Gregory Gurevich

PERT-type projects: time-cost tradeoffs under uncertainty

Factual and anecdotal evidence confirms that investments in projects are inherently risky, as most large projects fail to meet their on-time and on-budget objectives. In one KPMG survey, 67% of the companies said that their project management function was in need of improvement. To address this issue, we examine two currently used procedures for crashing the project completion time by additional budget and develop a new stochastic procedure for this purpose. We consider projects with various patterns of activities, where the randomness of their duration derives from external uncertainty, internal uncertainty or both and where the correlation between their actual cost and random duration is known. The objective is to optimize the budget allocation among project activities, i.e. to determine the optimized activity execution speeds. We aim to minimize the project budget or any chance-constrained project cost, subject to any chance-constrained project completion time. We conduct Monte Carlo comparisons of the relative efficiency of the alternative procedures for crashing the project completion time on PERT-type projects. Broad Monte Carlo simulations confirm that the newly developed procedure can be an efficient tool for project management.

A multinomial model for the machine interference problem with different service types and multiple operators

This paper proposes a model for a special case of the machine interference problem (MIP), where each of N identical machines randomly requests several different service types. Each request for a service type is fulfilled by an operator who can provide only one service type. The model allows the calculation of the expected interference (waiting) time in the queue for each service type, according to the multinomial distribution. The uniqueness of the model is that under its assumptions internal service order and queue discipline are not needed for the interference calculations. The model requires as inputs only the machine runtime and the average time of each service type that is needed to produce one unit. These inputs can be obtained by a common work measurement. The model enables practitioners to determine the optimal numbers of operators that are needed for each service type in order to minimize the cost per unit or maximize the profit, or to set other performance measures. To demonstrate the applicability of the model, a theoretical analysis and a case study are presented.

Calculation of the steady state waiting time distribution in the context of the machine interference problem

This paper proposes an extension of a multinomial model for the machine interference problem, where each of N identical machines randomly requests several different service types. Each request for a service is fulfilled by an operator who can provide only one type of service. The extended model is useful for the case in which there is a time limit for one service type (or more), such that it must be accomplished within a certain time from the moment of the request. A delay in the service above a given time spoils the product and makes it useless for its intended purpose. The model allows calculation of the exact distribution function of the steady state waiting time and total service time (waiting time + service time) for each type of requested service, for the first come first served (FCFS) queue discipline.

Optimizing Bundling Policy of Single-Period Products: Perspectives of Producers and Retailers

Combining different product types into standard discount bundles is a common strategy used by producers and wholesalers to increase overall sales profitability. While markets consist of many producers and retailers, a deal is typically made between a single producer and a single retailer. This paper deals with a producer who sells items separately, and considers setting and selling standard discount bundles. The purchased wholesale bundles are unpacked by the retailer and the items are sold to the end-users one by one. Thus, the end-user demand distribution is unchanged, but the retailers order quantity grows with the magnitude of the discount. The paper explores the effect of bundle price and content on the profits of both the producer/wholesaler and the retailer, and derives a general objective function composed of a linear combination of these profits. Moreover, the paper establishes the conditions for bundling profitability and presents a way to optimize the profit of each party (producer, or retailer) without reducing the other partys profit. A real-world case study and sensitivity analysis demonstrate the solutions applicability. The results indicate that bundling can be a coordination tool for increasing expected profit for both the producer and the retailer.

Machines interference problem with several operators and several service types that have different priorities

This paper proposes a model for a special case of the machine-repairman problem, which is also known as the machine interference problem (MIP), where each of N identical machines randomly requests several different service types that are provided by a group of K identical operators. Each service type has a different priority and the operators serve the machines according to these priorities. The model allows the calculation of the expected number of machines that are waiting for each type of service, based on the multinomial distribution. The model enables us to determine the optimal number of operators and the optimal queue discipline that minimises the total manufacturing cost per unit (TCU). The paper provides a proof that the sum of the expected number of machines that are waiting for all service types is a constant, and does not depend on the service priorities. The conclusion is that queue discipline has no influence on throughput or loads. To demonstrate the applicability of the model, a theoretical analysis and a real case study are presented.

Improving demand forecasting using change point analysis

A common phenomenon that decreases the accuracy of time series forecasting is the existence of change points in the data. This paper presents a method for time series forecasting with the possibility of a change point in the distribution of observations. The proposed method uses change point techniques to detect and estimate change points, and to improve the forecasting process by taking change points into account. The method can be applied to both stationary series and linear trend series. Change point analysis prevents the omission of relevant data as well as the forecasting that may be based on irrelevant data. The study concludes that change point techniques may increase the accuracy of forecasts, as is demonstrated in the real case study presented in this paper.

Distribution-Free Models for Machine Interference Problems

This paper presents binomial and multinomial models for special cases of the machine interference problem (MIP), where a production system consists of one or several groups of identical machines. All the machines produce the same product in parallel and independently of each other. Each machine randomly requests several different service types. The service is provided by a group of operators such that one operator can provide only one service type. The presented models allow the calculation of the expected interference time in the queue for each service type, depending on the number of operators. The key point is the fact that the proposed models do not use any restrictive assumptions about failure rate and service distribution, as the Markovian models. The expected interference times attained by utilization of the proposed models enable practitioners to determine the optimal number of operators in order to minimize the manufacturing cost per unit of product or maximize the total profit, or to set other performance measures.

Operating global production with heterogeneous plants under uncertain demands and rigid chance constrained deliveries

Abstract The monthly demands of a single product are forecasted and given by a distribution function for each month. The product can be manufactured in n plants with heterogeneous characters. Each plant has its specific stochastic production capability (random yield). The expected capability and the standard deviation of each plant increase by allocation of additional budgets that are known according to a pre-given plant’s capability-cost tradeoffs function. The problem is to determine the total budget needed and its distribution among the n plants in order to ensure in the most economic manner a complete fulfillment of the demands according to the due dates and the pre-given confidence levels (delivery chance constraints). A necessary and sufficient condition for the existence of unique optimal solution for the considered problem is provided. We propose a method for evaluating the optimal solution and demonstrate it through numerical examples.