Philip Kaminsky

Pricing and Manufacturing Decisions When Demand Is a Function of Prices in Multiple Periods

In most deterministic manufacturing decision models, demand is either known or induced by pricing decisions in the period that the demand is experienced. However, in more realistic market scenarios consumers make purchase decisions with respect to price, not only in the current period, but also in past and future periods. We model a joint manufacturing/pricing decision problem, accounting for that portion of demand realized in each period that is induced by the interaction of pricing decisions in the current period and in previous periods. We formulate a mathematical programming model and develop solution techniques. We identify structural properties of our models and develop closed-form solutions and effective heuristics for various special cases of our models. Finally, we conduct extensive computational experiments to quantify the effectiveness of our heuristics and to develop managerial insights.

Utilizing Forecast Band Refinement for Capacitated Production Planning

We present a model for forecast evolution that captures two notions related to forecasts: (1) forecasts are not exact; (2) forecasts over longer horizons are less certain than those over shorter horizons. We model the forecast of discrete demand as a band defined by the lower and upper bounds on demand, such that future forecasts lie within the current band. We develop a capacitated production planning model for a single product with terminal demand. We develop four heuristics for the problem and characterize their performance. In particular, two of the heuristics are optimal for the no holding-cost case. In our computational study, we analyze the performance of our heuristics and compare them to the optimal solution and to a simple heuristic that simulates common industrial practice using point forecasts. We find that two of our heuristics are very close to the optimal solution (less than 0.5% away from optimal on average under the conditions studied). Further, we consider forecast update patterns with primarily early, intermediate, and late information updates and provide insights on the effect of information update patterns on optimal costs.

Production and distribution policy in a two-stage stochastic push-pull supply chain

We consider a model of a two-stage push-pull production-distribution supply chain. The orders arrive at the final stage according to a Poisson process. Two separate operations, which take place at different locations with exponential service times, are required to convert the raw materials into finished goods. When the first operation is completed the intermediate inventory is held at the first stage and then transported to the second stage where the items are produced to order. The objective is to minimize the average sum of the production, transportation, and holding costs. We consider the optimal policy for a version of this model. Our experimental analysis demonstrates that this optimal policy is counter-intuitive. We develop a heuristic based on a deterministic version of this model, and computationally test the heuristic.

Probabilistic Analysis and Practical Algorithms for the Flow Shop Weighted Completion Time Problem

In the flow shop weighted completion time problem, a set of jobs has to be processed on m machines. Every machine has to process each one of the jobs, and every job has the same routing through the machines. The objective is to determine a sequence of the jobs on the machines so as to minimize the sum of the weighted completion times of all jobs on the final machine. In this paper, we present a characterization of the asymptotic optimal solution value for general distributions of the job processing times and weights. In particular, we show that the optimal objective value of this problem is asymptotically equivalent to certain single and parallel machine scheduling problems. This characterization leads to a better understanding of the effectiveness of the celebrated weighted shortest processing time algorithm, as well as to the development of an effective algorithm closely related to the profile fitting heuristic, which was previously utilized for flow shop makespan problems. Computational results show the effectiveness of WSPT and this modified profile fitting heuristic on a set of random test problems.

Asymptotic analysis of an on-line algorithm for the single machine completion time problem with release dates

In the single machine mean completion time problem with release dates, a set of jobs has to be processed non-preemptively on a single machine. No job can be processed before its release date, and the objective is to determine a sequence of the jobs on the machine which minimizes the sum of the completion times of all jobs. In this paper, we prove the asymptotic optimality of the shortest processing time among available jobs algorithm, in which at the completion time of any job, the next job to be scheduled is the shortest job among all those released but not yet processed. This algorithm is particularly attractive because it falls in the class of easy to implement and computationally inexpensive on-line algorithms.

Optimal spot market inventory strategies in the presence of cost and price risk

We consider a firm facing random demand at the end of a single period of random length. At any time during the period, the firm can either increase or decrease inventory by buying or selling on a spot market where price fluctuates randomly over time. The firm’s goal is to maximize expected discounted profit over the period, where profit consists of the revenue from selling goods to meet demand, on the spot market, or in salvage, minus the cost of buying goods, and transaction, penalty, and holding costs. We first show that this optimization problem is equivalent to a two-dimensional singular control problem. We then use a recently developed control-theoretic approach to show that the optimal policy is completely characterized by a simple price-dependent two-threshold policy. In a series of computational experiments, we explore the value of actively managing inventory during the period rather than making a purchase decision at the start of the period, and then passively waiting for demand. In these experiments, we observe that as price volatility increases, the value of actively managing inventory increases until some limit is reached.

Effective on-line algorithms for reliable due date quotation and large-scale scheduling

We consider the sequencing of a series of jobs that arrive at a single processor over time. At each job’s arrival time, a due date must be quoted for the job, and the job must complete processing before its quoted due date. The objective is to minimize the sum (or average) of quoted due dates, or equivalently, the average quoted lead time. In this paper, we propose on-line heuristics for this problem and characterize the conditions under which these heuristics are asymptotically optimal. Computational testing further demonstrates the relative effectiveness of these heuristics under various conditions.

The Asymptotic Optimality of the SPT Rule for the Flow Shop Mean Completion Time Problem

In the flow shop mean completion time problem, a set of jobs has to be processed onm-machines. Every machine has to process each one of the jobs, and every job has the same routing through the machines. The objective is to determine a sequence of the jobs on the machines so as to minimize the sum of the completion times of all jobs on the final machine. In this paper, we prove the asymptotic optimality of the Shortest Processing Time algorithm for any continuous, independent, and identically distributed job processing times.

A linear programming-based method for job shop scheduling

We present a decomposition heuristic for a large class of job shop scheduling problems. This heuristic utilizes information from the linear programming formulation of the associated optimal timing problem to solve subproblems, can be used for any objective function whose associated optimal timing problem can be expressed as a linear program (LP), and is particularly effective for objectives that include a component that is a function of individual operation completion times. Using the proposed heuristic framework, we address job shop scheduling problems with a variety of objectives where intermediate holding costs need to be explicitly considered. In computational testing, we demonstrate the performance of our proposed solution approach.

Basis Paths and a Polynomial Algorithm for the Multistage Production-Capacitated Lot-Sizing Problem

We consider the multilevel lot-sizing problem with production capacities (MLSP-PC), in which production and transportation decisions are made for a serial supply chain with capacitated production and concave cost functions. Existing approaches to the multistage version of this problem are limited to nonspeculative cost functions---up to now, no algorithm for the multistage version of this model with general concave cost functions has been developed. In this paper, we develop the first polynomial algorithm for the MLSP-PC with general concave costs at all of the stages, and we introduce a novel approach to overcome the limitations of previous approaches. In contrast to traditional approaches to lot-sizing problems, in which the problem is decomposed by time periods and is analyzed unidirectionally in time, we solve the problem by introducing the concept of a basis path, which is characterized by time and stage. Our dynamic programming algorithm proceeds both forward and backward in time along this basis path, enabling us to solve the problem in polynomial time.