A Logistics Scheduling Model with Fixed Procurement Time

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• A Logistics Scheduling Model with Fixed
  Procurement Time
• Cheng Hui

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Outline

• Background Introduction
• Model Description
• Theoretical results and algorithms used
• Numerical Results
• What needs to be finished
• QA

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Background Introduction

• A contract between supplier and workshop
  (manufacture)
• periodical procurement of raw material (period
  denoted by T)
• fixed delivery cost will be charged if workshop
  makes an order each
• time
• Given orders are made (n jobs), workshop has to
  follow a non-stop
• processing policy, which means if not all the
  orders are completed, we
• cannot let the workshop idle
• e.g. iron steel plant, very expensive setup up
  cost
• Aim at minimizing operation cost delivery cost
  WIP cost

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Model Description 1

• n jobs, processing time pj (weight wj) for job j,
  j 1,…,n
• Holding cost per unit time unit weight h 1
• Delivery cost U
• Procurement period T (Tgt pj)
• WIP cost of job j Fj Cj ßi
• Cj completion time of job j, ßi procurement
  time of job j

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Model Description 2

• Objective function is total delivery cost WIP
  cost
• k is the number of times the workshop procures
  raw material
• If we take the weight of jobs into consideration,
  then
• Objective function

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1
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Theoretical Results

• Consider the weighted case, both the special case
  (all the
• ratios between weight and processing time are the
  same)
• and general case.

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Performance Ratio (for special weighted case)

• The lower bound of optimal result can be
  estimated using
• Optimum is k, which is no bigger than
• (S is the total processing time)
• ti is the total processing time of the i-th
  procurement

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Algorithm adopted

• 1. Based on the LPT(longest processing time
  first) policy for k
• times procurement.
• 2. Aim at reducing the holding cost between all
  adjacent
• Procurement batches.
• 3. Given the sequence determined by the above
  procedures,
• use dynamic programming to recalculate the result
  and
• improve the result further
• The worst case performance ratio of our algorithm
  is

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Numerical Results
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What needs to be finished

• General weighted case
• Provide an algorithm with a bound
• Show numerical results based on the algorithm
  adopted

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• Thank you!
• Q A