Search results for: S. P. Sethi

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chapter

Hierarchical investment and production decisions in stochastic manufacturing systems

S. P. Sethi, M. Taksar, Q. Zhang

Lecture Notes in Control and Information Sciences > Stochastic Theory and Adaptive Control > 426-435

This paper presents an asymptotic analysis of hierarchical investment and production decisions in a manufacturing system with machines subject to breakdown and repair. The demand facing the system is assumed to be a given constant. The production capacity can be increased by purchasing a new machine at a fixed cost at some time in the future. The control variables are a pair of a Markov time to purchase...

article

An Incomplete Information Inventory Model with Presence of Inventories or Backorders as Only Observations

A. Bensoussan, M. Çakanyıldırım, J. A. Minjárez-Sosa, S. P. Sethi, more

Journal of Optimization Theory and Applications > 2010 > 146 > 3 > 544-580

In many real-life contexts, inventory levels are only incompletely observed due to non-observation of demand, discrepancies in transmitting sales data, transaction errors, spoilage, misplacement, or theft of inventory. We study a periodic review inventory system, where the demand is not observed and the unmet demand is backordered. As a result, the inventory manager cannot tell the exact quantities...

article

Optimal Advertising and Pricing in a New-Product Adoption Model

S. P. Sethi, A. Prasad, X. He

Journal of Optimization Theory and Applications > 2008 > 139 > 2 > 351-360

A model of new-product adoption is proposed that incorporates price and advertising effects. An optimal control problem that uses the model as its dynamics is solved explicitly to obtain the optimal price and advertising effort over time. The model has a great potential to be used in obtaining solutions and insights in a variety of differential game settings.

article

Dynamic Slotting and Pricing Decisions in a Durable Product Supply Chain

X. He, S. P. Sethi

Journal of Optimization Theory and Applications > 2008 > 137 > 2 > 363-379

We consider a supply chain in which a manufacturer sells an innovative durable product to an independent retailer over its life cycle. We assume that the product demand follows a Bass-type diffusion process and that it is determined by the market influences, retail price of the product, and shelf space allocated to it. We consider the following retailer profit optimization strategies: (i) the myopic...

article

Inventory Problems with Partially Observed Demands and Lost Sales

A. Bensoussan, M. Çakanyıldırım, J. A. Minjárez-Sosa, A. Royal, more

Journal of Optimization Theory and Applications > 2008 > 136 > 3 > 321-340

This paper considers the case of partially observed demand in the context of a multi-period inventory problem with lost sales. Demand in a period is observed if it is less than the inventory level in that period and the leftover inventory is carried over to the next period. Otherwise, only the event that it is larger than or equal to the inventory level is observed. These observations are used to...

article

Optimality of Base-Stock and (s, S) Policies for Inventory Problems with Information Delays

A. Bensoussan, M. Çakanyildirim, S. P. Sethi

Journal of Optimization Theory and Applications > 2006 > 130 > 2 > 153-172

Information delays exist when the most recent inventory information available to the inventory manager (IM) is dated; namely, the IM observes only the inventory level of an earlier period. We introduce information delays into the standard multiperiod stochastic inventory problem with backorders. We consider two types of information delays: (i) a constant delay and (ii) a random delay. We define an...

article

Periodic-Review Inventory Model with Three Consecutive Delivery Modes and Forecast Updates

Q. Feng, G. Gallego, S. P. Sethi, H. Yan, more

Journal of Optimization Theory and Applications > 2005 > 124 > 1 > 137-155

This paper is concerned with a periodic-review inventory system with three consecutive delivery modes (fast, medium, and slow) and demand forecast updates. At the beginning of each period, the inventory level and demand information are updated and decisions on how much to order using each of the three delivery modes are made. It is shown that there is a base-stock policy for fast and medium modes...

article

$${\cal K}$$ -Convexity¹ in $$\Re^{n}$$

G. Gallego, S. P. Sethi

Journal of Optimization Theory and Applications > 2005 > 127 > 1 > 71-88

We generalize the concept of K-convexity to an n-dimensional Euclidean space. The resulting concept of $${\cal K}$$ -convexity is useful in addressing production and inventory problems where there are individual product setup costs and/or joint setup costs. We derive some basic properties of $${\cal K}$$ -convex functions. We conclude the paper with some suggestions for future research.

article

Competitive Advertising Under Uncertainty: A Stochastic Differential Game Approach

A. Prasad, S. P. Sethi

Journal of Optimization Theory and Applications > 2004 > 123 > 1 > 163-185

We analyze optimal advertising spending in a duopolistic market where each firm's market share depends on its own and its competitor's advertising decisions, and is also subject to stochastic disturbances. We develop a differential game model of advertising in which the dynamic behavior is based on the Sethi stochastic advertising model and the Lanchester model of combat. Particularly important to...

article

Peeling Layers of an Onion: Inventory Model with Multiple Delivery Modes and Forecast Updates

S. P. Sethi, H. Yan, H. Zhang

Journal of Optimization Theory and Applications > 2001 > 108 > 2 > 253-281

This paper is concerned with a periodic review inventory system with fast and slow delivery modes and regular demand forecast updates. At the beginning of each period, on-hand inventory and demand information are updated. At the same time, decisions on how much to order using fast and slow delivery modes are made. Fast and slow orders are delivered at the end of the current and the next periods, respectively...

