Operations Management Feedback for control Transformation Network of activities Inputs Outputs Raw Materials Requests for Service Goods Services Flow Units Resources Labor & Capital

Process Flow Diagrams Activities: Material flows: Inventory / buffers: Mix Activities: Material flows: Inventory / buffers: Information: Work in Process Term 2, 2015 Joseph Milner, RSM 1340

Cook Custard Cool Freeze Work in Process Finished Goods Raw Material Pack Freeze Cool Cook Custard

Raw Material Cook Custard Pack Cool Freeze Work in Process Finished Goods

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Flow Unit: Batches are 100 liters ice cream packed 3/4 hr/b 1 hr/b Raw Material Cook Custard Pack Cool Freeze Work in Process Finished Goods 24 sec./l 2/3 hr/b 24 s l × 100 l batch × 1min 60s × 1hr 60min. = 2 3 hr/batch

Capacity of a single resource: Cook Custard Process Time: 3/4 hour per batch of 100 l-ice cream Capacity = 4/3 batch/hr

Process Time (for each freezer): Capacity of resources in parallel: 1 b/hr Freeze (Machine 1) Freeze (Machine 2) Process Time (for each freezer): 1 hour/ batch 1 b/hr Capacity = 1 b/hr + 1b/hr = 2 batches/hr

Capacity of resources in series: Cook Custard Cool Freeze Process Time: 3/4 hour/ 100 l Process Time: 3/4 hour/ 100 l Process Time: 1 hour/ 100 l 4/3 b/hr 4/3 b/hr 1 b/hr Capacity = Minimum(4/3, 4/3, 1) = 1 batch/hr

p = average service or process time per flow unit m = average service or process rate (flow units per hour) Observe p = 1/m

If service takes 15 minutes or p=1/4 hour, then you can serve m =4 customers per hour.

Flow Unit: Batches are 100 liters ice cream packed 3/4 hr/b 1 hr/b 4/3 b/hr 4/3 b/hr 1 b/hr Raw Material Cook Custard Pack Cool Freeze Work in Process Finished Goods 2/3 hr/b 3/2 b/hr 4/3 b/hr 4/3 b/hr 1 b/hr

2 b/hr 1 b/hr 4/3 b/h 4/3 b/hr 1 b/hr 3/2 b/hr 4/3 b/hr 4/3 b/hr Raw Material Cook Custard Pack Cool Freeze Work in Process Finished Goods 3/2 b/hr 4/3 b/hr 4/3 b/hr 1 b/hr 1 b/hr Minimum(2 b/hr, 3/2 b/hr) 3/2 b/hr

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3/4 liter-cream 1 liter ice cream 4/3 b/hr 150 l−cream hr 2 b/hr Cook Custard 4/3 b/hr 150 l−cream hr 2 b/hr Raw Material Prepare Cream 3/4 liter-cream 1 liter ice cream 150 l−cream hr × 1 l−ice cream 3 4 l−cream = 200 l−ice cream hr × 1 batch 100 l−ice cream = 2 batches hr

100 l- 95 l-packed ice cream × 100 l−ice cream batch = 150 l−ice cream hr 3/2 b/hr 100 l-ice cream /hr 95 l-packed/hr 1 b/hr Pack Freeze Work in Process Finished Goods 142.5 l-packed /hr 150 l-ice cream /hr 3/2 b/hr 100 l- ice cream 95 l-packed 100 l-ice cream /hr 95 l-packed/hr 1 b/hr 100 l−ice cream hr 150 l−ice cream hr × 95 l−packed 100 l−ice cream × 95 l−packed 100 l−ice cream = 142.5 l−packed hr = 95 l−packed hr

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m = number of resources available at a workstation Cook Custard Cool Freeze 2/3 hr/b 3/4 hr/b 1 hr/b 4/3 b/hr 1 b/hr 3/2 b/hr Work in Process Finished Goods Raw Material Pack Cook Custard Cool Freeze Freeze Cool Cook Custard x 2 cookers 2 coolers 2 freezers 1 packer 8/3 b/hr 2 b/hr 3/2 b/hr m = number of resources available at a workstation Capacity of a workstation = # of resources x service rate = m m

Fundamental Parameters of a System rB = Bottleneck and Process Capacity Tmin = Minimum Flow or System Process Time

