Operations Managers of manufacturing systems, distribution systems, and supply chains address lot sizing and scheduling problems as part of their duties. These problems are concerned with decisions related to the size of orders and their schedule. In general, products share or compete for common resources and thus require coordination of their replenishment decisions whether replenishment involves manufacturing operations or not. This research is concerned with joint replenishment problems (JRPs) which are part of multi-item lot sizing and scheduling problems in manufacturing and distribution systems in single echelon/stage systems. The principal purpose of this research is to develop three new periodic review policies for stochastic joint replenishment problem. It also highlights the lack of research on joint replenishment problems with different demand classes (DSJRP). Therefore, periodic review policy is developed for this problem where the inventory system faces different demand classes that are deterministic demand and stochastic demand. Heuristic Algorithms have been developed to obtain (near) optimal parameters for the three policies as well as a heuristic algorithm has been developed for DSJRP. Numerical tests against literature benchmarks have been presented.

In an e-retailing setting, the efficient utilization of inventory, storage space, and labor is paramount to achieving high levels of customer service and company profits. To optimize the storage space and labor, a retailer will split the warehouse into two storage regions with different densities. One region is for picking customer orders and the other to hold reserve stock. As a consequence, the inventory system for the warehouse is a multi-item two-stage, serial system. We investigate the problem when demand is stochastic and the objective is to minimize the total expected average cost under some space constraints. We generate an approximate formulation and solution procedure for a periodic review, nested ordering policy, and provide managerial insights on the trade-offs. In addition, we extend the formulation to account for shipping delays and advanced order information. / Singapore-MIT Alliance (SMA)

Inventory control problems constitute one of the most important research problems due to their connection with real life applications. Naturally, real life is full of uncertainty so are the most of the inventory problems. Unfortunately, it is a very challenging task to manage inventories effectively especially under uncertainty. This dissertation mainly deals with single-item, periodic review, and stochastic dynamic inventory control problems particularly on replenishment cycle control rule known as the (R, S) policy. Contribution of this thesis is multiold. In each chapter a particular research question is investigated. At the end of the day, we will be showing that non-stationary (R, S) policies are indispensable not only for its cost efficiency but its effectiveness and practicality. More specifically, the non-stationary (R, S) policy provides a convenient, efficient, effective, and modular solution for non-stationary stochastic inventory control problems.

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In this paper we first show that the gains achievable by integrating pricing and inventory control are usually small for classical demand functions. We then introduce reference price models and demonstrate that for this class of demand functions the benefits of integration with inventory control are substantially increased due to the price dynamics. We also provide some analytical results for this more complex model. We thus conclude that integrated pricing/inventory models could repeat the success of revenue management in practice if reference price effects are included in the demand model and the properties of this new model are better understood. (authors' abstract)

We propose a general methodology based on robust optimization to address the problem of optimally controlling a supply chain subject to stochastic demand in discrete time. The attractive features of the proposed approach are: (a) It incorporates a wide variety of phenomena, including demands that are not identically distributed over time and capacity on the echelons and links; (b) it uses very little information on the demand distributions; (c) it leads to qualititatively similar optimal policies (basestock policies) as in dynamic programming; (d) it is numerically tractable for large scale supply chain problems even in networks, where dynamic programming methods face serious dimensionality problems; (e) in preliminary computation experiments, it often outperforms dynamic programming based solutions for a wide range of parameters. / Singapore-MIT Alliance (SMA)

In this research, we consider production/inventory management decisions of a rmthat sells its product in two market segments during a nite planning horizon. In thebeginning of each period, the rm makes a decision on how much to produce basedon the production capacity and the current on-hand inventory available. After theproduction is made at the beginning of the period, the rm rst satises the stochasticdemand from customers in its primary market. Any primary market demand thatcannot be satised is lost. After satisfying the demand from the primary market, ifthere is still inventory on hand, all or part of the remaining products can be sold ina secondary market with ample demand at a lower price. Hence, the second decisionthat the rm makes in each period is how much to sell in the secondary market, orequivalently, how much inventory to carry to the next period.The objective is to maximize the expected net revenue during a nite planninghorizon by determining the optimal production quantity in each period, and theoptimal inventory amount to carry to the next period after the sales in primary andsecondary markets. We term the optimal inventory amount to be carried to the nextperiod as \economic retention quantity". We model this problem as a nite horizonstochastic dynamic program. Our focus is to characterize the structure of the optimalpolicy and to analyze the system under dierent parameter settings. Conditioning on given parameter set, we establish lower and upper bounds on the optimal policyparameters. Furthermore, we provide computational tools to determine the optimalpolicy parameters. Results of the numerical analysis are used to provide furtherinsights into the problem from a managerial perspective.

