This paper extends the single-period price and due date setting model for contingent Make-to-Order (MTO) firm into a finite-period stochastic system. Based on the revenue management framework (viewing every single available timeslot of production capacity as a perishable product), MTO firms can dynamically set price and due date to achieve highest average profitability per timeslot given a certain distribution pattern of future demand within a finite horizon. Heuristically, given a state of production system, admission control policy is then proposed to bid at the shadow price of the required timeslots or higher. An experimental simulation was performed and reported with insightful discussion.
In the context of Make-to-order bidding, after quoting the bid, the firm has to wait for customer's decision (to deny or award the job). The contingency of the decision affects the planned capacity allocation. Reserving available timeslots for contingent bids is equivalent to have overbooked capacity in a hotel or airline services. As suggested by [1] and [2], MTO firms can utilize the Markovian's state transition scheme to effectively manage the overbooking scheme that balances the penalty cost of tardiness and opportunity loss of subsequent bids.
[...] In each case, the simulation experiments on the single-period bidding Model (A.1) and on the proposed RM bidding model were performed for 20 replicates and the final experimental results were measured by averaging all runs in terms of total revenues (summation of winning bid prices), total penalty charges for tardiness, total profits (total revenue total penalty), and total number of winning bids. Their values were accumulated through the whole planning horizon. We also collected other information for analysis purposes, for example, the total number of requests and the total number of requests to bid at adjusted prices. [...]
[...] For a system with longer than 15 planning periods, RM bidding model should be purely equipped with FCFS sequencing rule, for it can better compromise between computational time and quality of solution Conclusions Applying the RM approach to the MTO bidding system, we incorporated prospective future demands pattern into the bidding model that dynamically determines the bidding price and the due date for each new order arrival. A dynamic programming algorithm was deployed to estimate the shadow price (also referred as marginal value) of required timeslots for the current state of production system, given the contingent orders in the bidding system of marketing department. [...]
[...] The model assumes standard content for each arrival and non-contingent orders Revenue Management Bidding Model In this section, we discuss the development of an RM decision model for an incoming bid in an MTO firm with a a finite-horizon RM bidding system and a decision rule. We consider an MTO system with n remaining production timeslot and a total contingent work content of ϕ which is comparable to the booked capacity in the traditional RM context. The optimization is for request i requiring x timeslots. [...]
[...] Extending the single-period contingent multiple product-class model of we propose in this paper a multi-period dynamic programming model that integrates the finite-time RM discipline into the contingent multiclass MTO bidding system. Such the integration leads the system to a class of dynamic price setting under dynamic capacity allocation of RM problem. Also, we evaluate the relative performance of the RM model in a simulated dynamic environment and provide some insightful discussion. Assumptions made in this work are as follows: the firm makes schedules with no pre-emption on a single workstation or a bottleneck station on which the line capacity is based, customers must confirm their order within the maximum confirmation lead time (time between the quotation time and the expected critical production start time), (iii) the production facility requires high investment cost so that costs of machine time and direct labor can be considered as fixed manufacturing costs, customers, once confirmed, cannot cancel the orders, machines are always in good condition, and raw materials and components are always available when needed, The work content of any class is in multiple units of production time slots. [...]
[...] ( ) For Model and the remainders, we define additional notations as follows: r A possible realization for all orders in the queue Ω, with probability Number of contingent orders in the queue Ω, ϕ( Ω r ) Total expected capacity required by orders in the queue as of realization Pni Γ n im Probability that there is a request for class i in the decision period Probability that a request for class i in the decision period n requires m timeslots, m { Mi}. [...]
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