Post on 31-Jan-2016
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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.