Title: Manufacturer optimal stock requirement and production rate to maximise the expected profit during peak time

Authors: Mahadev Ota; S. Srinivasan; C.D. Nandakumar; Khalid Waheed

Addresses: Department of Mathematics and Actuarial Science, B.S. Abdur Rahman Crescent Institute of Science and Technology, Chennai, 600048, Tamil Nadu, India ' Department of Mathematics and Actuarial Science, B.S. Abdur Rahman Crescent Institute of Science and Technology, Chennai, 600048, Tamil Nadu, India ' Department of Mathematics and Actuarial Science, B.S. Abdur Rahman Crescent Institute of Science and Technology, Chennai, 600048, Tamil Nadu, India ' Department of Management Studies, B.S. Abdur Rahman Crescent Institute of Science and Technology, Chennai, 600048, Tamil Nadu, India

Abstract: In today's competitive business world, the manufacturers have to face a very volatile market demand and hence need to take the decision accordingly so as to maximise their profit. For a manufacturer, the production rate is usually constant in the short run and may not be adequate to meet the demand during the upcoming peak period. Therefore he needs to keep some stocks as a reserve so as to meet the upcoming peak demand period. But storage space and holding costs are another concern. Considering these problems, this paper aims at developing a model considering the number of order as a Poisson process with individual demands following lognormal distribution and find the optimal initial stock requirement to meet the peak period demand which maximises the expected profit. In addition to this, waiting period for the first order, the time between the successive orders, probability of shortage of stock at a given initial level during the peak time, optimal initial stock requirement to keep the probability of shortage below a predetermined level has been discussed. The numerical examples suggest that an optimal solution can be obtained which would maximise the manufacturer expected profit.

Keywords: optimal initial stock; manufacturer model; production rate; peak time; probability of shortage; expected profit; Poisson process; compound distribution.

DOI: 10.1504/IJPM.2020.106542

International Journal of Procurement Management, 2020 Vol.13 No.2, pp.257 - 277

Received: 24 Aug 2018
Accepted: 17 Apr 2019
Published online: 09 Apr 2020 *

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