventory systems. Thus, in relation to the above context, it is to be affirmed that the article intended to study varied problems persistent within coordinated inventory also analysing the theories that are broadly executed in real practice. While ascertaining these objectives of the above stated article, it will be vital to mention that the models associated with coordinated inventory are widely executed at the time when several quantity of items get engaged into a replenishment and likewise expands the probability of sharing fixed costs in an efficient way (Fung & et. al., 2001). Aims: The below discussed aims were observed to be laid down in the article for attaining the above stated objectives. To possess a clear and better understanding about how the factor concerning considerable reductions in costs To ascertain conditions based on which considerable cost reductions could be accomplished in long run To determine the policy outcomes in relation to accomplish substantial cost reductions specifically when lead time does not become too short To recognise fixed costs engaged into replenishment Method Used: Similar to the above discussed articles, certain effective methods were also identified to get utilised in the article of Fung & et. al. (2001). This is mainly because for determining about how extensive level of cost reductions could be attained during the time when lead time does not appear to be short. Thus, in this similar context, it can be apparently observed that the article employed (T,S) policy for fulfilling the above stated objective. Specially mentioning, this policy has been taken into concern with the inclusion of service-level constraints and lead time (Fung & et. al. 2001). Results and Conclusion: While exploring the results relevant to the article of Fung & et. al. (2001), it can be found that considerable cost reductions could be attained by increasing the replenishment lead time and also raising the inventory levels as well. Based on the findings and results obtained in relation to the above stated article, it will be vital to mention that cost reductions generally increase with greater augmentation in lead time because huge figure of inventories are required for satisfying or fulfilling the demands as well as requirements for longer lead time (Fung & et. al. 2001). In terms of conclusion, it is to be affirmed that this particular article examined the significance of (T,S) policy in the context of multi-item inventory based systems. Based on the results obtained, it is evident that (T,S) policy is a better choice for resolving any sort of non-zero lead time based problems. This might be owing to the reason that with significant rise in service level, the accumulated savings of (T,S) policy decreased, which in turn, raises the probability of extensive cost reductions. Canorder 7 Objectives: The prime objective of the article “Multi-product batch replenishment strategies under stochastic demand and a joint capacity constraint” of Minner & Silver (2005) was ascertained to be analysing a multi-product inventory replenishment based problem with the inclusion of Poisson demands. This specific problem mainly represents the restriction of aggregate inventory level at any point of time by a common space or budget limitation. While focusing on this particular objective, it is to be affirmed that the replenishment of varied multiple products that tend to share a combined capacity often requires a better and effective coordinated control (Minner & Silver, 2005). Aims: In correspondence to the above depicted objective, the following aims have been manly prioritised that are much essential to consider for deriving positive results or consequences: Identifying exact multi-product inventory replenishment based problem with the incorporation of Poisson demands Making relevant decisions concerning problem formulation Finding out the best suitable replenishment quantities with the consideration of current inventories for addressing as well as mitigating the stated problem Analysing the restrictions imposed by the problem through making regular workings upon space or budget limitation Method Used: The consideration of N products with numbering n = 1 by an infinite planning horizon is reckoned to be one of the methods used in the article of Minner & Silver (2005). In relation to this method, the demand for each of the product i.e. n had been aligned with the demand rate symbolising λn. Apart from this, no permission has been provided for the consideration of backorders. More importantly, with the inclusion of n technique, an effective SMDP formulation was also duly considered, which represented an amalgamation of the inventory levels. This practice eventually turned into a quality as well as an effective multi-product batch replenishment based strategy for resolving the problem of aggregate inventory level being restricted by the prevalence of a common space or budget restraint (Minner & Silver, 2005). Results and Conclusion: The results depicted in the article portray that there lay certain reasons for which the problem concerning multi-product inventory replenishment with the enclosure of Poisson demands is erupted. In this regard, in accordance with the article of Minner & Silver (2005), one of such reasons has been apparently noted as inability towards building several blocks within the respective inventory capacity level. Apart from this, the other reason was ascertained to be failure in making effective investment related decisions (Minner & Silver, 2005). Based on the thorough analysis of the above stated article, it can be concluded that better formulation of diverse multiple-product batch replenishment based strategies based on joint-capacity constraint and random demands is able to solve problems that are associated benchmarking purpose. The main research findings of this article state the formation, development as well as the maintenance of a vibrant