Konstantin Kogan

Supply Chain Games: Operations Management And Risk Valuation

Supply Chains and Operations Modeling and Management.- Supply chain operations management.- Supply chain games: modeling in a static framework.- Supply chain games: modeling in a multi-period framework.- Intertemporal Supply Chain Management.- Supply chain games: modeling in an intertemporal framework.- Supply chain games: modeling in an intertemporal framework with periodic review.- Sustainable collaboration in supply chains.- Risk and Supply Chain Management.- Risk and supply chains.- Quality and supply chain management.

A polynomial algorithm for scheduling small-scale manufacturing cells served by multiple robots

Abstract The n-job, two-machine, multi-robot flowshop scheduling problem is considered with the objective of minimizing makespan. Various transportation, setup and loading/unloading effects arising in a modern flexible manufacturing cell are modeled by a graph representation of the technological process. An algorithm of O(n2) complexity is derived to solve the problem to optimality.

Scheduling a two-machine robotic cell: A solvable case

The paper deals with the scheduling of a robotic cell in which jobs are processed on two tandem machines. The job transportation between the machines is done by a transportation robot. The robotic cell has limitations on the intermediate space between the machines for storing the work-in-process. What complicates the scheduling problem is that the loading/unloading operation times are non-negligible. Given the total number of operationsn, an optimalO(n logn)-time algorithm is proposed together with the proof of optimality.

Dynamic conformance and design quality in a supply chain: an assessment of contracts’ coordinating power

We consider a two-echelon supply chain involving one manufacturer and one supplier who collaborate on improving both design and conformance quality. Design quality is supposed to increase product desirability, and therefore market demand, while conformance quality should reduce the proportion of defective items, and therefore increase the manufacturer’s sales revenue. We investigate how the supply chain parties allocate effort between design and conformance quality under both cooperative and non-cooperative settings in an intertemporal framework. Furthermore, we evaluate wholesale price contracts and revenue-sharing contracts in terms of their performance and coordination power. We show that although a revenue-sharing contract enables the manufacturer to effectively involve the supplier in quality improvement, neither contract type allows for perfect coordination resulting in the quality that can be achieved by a cooperative supply chain. We thus suggest a reward-based extension to the revenue-sharing contract, to ensure system-wide optimal quality performance. Importantly, we find that the supplier would be better off adopting a reward-based revenue sharing contract and refusing a standard revenue-sharing contract, while the opposite would be true for the manufacturer.

Risk and quality control in a supply chain: competitive and collaborative approaches

This paper provides a quantitative and comparative economic and risk approach to strategic quality control in a supply chain, consisting of one supplier and one producer, using a random payoff game. Such a game is first solved in a risk-neutral framework by assuming that both parties are competing with each other. We show in this case that there may be an interior solution to the inspection game. A similar analysis under a collaborative framework is shown to be trivial and not practical, with a solution to the inspection game being an ‘all or nothing’ solution to one or both the parties involved. For these reasons, the sampling random payoff game is transformed into a Neyman–Pearson risk constraints game, where the parties minimize the expected costs subject to a set of Neyman–Pearson risk (type I and type II) constraints. In this case, the number of potential equilibria can be large. A number of such solutions are developed and a practical (convex) approach is suggested by providing an interior (partial sampling) solution for the collaborative case. Numerical examples are developed to demonstrate the procedure used. Thus, unlike theoretical approaches to the solution of strategic quality control random payoff games, the approach we construct is both practical and consistent with the statistical risk Neyman–Pearson approach.

A supply chain under limited-time promotion: The effect of customer sensitivity

Abstract We consider a two-echelon supply chain with a supplier and a retailer facing stochastic customer demands. The supplier is a leader who determines a wholesale price. In response, the retailer orders products and sets a price which affects customer demands. The goal of both players is to maximize their profits. We find the Stackelberg equilibrium and show that it is unique, not only when the supply chain is in a steady-state but also when it is in a transient state induced by a supplier’s promotion. There is a maximum length to the promotion, however, beyond which the equilibrium ceases to exist. Moreover, if customer sensitivity increases, then the wholesale equilibrium price decreases, product orders increase and product prices drop. This effect, well-observed in real life, does not, however, necessarily imply that the promotion is always beneficial. Conditions for the profitability of a limited-time promotion are shown and analyzed numerically. We discuss both open-loop and feedback policies and derive the conditions necessary for them to remain optimal under stochastic demand fluctuations.

Multi-stage newsboy problem: A dynamic model

Abstract The newsboy problem is a well-known operations research model. Its various extensions have been applied to managing capacity and evaluating advanced orders in manufacturing, retail and service industries. This paper focuses on a dynamic, continuous-time generalization of the single-period newsboy problem. The problem is characterized by a number of the newsboys whose operations are organized and controlled in sequential stages. The objective is to minimize shortage and surplus costs occurring at the end of the period as in the classical newsboy problem, as well as intermediate surplus costs incurring at each time point along the period. We prove that this continuous-time problem can be reduced to a number of discrete-time problems. On this basis, a polynomial-time combinatorial algorithm is derived to find globally optimal solution when the system satisfies a certain capacity condition.

DGAP - The Dynamic Generalized Assignment Problem

The Generalized Assignment Problem (GAP) is a well-known operations research model. Given a set of tasks to be assigned to a group of agents and the cost of performing each task by each agent, the model allocates tasks to agents to minimize the total cost subject to the availability of a single resource type. The single resource is consumed by the agents when performing these tasks. In this paper, we add the impact of time to the model assuming that each task has a due date, and inventory cost as well as shortage cost is incurred when a task is finished ahead or after its due date, respectively. We formulate the continuous-time op-timal control model of the problem where identical tasks are grouped into jobs (or batches), each job is performed by each agent with a fixed (production) rate, while due dates are transformed into demand. As a result, analytical properties of the optimal behavior of such a dynamic system are derived. Based on those properties, an efficient time-decomposition procedure is developed to solve the problem.

Optimal allocation of inspection effort over a finite planning horizon

Abstract We address the problem of managing the intensity, sequence and timing of inspection effort in an N-stage production system with M inspection activities possible at each stage. The objective is to minimize the sum of the inspection costs and the penalties caused by undetected defects. By means of the maximum principle we prove several properties or the optimal solution, which allow us to reduce the continuous-time inspection effort allocation problem to a combinatorial one. We suggest an efficient algorithm that solves the problem in 0(NM2 + N2) time.

Capacity planning by the dynamic multi-resource generalized assignment problem (DMRGAP)

The allocation of available capacity among competing demand and users is a problem encountered in areas such as job shop scheduling, the trucking industry and distributed computer systems. In all these areas a model known as the Multi-Resource Generalized Assignment Problem (MRGAP) has been proposed as a tool to assign available capacity among the competing applications. In this paper we extend the MRGAP model to the case where demand varies over time and capacity assignments are dynamic. We show that the extended model can be used for strategic capacity planning and we develop efficient solution procedures to solve the dynamic version of MRGAP.