article

Stochastic Multiproduct Inventory Models with Limited Storage

D. Beyer, S. P. Sethi, R. Sridhar

Journal of Optimization Theory and Applications > 2001 > 111 > 3 > 553-588

This paper studies multiproduct inventory models with stochastic demands and a warehousing constraint. Finite horizon as well as stationary and nonstationary discounted-cost infinite-horizon problems are addressed. Existence of optimal feedback policies is established under fairly general assumptions. Furthermore, the structure of the optimal policies is analyzed when the ordering cost is linear and...

article

Hierarchical Production Control in Dynamic Stochastic Jobshops with Long-Run Average Cost

S. P. Sethi, H. Zhang, Q. Zhang

Journal of Optimization Theory and Applications > 2000 > 106 > 2 > 231-264

We consider a production planning problem for a dynamic jobshop producing a number of products and subject to breakdown and repair of machines. The machine capacities are assumed to be finite-state Markov chains. As the rates of change of the machine states approach infinity, an asymptotic analysis of this stochastic manufacturing systems is given. The analysis results in a limiting problem in which...

article

The Classical Average-Cost Inventory Models of Iglehart and Veinott–Wagner Revisited

D. Beyer, S. P. Sethi

Journal of Optimization Theory and Applications > 1999 > 101 > 3 > 523-555

This paper revisits the classical papers of Iglehart (Ref. 1) and Veinott and Wagner (Ref. 2) devoted to stochastic inventory problems with the criterion of long-run average cost minimization. We indicate some of the assumptions that are used implicitly without verification in their stationary distribution approach to the problems and provide the missing (nontrivial) verification. In addition to completing...

article

Near Optimization of Dynamic Systems by Decomposition and Aggregation

S. P. Sethi, Q. Zhang

Journal of Optimization Theory and Applications > 1998 > 99 > 1 > 1-22

This paper is concerned with the reduction of a class of optimal control problems to simpler problems by using decomposition and aggregation. Decomposition is shown to provide a good approximation when the system dynamics involve nearly decomposable matrices or variables with strong and weak interactions. Aggregation provides a good approximation if each of the decomposed matrices has one or more...

article

Inventory Models with Markovian Demands and Cost Functions of Polynomial Growth

D. Beyer, S. P. Sethi, M. Taksar

Journal of Optimization Theory and Applications > 1998 > 98 > 2 > 281-323

This paper studies stochastic inventory problems with unbounded Markovian demands, ordering costs that are lower semicontinuous, and inventory/backlog (or surplus) costs that are lower semicontinuous with polynomial growth. Finite-horizon problems, stationary and nonstationary discounted-cost infinite-horizon problems, and stationary long-run average-cost problems are addressed. Existence of optimal...

article

Consumption-Investment Problem with Subsistence Consumption, Bankruptcy, and Random Market Coefficients

A. Cadenillas, S. P. Sethi

Journal of Optimization Theory and Applications > 1997 > 93 > 2 > 243-272

We consider a general continuous-time finite-horizon single-agent consumption and portfolio decision problem with subsistence consumption and value of bankruptcy. Our analysis allows for random market coefficients and general continuously differentiable concave utility functions. We study the time of bankruptcy as a problem of optimal stopping, and succeed in obtaining explicit formulas for the optimal...

article

Average Cost Optimality in Inventory Models with Markovian Demands

D. Beyer, S. P. Sethi

Journal of Optimization Theory and Applications > 1997 > 92 > 3 > 497-526

This paper is concerned with long-run average cost minimization of a stochastic inventory problem with Markovian demand, fixed ordering cost, and convex surplus cost. The states of the Markov chain represent different possible states of the environment. Using a vanishing discount approach, a dynamic programming equation and the corresponding verification theorem are established. Finally, the existence...

article

Optimal Production Planning in a Stochastic Manufacturing System with Long-Run Average Cost

S. P. Sethi, W. Suo, M. I. Taksar, Q. Zhang

Journal of Optimization Theory and Applications > 1997 > 92 > 1 > 161-188

This paper is concerned with the optimal production planning in a dynamic stochastic manufacturing system consisting of a single machine that is failure prone and facing a constant demand. The objective is to choose the rate of production over time in order to minimize the long-run average cost of production and surplus. The analysis proceeds with a study of the corresponding problem with a discounted...

article

Degenerate Diffusion Processes in Portfolio Management

J. P. Lehoczky, S. P. Sethi, S. E. Shreve

01982 American Control Conference > 1982 > 517 - 520

1982 American Control Conference

The method of variational inequalities is a useful theoretical tool in stochastic control, but there are few problems in which this method leads to an explicit solution. We present such a problem drawn from portfolio management. An agent can distribute his wealth between two investments, one risky and the other risk-free. He can also consume his wealth, and wishes to manage his portfolio and consumption...

article

Degenerate diffusion processes in portfolio management

J. P. Lehoczky, S. P. Sethi, S. E. Shreve

American Control Conference > 1982 > 19 > 517 - 520

American Control Conference

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