What is the bottleneck rate? (batches per hour) Bottleneck = Packing rB = 3/2 batch per hour

What is the system process time? (hours)

3/4 hr/b 1 hr/b 2/3 hr/b Raw Material Cook Custard Pack Cool Freeze Work in Process Finished Goods 2/3 hr/b

What is the system process time? (hours) TMin = 3/4 + 3/4 + 1 + 2/3 = 3.167 hrs = 3:10 hrs

Process Utilization and Capacity Utilization Throughput Rate Process Capacity Process Utilization = (Resource) Throughput Rate Process Capacity Utilization of Resource = Capacity Requested by Demand Available Capacity Implied Utilization =

Ice cream making process utilization at TH=1.5 batches/hr 1.5/1.5 = 100% Cooking process utilization = Cooling process utilization = Freezing process utilization = Packing process utilization = 1.5 / (2 x 4/3) = 57% 1.5 / (2 x 1) = 75% 1.5 / (1 x 3/2) = 100% If the demand is 2 batches per hour, Implied Utilization of Freezing = Implied Utilization of Packing = 2 / 2 = 100% 2 / (3/2) = 133%

Define a “job” (flow unit) = Batch of 100 liters – ice cream (3/2) / (8/3) Cooker 3/4 hr 4/3 b/hr 2 8/3 57% Cooler 3/4 hr 4/3 b/hr 2 8/3 57% 3/2 b/hr Freezer 1 hr 1 b/hr 2 75% Packer 2/3 hr 3/2 b/hr 1 3/2 100% *assuming system is processing at full capacity

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Flow Unit = 1 batch of 50 croissants RM: Dough Mix Pack WIP: Finished Goods Bake Proof Roll & Cut Fill & Fold Filling 5 min/b 15min/b 10 min/b 5min/b 20min/b 10min/b 5 min/50 Croissants 15min/50 10 min/50 5min/50 20min/50 10min/50

∞ RM: Dough Mix Pack WIP: Finished Goods Bake Proof Roll & Cut Fill & Fold Filling 5 min/b 15min/b 10 min/b 5min/b 20min/b 10min/b ∞

∞ ∞ Define a “job” (flow unit) = 1 batch of 50 croissants 1 1/6 hr Mix Filling 1 1/6 hr 10 min. 6 b/hr 6 b/hr 100% Mix and Roll Dough 1 5 + 5 min. 1/6 hr 6 b/hr 6 b/hr 100% 6 b/hr 1/4 hr ∞ ∞ Proof 4 b/hr Fill and Fold 1/12 hr 12 b/hr 1 12 b/hr 50% 1/3 hr 3 b/hr 2 6 b/hr 100% Oven 1/6 hr 6 b/hr 1 6 b/hr 100% Pack *assuming system is processing at full capacity

What is the bottleneck rate? (batches per hour) What is the system process time? (hours) Bottleneck = All but Fill and Fold rB = 6 batches per hour

Flow Unit = 1 batch of 50 croissants RM: Dough Mix Pack WIP: Finished Goods Bake Proof Roll & Cut Fill & Fold Filling 5 min/b 15min/b 10 min/b 5min/b 20min/b 10min/b

What is the bottleneck rate? (batches per hour) What is the system process time? (hours) Bottleneck = All but Fill and Fold rB = 6 batches per hour TMin = 5 min + 15 min + 5 min + 5 min + 20 min +10 min = 60 min = 1 hr

5 min. / batch 60% 20 min. / batch 40% Average unit Fill & Fold 20 min. / batch 40% Average unit p = 5 min. x 60% + 20 min. 40% = 11 min. = 0.1833 hr.

∞ ∞ Define a “job” (flow unit) = 1 batch of 50 croissants 60/40 mix Mix Filling 1/6 hr 6 b/hr 1 6 b/hr 90.9% 100% Mix and Roll Dough 1/6 hr 6 b/hr 90.9% 100% 6 b/hr 1 6 b/hr 5.45 b/hr 1/4 hr ∞ ∞ Proof 4 b/hr 5.45 b/hr Fill and Fold 0.1833 hr 5.45b/hr 1 50% 100% 1/3 hr 2 90.9% 3 b/hr 6 b/hr 100% Oven 1/6 hr 6 b/hr 1 6 b/hr 90.9% 100% Pack *assuming system is processing at full capacity

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