UPS: UPS: Small Sort Small Sort

DesignDesign

Adrian Diaz

Daniel Carlisle

Lacey Davis

HistoryHistory

• To transport packages most efficiently, UPS has developed an elaborate network of “hubs” or central sorting facilities. Each “hub” is fed by a number of local operating centers, which serve as the home base for UPS pickup and delivery.

• Small packages, small enough to palm, are sorted into groups, or bags, cutting down on the handling time. Bags and small packages coming into the plant are sorted in a special area called the Small Sort Division.

Problem BackgroundProblem Background

The current problem in the Mesquite hub is the Small Sort Design Layout.

There are four different areas which the packages may be sorted into:

Primary – consists of 48 bins (24 left and 24 right)

Secondary One – consists of 108 bins

Secondary Two – consists of 108 bins

Secondary Three – consists of 72 bins

Problem BackgroundProblem Background

• Each destination is assigned a specific bin(s) with a specified TMU (Time Measurement Unit associated with the time used to distribute a package to a particular bin)

• The bins near the center have the lowest TMU values.

• As packages travel from Primary to each successive Secondary, the TMU’s increase significantly.

Problem OverviewProblem Overview

• The current problem is that the destinations with larger volumes are not necessarily assigned to the bins with the lower TMUs, demanding more time and energy from the sorter. The system is not operating in the most efficient manner.

Problem OverviewProblem Overview

• Currently, the bins do not consistently serve the same destinations through all three shifts, Day, Night, and Twilight.

• Destinations requiring more than one bin may be scattered, further complicating the sorters job.

AnalysisAnalysis

• The bins with the same destinations need to be next to each other.

• Given the maximum capacity of two hundred packages in a bin per shift, the number of bins per destination needs to be reevaluated.

Maximum:

- Two bins in Primary

- Four bins in Secondary

*Except Mesquite and Dallas which are locked at the number of bins

AnalysisAnalysis

• Bins need to be serving same destination for all three shifts.

-Must take a total averaged volume for each shift, Day, Night and Twilight.

Example: Chicago (CCHIL) has the following volumes:

Day: 119

Night: 73

Twilight: 112

Average Volume: 101.3

ModelModel

The objective function minimizes the “bin layout” cost (the total cost of summing all the averaged destination volumes times their bin(s) TMU values):

Minimize Σ Σ Ai * Bj

where

A = destination’s average volume

B = bin TMU value

a = total number of destinations

b = total number of bins

a b

i=1 j=1

ExampleExample

Average Volumes:

Dallas – 6 Houston – 5 Austin – 4 San Antonio – 3

TMU’s:

BIN 1BIN 110

BIN 2BIN 220

BIN 3BIN 330

BIN 4BIN 440

The clear choice is to assign:

Dallas → Bin 1 Houston → Bin 2

Austin → Bin 3 San Antonio → Bin 4

With the minimal “bin layout” cost of:

6*10 + 5*20 + 4*30 + 3*40 = 400

MethodMethod

To solve our LP, we used AMPL, a powerful and comprehensive algebraic modeling language for linear and non-linear optimization problems.

We treated the problem as an “assignment problem”

Main ConstraintsMain Constraints

1. There must be five bins assigned to Mesquite (MESTX) and eight assigned to Dallas (DALTX). They must be in the Primary Sort.

2. Each bin has a maximum capacity of two hundred packages per shift. (So if one destination has 350, they must have two bins)

3. Primary – No more than two bins per destination*

Secondary – No more than four bins per destination

*Except Dallas and Mesquite

Sub-problemsSub-problems

We broke the problem in two pieces

Primary Secondary

solving each as a separate problem

Model FileModel File

set O;set D;param a {i in O} default 1;param r {j in D};param c {i in O, j in D};var x {i in O, j in D} >= 0;minimize cost: sum {i in O, j in D} c[i,j] * x[i,j];subject to supply {i in O}: sum {j in D} x[i,j] <= a[i];subject to demand {j in D}: sum {i in O} x[i,j] >= r[j];

