On Setup Cost Reduction in the Economic Lot-Sizing Model Without Speculative Motives

An important special case of the economic lot-sizing problem is the one in which there are no speculative motives to hold inventory, i.e., the marginal cost of producing one unit in some period plus the cost of holding it until some future period is at least the marginal production cost in the latter period. It is already known that this special case can be solved in linear time. In this paper we study the effects of reducing all setup costs by the same amount. It turns out that the optimal solution changes in a very structured way. This fact will be used to develop faster algorithms for several problems that can be reformulated as parametric lot-sizing problems. One result, worth a sepparate mention, is an algorithm for the so-called dyna-mic lot-.sizing proble-m with learning effects in setups. This algorithm has a complexity that is of the same order as the fastest algorithm known so far, but it is valid for a more general class of models than usually considered. OR/MS subject classification: Analysis of algorithms, computational complexity: parametric economic lot-sizing problem; Dynamic programming /optimal control, applications: parametric economic lot-sizing problem; Inventory/)production, planning horizon: setup cost reduction in economic lot-sizing molel

On the P-Coverage Problem on the Real Line

In this paper we consider the p-coverage problem on the real line. We first give a detailed description of an algorithm to solve the coverage problem without the upper bound p on the number of open facilities. Then we analyze how the structure of the optimal solution changes if the setup costs of the facilities are all decreased by the same amount. This result is used to develop a parametric approach to the p-coverage problem which runs in O (pn log n) time, n being the number of clients.Economics ;

A Polynomial Time Algorithm for a Deterministic Joint Pricing and Inventory Model

In this paper we consider the uncapacitated economic lot-size model, where demand is adeterministic function of price. In the model a single price need to be set for all periods. Theobjective is to find an optimal price and ordering decisions simultaneously. In 1973 Kunreuther and Schrage proposed an heuristic algorithm to solve this problem. The contribution of our paper is twofold. First, we derive an exact algorithm to determine the optimal price and lot-sizing decisions. Moreover, we show that our algorithm boils down to solving a number of lot-sizing problems that is quadratic in the number of periods, i.e., the problem can be solved in polynomial time.pricing;inventory;production;lot-sizing

A holding cost bound for the economic lot-sizing problem with time-invariant cost parameters

In this paper we derive a new structural property for an optimal solution of the economic lot-sizing problem with time-invariant cost parameters. We show that the total holding cost in an order interval of an optimal solution is bounded from above by a quantity proportional to the setup cost and the logarithm of the number of periods in the interval. Since we can also show that this bound is tight, this is in contrast to the optimality property of the economic order quantity (EOQ) model, where setup cost and holding cost are perfectly balanced. Furthermore, we show that this property can be used for the design of a new heuristic and that the result may be useful in worst case analysis.

Supply chain collaboration

In the past, research in operations management focused on single-firm analysis. Its goal was to provide managers in practice with suitable tools to improve the performance of their firm by calculating optimal inventory quantities, among others. Nowadays, business decisions are dominated by the globalization of markets and increased competition among firms. Further, more and more products reach the customer through supply chains that are composed of independent firms. Following these trends, research in operations management has shifted its focus from single-firm analysis to multi-firm analysis, in particular to improving the efficiency and performance of supply chains under decentralized control. The main characteristics of such chains are that the firms in the chain are independent actors who try to optimize their individual objectives, and that the decisions taken by a firm do also affect the performance of the other parties in the supply chain. These interactions among firms’ decisions ask for alignment and coordination of actions. Therefore, game theory, the study of situations of cooperation or conflict among heterogenous actors, is very well suited to deal with these interactions. This has been recognized by researchers in the field, since there are an ever increasing number of papers that applies tools, methods and models from game theory to supply chain problems

Sensitivity Analysis of the Economic Lot-Sizing Problem

In this paper we study sensitivity analysis of the uncapacitated single level economic lot-sizing problem, which was introduced by Wagner and Whitin about thirty years ago. In particular we are concerned with the computation of the maximal ranges in which the numerical problem parameters may vary individually, such that a solution already obtained remains optimal. Only recently it was discovered that faster algorithms than the Wagner-Whitin algorithm exist to solve the economic lot-sizing problem. Moreover, these algorithms reveal that the problem has more structure than was recognized so far. When performing the sensitivity analysis we exploit these newly obtained insights

A Note on "Stability of the Constant Cost Dynamic Lot Size Model" by K. Richter

In a paper by K. Richter the stability regions of the dynamic lot size model with constant cost parameters are analyzed. In particular, an algorithm is suggested to compute the stability region of a so-called generalized solution. In general this region is only a subregion of the stability region of the optimal solution. In this note we show that in a computational effort that is of the same order as the running time of Richter's algorithm, it is possible to partition the parameter space in stability regions such that every region corresponds to another optimal solution

Conceptual design optimization study

The feasibility of applying multilevel functional decomposition and optimization techniques to conceptual design of advanced fighter aircraft was investigated. Applying the functional decomposition techniques to the conceptual design phase appears to be feasible. The initial implementation of the modified design process will optimize wing design variables. A hybrid approach, combining functional decomposition techniques for generation of aerodynamic and mass properties linear sensitivity derivatives with existing techniques for sizing mission performance and optimization, is proposed

Mitigating the Cost of Anarchy in Supply Chain Systems

In a decentralized two-stage supply chain where a supplier serves a retailer who, in turn, serves end customers, operations decisions based on local incentives often lead to suboptimal system performance. Operating decisions based on local incentives may in such cases lead to a degree of system disorder or anarchy, wherein one party's decisions put the other party and/or the system at a disadvantage. While models and mechanisms for such problem classes have been considered in the literature, little work to date has considered such problems under nonstationary demands and fixed replenishment order costs. This paper models such two-stage problems as a class of Stackelberg games where the supplier announces a set of time-phased ordering costs to the retailer over a discrete time horizon of finite length, and the retailer then creates an order plan, which then serves as the supplier's demand. We provide metrics for characterizing the degree of efficiency (and anarchy) associated with a solution, and provide a set of easily understood and implemented mechanisms that can increase this efficiency and reduce the negative impacts of anarchic decisions