heuristic for determining the replenishment quantities with consideration of the given inventory levels. This certainly contributes in making better replenishment decisions with the identification of collective inventory constraints, which in turn resolves the problem pertaining to multi-product inventory replenishment. Canorder 8 Objectives: The calculation of can-order policies relevant to joint-replenishment problem by adopting and following the compensation approach was deemed to be one of the chief objectives of the article propounded by Melchiors (2002). Apart from this, the other objective of the article can be ascertained as analysing the problem of stochastic joint replenishment based problem, which do impose considerable impacts on refurbishing replenishment cost structure of savings. In the background of attaining these objectives, the article focused on elaborating two sorts of policies that encompass periodic replenishment and can-order policies (Melchiors, 2002). Aims: For the purpose of accomplishing the aforementioned objectives, the following aims were framed: Continuous review of replenishment items that face Poisson demands Determination of fixed expenses related to replenishment Consideration of problem concerning stochastic joint replacement Implementation of two sorts of policies namely periodic replacement and can-order Presentation of a new mechanism for computing can-order based policies Method Used: In accordance with the article of “Calculating can-order policies for the joint replenishment problem by the compensation approach” of Melchiors (2002), certain methods were apparently observed to be taken into concern for the computation of can-order policies. In this similar context, the literatures presented in the article emphasised the utilisation of two particular policies or methods that entail periodic replenishment and can-order. In relation to the article of Melchiors (2002), it is to be affirmed that the policy of can-order performs better at the time when the major ordering expenses become certainly low. On the other hand, as per the observation made in the article of Melchiors (2002), it can be found that the policy of periodic replenishment performs better when the major ordering expenses become comparatively high. Results and Conclusion: By the utilisation of compensation method, a result was obtained that the costs relating to can-order policies lay closer to that of the policies associated with optimal can-order strategies. However, it will be vital to mention in this similar concern that the differences persisting within the above stated policies do impose extensive level of impact on determining joint-replenishment based problem. While discussing about the results of the article of Melchiors (2002), it can be ascertained that the compensation approach is applied at certain situations wherein the major ordering costs are increased by a considerable level. Thus, in conclusion, it can be affirmed that the compensation approach can be duly considered as one of the best-suited approaches for calculating can-order policies. This might be owing to the reason that the above stated compensation approach tends to balance the major as well as the minor ordering costs in an efficient way. Canorder 9 Objectives: One of the chief objectives of this article “Coordinated replenishments in inventory systems with correlated demands” by Liu & Yuan (2000) was reckoned as analysing the factor of demand correlation, which is being prevalent amid distinct inventory items. Based on the article of Liu & Yuan (2000), it was found that the above stated factor i.e. demand correlation is deemed to be common in practical systems of multi-item inventory. Aims: to ascertain that the above stated objective has been duly achieved, certain aims were formulated that have been listed hereunder. To determine the factors influencing demand correlation To ascertain the level of coordinated replenishments To analyse the expression of total replenishment costs To work upon formulating an explicit formula based on which such replenishment costs can be computed To find out the association persisting between demand correlation and replenishment coordination Method Used: Based on the article of Liu & Yuan (2000), it can be apparently observed that the method of a continuous review inventory was used for ascertaining the demand correlation prevalent within distinct inventory items. While discussing about the methods adopted and executed for determining the association persistent between demand correlation and inventory items, it was found that replenishment coordination has been one of the debated topics or researches based on multi-item inventory models for several years. In this similar context, amongst the prevalence of numerous replenishment based policies, the can-order method was also adopted as well as used in the article propounded by Liu & Yuan (2000). Under this particular method, various significant aspects were taken into concern for deriving positive outcomes. Such aspects can be reckoned as Poisson procedure, multi-item inventory system, lead time and inventory cost structure or savings (Liu & Yuan, 2000). Results and Conclusion: The results depicted in this article of Liu & Yuan (2000) clearly portrayed the role play by can-order policy in determining demand correlation in terms of taking advantages of lowering down the higher inventory expenses and utilising the available resources efficiently. In addition, the results also portrayed the fact that policy of coordinated replenishment increases the savings of demand covariance, which in turn, lessens the total costs of independent demand variables (Liu &Yuan, 2000). Therefore, in relation to the above context, it can be affirmed that with consideration of correlated demands, it is quite possible as well as valuable to use the policies of coordinated replenishment in increasing or lessening demand