OutputOutput

1 MESTX 7 BURMD 13 DALTX 19 DALTX

2 MESTX 8 ATLGA 14 DALTX 20 DALTX

3 MESTX 9 ATLGA 15 DALTX 21 PHOAZ

4 MESTX 10 BELTX 16 DALTX 22 PHOAZ

5 MESTX 11 BELTX 17 DALTX 23 EPATX

6 MYKTX 12 MYKTX 18 DALTX 24 EPATX

25 LONTX 31 JACFL 37 SSPTX 43 LUBTX

26 LONTX 32 JACFL 38 SSPTX 44 LUBTX

27 WACTX 33 DENTX 39 MONAL 45 GRENC

28 WACTX 34 DENTX 40 MONAL 46 GRENC

29 CHEMA 35 ABITX 41 ALTTX 47 ALBNM

30 CHEMA 36 ABITX 42 ALTTX 48 ALBNM

Primary Left Primary Right

OutputOutput

49 MIDOH

55 OAKWI

61 AUSTX

67 SANTX

73 LITAR

79 DFWAS

85 NBACA

91 EFDTX

97 ANGTX

50 DENCO

56 SMATX

62 AUSTX

68 SANTX

74 LITAR

80 DFWAS

86 DFWAS

92 KANKS BAYTX

51 BEMTX

57 POROR

63 AUSTX

69 SANTX

75 TOLOH

81 JACMS

87 DFWAS

93 VICTX

99 SALUT

52 CCHIL

58 CONTX

64 AUSTX

70 SANTX

76 TOLOH

82 TEXTX

88 BRNTX

94 PAMTX

100 HARTX

53 HARPA

59 COLSC

65 GVICA

71 GVICA

77 SHRTX

83 SAGTX

89 HOUTX

95 HOUTX

101 HOUTX

54 BROTX

60 SBRCA

66 GVICA

72 DENCO

78 LITAR

84 JEFIL

90 SDFAS

96 BWNTX

102 HOUTX

Secondary One

OutputOutput

Secondary Two

103 LVATX

109 SPRAR

115 SYRNY

121 TEXAR

127 LARTX

133 LEXKY

139 RALNC

145 PLATX

151 HARAR

104 GNBRY

110 SEAWA

116 SPRAR

122 ODESA

128 I81IN

134 PALTX

140 WICKS

146 VERTX

152 ALPTX

105 LENKS

111 ROAVA

117 PARNJ

123 MIDTX

129 EARMO

135 TULOK

141 DESIA

147 ONTCA

153 MEANJ

106 STATX

112 STATX

118 STATX

124HIAFL

130 MIETX

136 OAKTN

142 OKLOK

148 TYLTX

154 PTATX

107 STATX

113 WFATX

119 FORTX

125 FORTX

131 NEWPA

137 CORTX

143 OKLOK

149 TYLTX

155 NORLA

108 AMATX

114 LUFTX

120 FORTX

126 FORTX

132 STPMN

138 SHRLA

144 OMANE

150 ARMOK

156 WGRPA

InterpretationInterpretation

• Secondary Three has been eliminated – reduces overall amount of work for the sorting process and results in extra space in the hub.

• Some slight adjustments were made to place bins next to each other, although never changing any destination to a different TMU value.

• New layout is much more efficient and timely.

Bin Layout CostBin Layout Cost

Primary: 700,066.6091 Primary: 636,736.14

Secondary: 1,061,563.316 Secondary: 1,036,951.94

Total: 1,761,629.925 Total: 1,673,688.08

The proposed bin layout reduces the cost by approximately 5%.

Original Layout Proposed Layout

DrawbacksDrawbacks

• May take time for employees to become familiar with new layout

• Cost of implementing the new layout

• Model does not take into account the different volumes for the three shifts, rather works on the average

ConclusionConclusion

• The long term benefits outweigh the short-term costs

• The proposed layout results in a much more efficient and effective Small Sort division

• The bin layout cost was reduced by approximately 5%

• The elimination of Secondary Three provides new ways to utilize the freed sort space.