Production and Transportation Integration for a MaketoOrder Manufacturing Company with a CommittoDel

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Production and Transportation Integration for a
Make-to-Order Manufacturing Company with a
Commit-to-Delivery Business Mode

• Kathryn E. Stecke
• Xuying Zhao
• University of Texas at Dallas

2
Outline

• Problem and motivation
• Literature review
• Problem settings
• Analysis when partial delivery is allowed
• Analysis when partial delivery is not allowed
• Extensions
• Conclusions

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Ship and Delivery Dates

• Ship date the date when a manufacturing company
  gives products to a logistics company to deliver
  to a customer.
• Delivery date the date when the logistics
  company delivers products to a customer.

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Two Business Modes

• Commit-to-ship
• the manufacturing company commits a ship date for
  an order.
• Customers pre-specify a shipping mode, e.g.,
  overnight shipping.
• Commit-to-delivery
• the manufacturing company commits a delivery date
  for an order.
• The ship mode can be decided dynamically by the
  company.

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Commit-to-ship at Dell
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Profit increase opportunity in Dell

• Dell ships 95 of customer orders within eight
  hours.
• Based on this fact, Dell could increase profit by
  adopting commit-to-delivery.
• For example
• Customers pay 469 for a computer and 160 for
  overnight shipping.
• Dell gets 469 in commit-to-ship.
• Dell promises a 5-days-later ship date. The
  logistics company gets 160.
• Dell gets 529 in commit-to-delivery.
• Dell could ship the order within eight hours by
  adjusting the production schedule. Then a slow
  ship mode can be adopted. The logistics company
  gets 100. Dell gets 46960.
• Profit increases over 10.

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Problem Description

• Production schedule is important when adopting a
  commit-to-delivery mode.
• A good production schedule saves shipping costs.
• A bad production schedule incurs expediting
  costs.
• How to schedule production for accepted orders so
  that
• All orders meet their delivery due dates.
• The total shipping cost is reduced as much as
  possible.

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Literature Review

• Our research is related to two literature
  streams
• 1. Production scheduling
• Pinedo (2000),
• 2. Integration between transportation and
  production
• Bhatnagar, Chandra, and Goyal (1993), Thomas and
  Griffin (1996), and Sarmiento and Nagi (1999),
  Chen and Vairaktarakis (2005)

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Production Environment

• Finished products are assembled from
  partly-finished products and customized
  components.
• Differences among orders exist in different
  models/types of components.
• Switching production from one order to another
  order rarely incurs any extra production costs.

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Production Schedule Setting

• We specify the production schedule for n new,
  just arrived orders with delivery due dates.
• A manufacturer can wait for customer orders to
  accumulate as long as its master production
  schedule is not empty.
• The schedule for the n new orders will be added
  to the end of the current master production
  schedule.

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Transportation Setting

• Outsourced to a third party logistics company,
  e.g., FedEx
• The logistics company comes to collect products
  at the end of each day.

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Shipping Cost Setting
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Shipping Cost Setting

• The shipping cost is a general function of
  shipping time and the quantity of computers
  shipped.
• From the table in the previous slide, shipping
  cost is convex decreasing in shipping time.
• From the table in the previous slide, shipping
  cost is linearly increasing with shipping weight.
  
• Since all computers weights are similar,
  shipping cost is linearly increasing with the
  quantity of computers shipped.

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Problem Settings Summary

• Orders
• There are n orders to be scheduled for
  production
• Each order Oi has a production due date di and
  requires quantity Qi.
• Production
• The production planning horizon is m days
• Daily production capacity is c products
• Single machine or a paced assembly line
• Transportation
• Outsourced to a third party logistics company,
  e.g., FedEx
• The logistics company comes to collect products
  at the end of each day.

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Table of Notation
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Process Timeline
d1
r10
Production Planning Horizon
O1

2
m
1
3
0
t12
t11
Ship cost for one order i G(ri, Qi), convex
decreasing with ri and linearly increasing with Qi
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Feasibility Condition
where denotes a set of orders having a
production due date on or before production day j
in the planning horizon.
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When Partial Delivery is Allowed
Quantity produced in day j for order i
MIP-PD
Ship date is the same as the production date
Order i is produced before its due date
Daily production capacity constraint
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When Partial Delivery is Allowed

• MIP-PD
• Totally unimodular
• ILOG CPLEX
• Algorithm
• Nonpreemptive Earliest Due Date Schedule (NEDD)
  orders are sorted according to earliest due date
  first and processed nonpreemptively and
  continuously without idle time.

Production Planning Horizon

O1
O2
O3
O4
O5

0
2
1
m
3
d11
d2d32
d4 d5 3
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When Partial Delivery is Not Allowed
Yij1 means that the last product in order i is
produced in day j.
MIP-NPD
The ship date is the last products production
date.
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When Partial Delivery is Not Allowed
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When Partial Delivery is Not Allowed
Cj number of products which are produced in day
j but shipped in day j1 or later.
C1150
C2160
Production Planning Horizon

O1
O2
O3

(100)
(150)
(90)
(160)
(100)
2
m
1
0
(100)
(15090)
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When Partial Delivery is Not Allowed

• Algorithm NPD try to reduce each Cj as much as
  possible.
• Get an initial feasible schedule by NEDD.
• Start reducing Cm-1 by producing smaller orders
  first.
• Reduce each Cj the same way.
• The algorithm stops when C1 is reduced.

Cm-1
O1
O3
O5
O2
O4
Cm-1
O1
O3
O5
O2
O4
Day m
Day m-1
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Estimated Shipping Cost Function

• Suppose that a computer weighs 50 lbs.
• Shipping cost 2884/(1ri).

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Numerical Test Settings

• di integer with a uniform distribution in the
  interval 1, m
• Qi integer with a uniform distribution in the
  interval 1, mc
• c
• 10 computers/day in the tests where n5, m5 and
  n8, m8.
• 500 computers/day in the tests where n500 and m8

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Algorithm Performance When n5 and m5
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Algorithm Performance When n8 and m8
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Performance of Lower Bounds When n5 and m5
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Performance of Lower Bounds When n8 and m8
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Algorithm Performance When n500 and m15
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When orders are small

• Most orders in Dell require only one or two
  computers.
• Thus, we test our heuristic algorithm NPD when
  orders are small
• 75 Qi1
• 25 Qi2
• 5 Qi is an integer from a uniform distribution
  in the interval 3, 10.

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Algorithm Performance when orders are small
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Extensions

• Considering customer locations in the shipping
  cost function
• Considering quantity discounts in the shipping
  cost function

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Shipping Cost Varies with Customer Locations
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Considering Customer Locations in Models

• When partial delivery is allowed.
• When partial delivery is not allowed

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Considering Quantity Discounts

• Some 3PL companies offer quantity discounts when
  multiple items are sent in a batch.
• When partial delivery is allowed, there exists a
  tradeoff.
• We propose another MIP to consider this tradeoff

O1

(150)
(150)
2
m
1
0
(300)
(0)
(150)
(150)
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Conclusions

• We analyzed a production and transportation
  integration problem for make-to-order industries.
• When partial delivery is allowed, NEDD provides
  the optimal production schedule.
• Mixed integer programming model MIP-PD
• Totally unimodular
• ILOG CPLEX
• When partial delivery is not allowed, an
  effective and efficient heuristic algorithm is
  provided.
• Mixed integer programming model MIP-NPD
• Heuristic algorithm NPD

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Thank You!