Coordination of Outsourced Operations to Minimize Weighted Flow Time and Capacity Booking Costs

Abstract

A set of manufacturers outsources certain operations to a single third party following the announcement of a booking price for each available day of production. Knowing these costs, manufacturers book available production days in a first-come-first-serve order to optimize their individual cost. The cost for each manufacturer consists of booking and work-in-progress costs, as expressed by the weighted flow time. When window booking is completed, the third party identifies a schedule that minimizes the total cost incurred by all manufacturers. This coordination reduces the total cost but may result in higher costs for a subset of manufacturers. For this reason, the third party devises a savings sharing scheme with which the monetary benefit for each manufacturer is greater. In this article we present algorithms for the problem considered, as well as savings-sharing schemes that make coordination a better alternative for all parties. The highlight of our experiments is that the costs of the production chain can be reduced by an average of 32% if one-third of the members let the third party cover their increased work-in-progress cost in exchange for 38%-53% of the total savings.coordination, cooperative games, incentives, outsourcing, supply chain management, production planning and scheduling

Decentralized subcontractor scheduling with divisible jobs

“…Aydinliyim and Vairaktarakis (2010) study a cooperative game where coalitions of agents reschedule their reserved time intervals to obtain savings. They prove non-emptiness of the core and the convexity of the corresponding game.…”

Scheduling with variable time slot costs

“…A recent article of Aydinliyim and Vairaktarakis [1] is probably the one mostly related to our work. In Reference 1, a set of manufacturers outsources certain operations to a third party who announces a price for each available time period of production.…”

“…For example, π k = η k π 0 , where π 0 is a constant. For such a representation of the time slot costs, its input size is O (1). As a result, an algorithm with a running time bounded by a polynomial function of n and K is no longer a polynomial-time algorithm.…”

“…We have some general results on cases where the time slot costs {π k } are non-decreasing with time, i.e., k 1 …”

“…We now consider the problem 1 | slotcost | (C j + k∈s j π k ) for the case where the time slot costs {π k } are non-increasing with respect to time index k, i.e., k 1 …”