| In standard dynamic economic lot-sizing models, a sequence of demands for a single good over a finite and discrete planning horizon must be satisfied at minimum production and inventory holding cost, where the cost parameters and demands are assumed to be known. In this dissertation, we study variations of dynamic economic lot-sizing models by integrating more decisions and adding more constraints. For each model, either we identify polynomially solvable cases and present solution algorithms or present approximation schemes.; In our first model, we integrate pricing decisions and backlogging under nonstationary production capacities. We present a fully polynomial time approximation scheme for this model.; In our second model, we consider a setting where any remaining capacity is transferred to the next production period. This is in contrast with traditional capacitated lot-sizing models, where the quantity produced in each period is limited by some capacity, but any capacity remaining at the end of a period is essentially lost. We prove that this problem is NP-hard for general cost functions and provide a fully polynomial time approximation scheme for the case when all cost functions are nondecreasing. We then develop a dynamic programming approach that solves the problem in polynomial time when all cost functions are concave.; In our third model, we consider a two-echelon supply chain consisting of a supplier and a manufacturer, where a sequence of deterministic but nonstationary demands of the manufacturer for a single good needs to be satisfied over a finite horizon. We assume stationary production capacities. In particular, we consider an integrated model that minimizes total system costs, consisting of production, inventory, transportation, backlogging, and subcontracting costs.; In our last model, we consider a multi-warehouse multi-retailer model in a stochastic demand setting. In this model, we consider a single period, where we do not know the exact demand, but its distribution. Moreover, warehouses have capacities on the amount they can supply. For each retailer, we have newsvendor type costs, and we also have the costs for assigning each retailer to each warehouse. We solve an assignment and capacity allocation problem. |