covariance. It is worth mentioning that increase or decrease of this demand covariance certainly assists in determining total optimal costs and more importantly inventory savings. Comparison of the Results Certain results were found to be dissimilar in the provided articles that focused on establishing a coordinated inventory based control system for ascertaining the actual replenishment costs and savings structure. This can be justified with reference to two particular articles i.e. “A Control System for Coordinated Inventory Replenishment” by Silver (1974) and “A Coordinated Inventory Control System for Compound Poisson Demand and Zero Lead Time” by Thompstone & Silver (1975). In relation to the article of Silver (1974), it can be perceived that an attempt was made to determine the systems of coordinating items specifically for the purpose of replenishment. Based on the derived research findings and results obtained, it can be found that an extensive level of savings, which was measured by averaging 18.8%, can be made possible through the procedure of forming, developing as well as maintaining effective coordination (Silver, 1974). In comparison, the results relating to the above context were deemed to be different from that of Thompstone & Silver (1975). This particular article emphasised coordinating the control of a single replenishment cost or a group of the same towards making substantial level of cost savings. Specially mentioning, the results depicted in the article represent the fact that substantial savings by averaging 15.9% can be made possible by the making of effective coordination of replenishment costs or savings structure (Thompstone & Silver, 1975). However, significant differences can be apparently noted to be persisted amid certain provided articles particularly in relation to the methods used for computing coordinated replenishments in the respective inventory systems. Justifiably, with regards to the article of “Coordinated replenishments in inventory systems with correlated demands” by Liu & Yuan (2000), it can be found that methods such as Markovian model and an incessant review inventory system were utilised for determining coordinated replenishments in context of inventory systems. In contrast, according to the article of “Calculating can-order policies for the joint replenishment problem by the compensation approach” of Melchiors (2002), the methods including periodic replenishment and can-order were executed for attaining the above stated objective. More importantly, the results of these two articles were varied based on the factors about dominating the stated methods and calculating replenishment costs or savings structure. Conclusion to the Review Based on the review of the above selected articles, it can be ascertained that the can-order replenishment system is mainly calculated by the adoption and efficient execution of varied strategies or approaches. Identifiably, these approaches or policies include periodic replenishment and demand correlation. As per the review of certain selected articles, it has been apparently observed that the policy concerning periodic replenishment performs better and efficiently during the time when the major ordering expenditures become relatively high. On the other hand, the policy of demand correlation signifies exponential growth of different replenishment inventory based items. Throughout the review procedure of selected articles, varied joint-replenishment based problems were examined and likewise analysed the ways based on which such problems or issues could be addressed as well as resolved for deriving positive outcomes. In this regard, one of such problems included stochastic joint-replenishment problem. Specially mentioning, while reviewing the selected articles, several methods or techniques were identified to develop this replenishment systems in the form of ascertaining appropriate inventory items and determining suitable replenishment cost structures. It is projected that these systems or policies would eventually support in establishing a well-coordinated inventory replenishment system, resulting in attaining greater insights about the costs involved in such system. This will in turn facilitate to ascertain better control of such costs in the long run. Proper management of inventory replenishment system can be a decisive factor in order to manage the inventory for an organisation. References Federgruen, A. & et. al., 1984. Coordinated Replenishments in A Multi-Item Inventory System with Compound Poisson Demands. Management Science, Vol. 30, No. 3, pp. 344-357. Fung, R. Y. K. & et. al., 2001. (T, S) Policy for Coordinated Inventory Replenishment Systems under Compound Poisson Demands. Production Planning & Control, Vol. 12, No. 6, pp. 575-583. Kayis, E. & et. al., 2008. A Note on the Can-Order Policy for the Two-Item Stochastic Joint-Replenishment Problem. IIE Transactions, Vol. 80, pp. 84-92. Liu, L. & Yuan, X. M., 2000. Coordinated Replenishments In Inventory Systems With Correlated Demands. European Journal of Operational Research, Vol. 123, pp. 490-503. Minner, S. & Silver, E. A., 2005. Multi-Product Batch Replenishment Strategies under Stochastic Demand and a Joint Capacity Constraint. IIE Transactions, Vol. 37, pp. 469-479. Melchiors, P., 2002. Calculating Can-Order Policies for the Joint Replenishment Problem by the Compensation Approach. European Journal of Operational Research, Vol. 141, pp. 587-595. Silver, E. A., 1981. Establishing Reorder Points in the (S,c,s) Coordinated Control System Under Compound Poisson Demand. Int. J. Prod. Res., Vol. 19, No. 6, pp. 743-750. Silver, E. A., 1974. A Control System for Coordinated Inventory Replenishment. Int. J. Prod. Res., Vol. 12, No. 6, pp. 647-671. Thompstone, R. M. & Silver, E. A., 1975. A Coordinated Inventory Control System for Compound Poisson Demand and Zero Lead Time. Int. J. Prod. Res., Vol. 13, No. 6, pp. 581-602. Read More