This thesis studies a single item periodic review inventory problem with stochastic demand, random price and quotation cost. It differs from the traditional inventory model in that at the beginning of each period, a decision is made whether to pay the quotation cost to get the price information. If it is decided to request a price quote then the next decision is on how many units to order; otherwise, there will be no order. An (r, S1, S2) policy with r < S2, S1 <= S2 is proposed for the problem with two prices. It prescribes that when the inventory is less than or equal to r, the price quotation is requested; if the higher price is quoted, then order up to S1, otherwise to S2. There are two cases, r < S1 or S1 <= r. In the first case, every time the price is quoted, an order is placed. It is a single reorder point two order-up-to levels policy that can be considered as an extension of the (s, S) policy. In the second case, S1 <= r, it is possible to “request a quote but not buy” if the quoted price is not favorable when the inventory is between S1 and r. Two total cost functions are derived for the cases r < S1 <= S2 and S1 <= r < S2 respectively. Then optimization algorithms are devised based on the properties of the cost functions and tested in numerical study. The algorithms successfully find the optimal policies in all of the 135 test cases. Compared to the exhaustive search, the running time of the optimization algorithm is reduced significantly. The numerical study shows that the optimal (r, S1, S2) policy can save up to 50% by ordering up to different levels for different prices, compared to the optimal (s, S) policy. It also reveals that in some cases it is optimal to search price speculatively, that is with S1 < r, to request a quote but only place an order when the lower price is realized, when the inventory level is between S1 and r.

This thesis studies a single item periodic review inventory problem with stochastic demand, random price and quotation cost. It differs from the traditional inventory model in that at the beginning of each period, a decision is made whether to pay the quotation cost to get the price information. If it is decided to request a price quote then the next decision is on how many units to order; otherwise, there will be no order. An (r, S1, S2) policy with r < S2, S1 <= S2 is proposed for the problem with two prices. It prescribes that when the inventory is less than or equal to r, the price quotation is requested; if the higher price is quoted, then order up to S1, otherwise to S2. There are two cases, r < S1 or S1 <= r. In the first case, every time the price is quoted, an order is placed. It is a single reorder point two order-up-to levels policy that can be considered as an extension of the (s, S) policy. In the second case, S1 <= r, it is possible to “request a quote but not buy” if the quoted price is not favorable when the inventory is between S1 and r. Two total cost functions are derived for the cases r < S1 <= S2 and S1 <= r < S2 respectively. Then optimization algorithms are devised based on the properties of the cost functions and tested in numerical study. The algorithms successfully find the optimal policies in all of the 135 test cases. Compared to the exhaustive search, the running time of the optimization algorithm is reduced significantly. The numerical study shows that the optimal (r, S1, S2) policy can save up to 50% by ordering up to different levels for different prices, compared to the optimal (s, S) policy. It also reveals that in some cases it is optimal to search price speculatively, that is with S1 < r, to request a quote but only place an order when the lower price is realized, when the inventory level is between S1 and r.

In this research, we consider production/inventory management decisions of a rmthat sells its product in two market segments during a nite planning horizon. In thebeginning of each period, the rm makes a decision on how much to produce basedon the production capacity and the current on-hand inventory available. After theproduction is made at the beginning of the period, the rm rst satises the stochasticdemand from customers in its primary market. Any primary market demand thatcannot be satised is lost. After satisfying the demand from the primary market, ifthere is still inventory on hand, all or part of the remaining products can be sold ina secondary market with ample demand at a lower price. Hence, the second decisionthat the rm makes in each period is how much to sell in the secondary market, orequivalently, how much inventory to carry to the next period.The objective is to maximize the expected net revenue during a nite planninghorizon by determining the optimal production quantity in each period, and theoptimal inventory amount to carry to the next period after the sales in primary andsecondary markets. We term the optimal inventory amount to be carried to the nextperiod as \economic retention quantity". We model this problem as a nite horizonstochastic dynamic program. Our focus is to characterize the structure of the optimalpolicy and to analyze the system under dierent parameter settings. Conditioning on given parameter set, we establish lower and upper bounds on the optimal policyparameters. Furthermore, we provide computational tools to determine the optimalpolicy parameters. Results of the numerical analysis are used to provide furtherinsights into the problem from a managerial perspective.