Question

Kinga Doll Company manufactures eight versions of its popular girl doll, Shari. The company operates on a 40-hour work week. The eight versions differ in doll skin, hair, and eye color, enabling most children to have a doll with a similar appearance to them. It currently sells an average of 4,000 dolls (spread equally among its eight versions) per week to boutique toy retailers. In simplified terms, doll making at Kinga involves three basic operations: molding the body and hair, painting the face, and dressing the doll. Changing over between versions requires setup time at the molding and painting stations due to the different colors of plastic pellets, hair, and eye color paint required. Table 7.5 lists the setup times for a batch and the activity times for each unit at each step. modeling set up 15 and processing time 0.25. painting setup 30 and processing time 0.15 dressing no setup and 0.3 processing time. A. which batch size would minimize inventory without decreasing the process capacity? B. what is the utilization of modeling in dolls in hour with batch size 800 dolls?

Answer 1

1.

Batch size=475

Capacity expressed in number of dolls per hour

The process capacity of molding =475 / (18+(.24*475)) = 3.6 dolls/minute = 215.9 dolls/hour.

The process capacity of painting = 475 / (29+(.17*475)) = 4.33dolls/minute = 259.7 dolls/hour.

The process capacity of dressing = 475 /( 0+.27*475) = 3.7 dolls/minute = 222.2 dolls/hour.

Therefore, the process capacity = 215.9 dolls/hour 0r 216 dolls/hour

Dressing is the bottleneck with long processing time

2.

The process capacity of molding =900 / (18+(.24*900)) = dolls/minute = 230.8 dolls/hour.

The process capacity of painting = 900 / (29+(.17*900)) = 4.76 dolls/minute = 296.7 dolls/hour.

The process capacity of dressing = 900 /( 0+.27*900) = 3.33 dolls/minute =222.2 dolls/hour.

The capacity of the bottle neck is the capacity of the process .Therefore, the process capacity = 222.2 dolls/hour

Flow rate = minimum {available input, demand, process capacity}

Input is not a constraint or at least not mentioned in the case

Demand =4000 dolls in 40 work hours = 100 dolls per hour

The process capacity = 222.2 dolls/hour

The flow rate/throughput rate is equal to demand, 100 dolls/hour

At a batch size of 900, the process is demand-constrained and the flow rate is set by demand: 4,000 dolls per week @ 40 hr/wk = 100 dolls/hr =100/60 dolls per minute =1.667 dolls per minute

Utilization for setup resource = Flow rate x Processing time

Utilization for non-setup resource = Flow rate / Capacity

Molding is resource requiring set up

Utilization for Molding = Flow rate x Processing time of resource

= 1.667 * 0.24 =40%

3.

We want to find the smallest batch size that can meet the Demand of 100 dolls per hour or 1.667 dolls per minute.

We have to find the batch sizes for molding and painting to met this demand

Batch size= Flow rate × Setup time / [1 – ( Flow rate× processing time) ]

Molding = 1.667 * 18/(1-(1.667*0.24)) =50.02

Painting =1.667* 29/(1-(1.667*0.17)) = 67.46

A batch of 67.46 or 68 units is the smallest batch size so that both Molding and Painting can produce 1.667 units per minute . this minimizes inventory without decreasing process capacity

.4

Inventory decreases with decrease in batch size.

Since the process is primarily demand constrained ,Here batch can be significantly reduced without affecting flow rate.

We want to find the smallest batch size that can meet the flow rate of 100 dolls per hour or 1.667 dolls per minute.

We have to find the batch sizes for molding and painting to meet this flow rate

Setting Capacity to meet demand =1.667 dolls per minute

Batch size= (capacity x setup time) / (1 – capacity x processing time)

Molding = 1.667 * 18/(1-(1.667*0.24)) =50.02

Painting =1.667* 29/(1-(1.667*0.17)) = 67.46

A batch of 67.46 or 68 units is the smallest batch size so that both Molding and Painting can produce 1.667 units per minute . This minimizes inventory without decreasing flow rate.